repo_id stringlengths 19 138 | file_path stringlengths 32 200 | content stringlengths 1 12.9M | __index_level_0__ int64 0 0 |
|---|---|---|---|
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/status/BUILD | load("@rules_cc//cc:defs.bzl", "cc_library", "cc_test")
load("//tools:cpplint.bzl", "cpplint")
load("//tools/install:install.bzl", "install")
package(
default_visibility = ["//visibility:public"],
)
install(
name = "install",
library_dest = "common/lib",
targets = [
":libstatus.so",
],
visibility = ["//visibility:public"],
)
cc_library(
name = "status",
hdrs = ["status.h"],
srcs = ["libstatus.so"],
deps = [
"//modules/common_msgs/basic_msgs:error_code_cc_proto",
"//modules/common/util:util_tool",
"@com_google_protobuf//:protobuf",
],
alwayslink = True,
)
cc_binary(
name = "libstatus.so",
srcs = ["status.h"],
deps = [
"//modules/common_msgs/basic_msgs:error_code_cc_proto",
"//modules/common/util:util_tool",
"@com_google_protobuf//:protobuf",
],
linkshared = True,
linkstatic = True,
)
cc_test(
name = "status_test",
size = "small",
srcs = ["status_test.cc"],
deps = [
":status",
"@com_google_googletest//:gtest_main",
],
)
cpplint()
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/factorial.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file factorial.h
* @brief Meta programming for computing factorial
*/
#pragma once
#include <cstdint>
namespace apollo {
namespace common {
namespace math {
template <uint64_t N>
struct Factorial {
enum { value = N * Factorial<N - 1>::value };
};
template <>
struct Factorial<0> {
enum { value = 1 };
};
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/kalman_filter_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/kalman_filter.h"
#include "gtest/gtest.h"
namespace apollo {
namespace common {
namespace math {
class KalmanFilterTest : public ::testing::Test {
public:
EIGEN_MAKE_ALIGNED_OPERATOR_NEW
public:
KalmanFilterTest() : kf_() {}
virtual void SetUp() {
// Initial state
Eigen::Matrix<double, 2, 1> x;
x(0, 0) = 0.0;
x(1, 0) = 1.0;
// Initial state belief covariance
Eigen::Matrix<double, 2, 2> P;
P.setZero();
P(0, 0) = 0.1;
P(1, 1) = 0.1;
// Transition matrix
Eigen::Matrix<double, 2, 2> F;
F.setZero();
F(0, 0) = 1.0;
F(0, 1) = 1.0;
F(1, 1) = 1.0;
// Transition noise covariance
Eigen::Matrix<double, 2, 2> Q;
Q.setZero();
Q(0, 0) = 0.01;
Q(1, 1) = 0.01;
// Observation matrix
Eigen::Matrix<double, 1, 2> H;
H.setIdentity();
// Observation noise covariance
Eigen::Matrix<double, 1, 1> R;
R(0, 0) = 0.5 * 0.5;
// Control matrix
Eigen::Matrix<double, 2, 1> B;
B[0] = 0.5 * 1.0 * 1.0;
B[1] = 1.0;
kf_.SetStateEstimate(x, P);
kf_.SetTransitionMatrix(F);
kf_.SetTransitionNoise(Q);
kf_.SetObservationMatrix(H);
kf_.SetObservationNoise(R);
kf_.SetControlMatrix(B);
}
protected:
KalmanFilter<double, 2, 1, 1> kf_;
};
TEST_F(KalmanFilterTest, SyntheticTrackingTest) {
kf_.Predict();
Eigen::Matrix<double, 2, 1> state = kf_.GetStateEstimate();
Eigen::Matrix<double, 2, 2> state_cov = kf_.GetStateCovariance();
EXPECT_DOUBLE_EQ(1.0, state(0, 0));
EXPECT_DOUBLE_EQ(1.0, state(1, 0));
EXPECT_NEAR(0.21, state_cov(0, 0), 0.001);
EXPECT_NEAR(0.10, state_cov(0, 1), 0.001);
EXPECT_NEAR(0.10, state_cov(1, 0), 0.001);
EXPECT_NEAR(0.11, state_cov(1, 1), 0.001);
Eigen::Matrix<double, 1, 1> z;
z(0, 0) = 1.0;
kf_.Correct(z);
state = kf_.GetStateEstimate();
state_cov = kf_.GetStateCovariance();
EXPECT_DOUBLE_EQ(1.0, state(0, 0));
EXPECT_DOUBLE_EQ(1.0, state(1, 0));
EXPECT_NEAR(0.11413, state_cov(0, 0), 0.001);
EXPECT_NEAR(0.05348, state_cov(0, 1), 0.001);
EXPECT_NEAR(0.05348, state_cov(1, 0), 0.001);
EXPECT_NEAR(0.08826, state_cov(1, 1), 0.001);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/polygon2d.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/polygon2d.h"
#include <algorithm>
#include <cmath>
#include <limits>
#include <utility>
#include "absl/strings/str_cat.h"
#include "absl/strings/str_join.h"
#include "cyber/common/log.h"
#include "modules/common/math/math_utils.h"
#include "modules/common/util/string_util.h"
namespace apollo {
namespace common {
namespace math {
Polygon2d::Polygon2d(const Box2d &box) {
box.GetAllCorners(&points_);
BuildFromPoints();
}
Polygon2d::Polygon2d(std::vector<Vec2d> points) : points_(std::move(points)) {
BuildFromPoints();
}
double Polygon2d::DistanceTo(const Vec2d &point) const {
CHECK_GE(points_.size(), 3U);
if (IsPointIn(point)) {
return 0.0;
}
double distance = std::numeric_limits<double>::infinity();
for (int i = 0; i < num_points_; ++i) {
distance = std::min(distance, line_segments_[i].DistanceTo(point));
}
return distance;
}
double Polygon2d::DistanceSquareTo(const Vec2d &point) const {
CHECK_GE(points_.size(), 3U);
if (IsPointIn(point)) {
return 0.0;
}
double distance_sqr = std::numeric_limits<double>::infinity();
for (int i = 0; i < num_points_; ++i) {
distance_sqr =
std::min(distance_sqr, line_segments_[i].DistanceSquareTo(point));
}
return distance_sqr;
}
double Polygon2d::DistanceTo(const LineSegment2d &line_segment) const {
if (line_segment.length() <= kMathEpsilon) {
return DistanceTo(line_segment.start());
}
CHECK_GE(points_.size(), 3U);
if (IsPointIn(line_segment.center())) {
return 0.0;
}
if (std::any_of(line_segments_.begin(), line_segments_.end(),
[&](const LineSegment2d &poly_seg) {
return poly_seg.HasIntersect(line_segment);
})) {
return 0.0;
}
double distance = std::min(DistanceTo(line_segment.start()),
DistanceTo(line_segment.end()));
for (int i = 0; i < num_points_; ++i) {
distance = std::min(distance, line_segment.DistanceTo(points_[i]));
}
return distance;
}
double Polygon2d::DistanceTo(const Box2d &box) const {
CHECK_GE(points_.size(), 3U);
return DistanceTo(Polygon2d(box));
}
double Polygon2d::DistanceTo(const Polygon2d &polygon) const {
CHECK_GE(points_.size(), 3U);
CHECK_GE(polygon.num_points(), 3);
if (IsPointIn(polygon.points()[0])) {
return 0.0;
}
if (polygon.IsPointIn(points_[0])) {
return 0.0;
}
double distance = std::numeric_limits<double>::infinity();
for (int i = 0; i < num_points_; ++i) {
distance = std::min(distance, polygon.DistanceTo(line_segments_[i]));
}
return distance;
}
double Polygon2d::DistanceToBoundary(const Vec2d &point) const {
double distance = std::numeric_limits<double>::infinity();
for (int i = 0; i < num_points_; ++i) {
distance = std::min(distance, line_segments_[i].DistanceTo(point));
}
return distance;
}
bool Polygon2d::IsPointOnBoundary(const Vec2d &point) const {
CHECK_GE(points_.size(), 3U);
return std::any_of(
line_segments_.begin(), line_segments_.end(),
[&](const LineSegment2d &poly_seg) { return poly_seg.IsPointIn(point); });
}
bool Polygon2d::IsPointIn(const Vec2d &point) const {
CHECK_GE(points_.size(), 3U);
if (IsPointOnBoundary(point)) {
return true;
}
int j = num_points_ - 1;
int c = 0;
for (int i = 0; i < num_points_; ++i) {
if ((points_[i].y() > point.y()) != (points_[j].y() > point.y())) {
const double side = CrossProd(point, points_[i], points_[j]);
if (points_[i].y() < points_[j].y() ? side > 0.0 : side < 0.0) {
++c;
}
}
j = i;
}
return c & 1;
}
bool Polygon2d::HasOverlap(const Polygon2d &polygon) const {
CHECK_GE(points_.size(), 3U);
if (polygon.max_x() < min_x() || polygon.min_x() > max_x() ||
polygon.max_y() < min_y() || polygon.min_y() > max_y()) {
return false;
}
return DistanceTo(polygon) <= kMathEpsilon;
}
bool Polygon2d::Contains(const LineSegment2d &line_segment) const {
if (line_segment.length() <= kMathEpsilon) {
return IsPointIn(line_segment.start());
}
CHECK_GE(points_.size(), 3U);
if (!IsPointIn(line_segment.start())) {
return false;
}
if (!IsPointIn(line_segment.end())) {
return false;
}
if (!is_convex_) {
std::vector<LineSegment2d> overlaps = GetAllOverlaps(line_segment);
double total_length = 0;
for (const auto &overlap_seg : overlaps) {
total_length += overlap_seg.length();
}
return total_length >= line_segment.length() - kMathEpsilon;
}
return true;
}
bool Polygon2d::Contains(const Polygon2d &polygon) const {
CHECK_GE(points_.size(), 3U);
if (area_ < polygon.area() - kMathEpsilon) {
return false;
}
if (!IsPointIn(polygon.points()[0])) {
return false;
}
const auto &line_segments = polygon.line_segments();
return std::all_of(line_segments.begin(), line_segments.end(),
[&](const LineSegment2d &line_segment) {
return Contains(line_segment);
});
}
int Polygon2d::Next(int at) const { return at >= num_points_ - 1 ? 0 : at + 1; }
int Polygon2d::Prev(int at) const { return at == 0 ? num_points_ - 1 : at - 1; }
void Polygon2d::BuildFromPoints() {
num_points_ = static_cast<int>(points_.size());
CHECK_GE(num_points_, 3);
// Make sure the points are in ccw order.
area_ = 0.0;
for (int i = 1; i < num_points_; ++i) {
area_ += CrossProd(points_[0], points_[i - 1], points_[i]);
}
if (area_ < 0) {
area_ = -area_;
std::reverse(points_.begin(), points_.end());
}
area_ /= 2.0;
CHECK_GT(area_, kMathEpsilon);
// Construct line_segments.
line_segments_.reserve(num_points_);
for (int i = 0; i < num_points_; ++i) {
line_segments_.emplace_back(points_[i], points_[Next(i)]);
}
// Check convexity.
is_convex_ = true;
for (int i = 0; i < num_points_; ++i) {
if (CrossProd(points_[Prev(i)], points_[i], points_[Next(i)]) <=
-kMathEpsilon) {
is_convex_ = false;
break;
}
}
// Compute aabox.
min_x_ = points_[0].x();
max_x_ = points_[0].x();
min_y_ = points_[0].y();
max_y_ = points_[0].y();
for (const auto &point : points_) {
min_x_ = std::min(min_x_, point.x());
max_x_ = std::max(max_x_, point.x());
min_y_ = std::min(min_y_, point.y());
max_y_ = std::max(max_y_, point.y());
}
}
bool Polygon2d::ComputeConvexHull(const std::vector<Vec2d> &points,
Polygon2d *const polygon) {
CHECK_NOTNULL(polygon);
const int n = static_cast<int>(points.size());
if (n < 3) {
return false;
}
std::vector<int> sorted_indices(n);
for (int i = 0; i < n; ++i) {
sorted_indices[i] = i;
}
std::sort(sorted_indices.begin(), sorted_indices.end(),
[&](const int idx1, const int idx2) {
const Vec2d &pt1 = points[idx1];
const Vec2d &pt2 = points[idx2];
const double dx = pt1.x() - pt2.x();
if (std::abs(dx) > kMathEpsilon) {
return dx < 0.0;
}
return pt1.y() < pt2.y();
});
int count = 0;
std::vector<int> results;
results.reserve(n);
int last_count = 1;
for (int i = 0; i < n + n; ++i) {
if (i == n) {
last_count = count;
}
const int idx = sorted_indices[(i < n) ? i : (n + n - 1 - i)];
const Vec2d &pt = points[idx];
while (count > last_count &&
CrossProd(points[results[count - 2]], points[results[count - 1]],
pt) <= kMathEpsilon) {
results.pop_back();
--count;
}
results.push_back(idx);
++count;
}
--count;
if (count < 3) {
return false;
}
std::vector<Vec2d> result_points;
result_points.reserve(count);
for (int i = 0; i < count; ++i) {
result_points.push_back(points[results[i]]);
}
*polygon = Polygon2d(result_points);
return true;
}
bool Polygon2d::ClipConvexHull(const LineSegment2d &line_segment,
std::vector<Vec2d> *const points) {
if (line_segment.length() <= kMathEpsilon) {
return true;
}
CHECK_NOTNULL(points);
const size_t n = points->size();
if (n < 3) {
return false;
}
std::vector<double> prod(n);
std::vector<int> side(n);
for (size_t i = 0; i < n; ++i) {
prod[i] = CrossProd(line_segment.start(), line_segment.end(), (*points)[i]);
if (std::abs(prod[i]) <= kMathEpsilon) {
side[i] = 0;
} else {
side[i] = ((prod[i] < 0) ? -1 : 1);
}
}
std::vector<Vec2d> new_points;
for (size_t i = 0; i < n; ++i) {
if (side[i] >= 0) {
new_points.push_back((*points)[i]);
}
const size_t j = ((i == n - 1) ? 0 : (i + 1));
if (side[i] * side[j] < 0) {
const double ratio = prod[j] / (prod[j] - prod[i]);
new_points.emplace_back(
(*points)[i].x() * ratio + (*points)[j].x() * (1.0 - ratio),
(*points)[i].y() * ratio + (*points)[j].y() * (1.0 - ratio));
}
}
points->swap(new_points);
return points->size() >= 3U;
}
bool Polygon2d::ComputeOverlap(const Polygon2d &other_polygon,
Polygon2d *const overlap_polygon) const {
CHECK_GE(points_.size(), 3U);
CHECK_NOTNULL(overlap_polygon);
ACHECK(is_convex_ && other_polygon.is_convex());
std::vector<Vec2d> points = other_polygon.points();
for (int i = 0; i < num_points_; ++i) {
if (!ClipConvexHull(line_segments_[i], &points)) {
return false;
}
}
return ComputeConvexHull(points, overlap_polygon);
}
double Polygon2d::ComputeIoU(const Polygon2d &other_polygon) const {
Polygon2d overlap_polygon;
if (!ComputeOverlap(other_polygon, &overlap_polygon)) {
return 0.0;
}
double intersection_area = overlap_polygon.area();
double union_area = area_ + other_polygon.area() - overlap_polygon.area();
return intersection_area / union_area;
}
bool Polygon2d::HasOverlap(const LineSegment2d &line_segment) const {
CHECK_GE(points_.size(), 3U);
if ((line_segment.start().x() < min_x_ && line_segment.end().x() < min_x_) ||
(line_segment.start().x() > max_x_ && line_segment.end().x() > max_x_) ||
(line_segment.start().y() < min_y_ && line_segment.end().y() < min_y_) ||
(line_segment.start().y() > max_y_ && line_segment.end().y() > max_y_)) {
return false;
}
Vec2d first;
Vec2d last;
return GetOverlap(line_segment, &first, &last);
}
bool Polygon2d::GetOverlap(const LineSegment2d &line_segment,
Vec2d *const first, Vec2d *const last) const {
CHECK_GE(points_.size(), 3U);
CHECK_NOTNULL(first);
CHECK_NOTNULL(last);
if (line_segment.length() <= kMathEpsilon) {
if (!IsPointIn(line_segment.start())) {
return false;
}
*first = line_segment.start();
*last = line_segment.start();
return true;
}
double min_proj = line_segment.length();
double max_proj = 0;
if (IsPointIn(line_segment.start())) {
*first = line_segment.start();
min_proj = 0.0;
}
if (IsPointIn(line_segment.end())) {
*last = line_segment.end();
max_proj = line_segment.length();
}
for (const auto &poly_seg : line_segments_) {
Vec2d pt;
if (poly_seg.GetIntersect(line_segment, &pt)) {
const double proj = line_segment.ProjectOntoUnit(pt);
if (proj < min_proj) {
min_proj = proj;
*first = pt;
}
if (proj > max_proj) {
max_proj = proj;
*last = pt;
}
}
}
return min_proj <= max_proj + kMathEpsilon;
}
void Polygon2d::GetAllVertices(std::vector<Vec2d> *const vertices) const {
if (vertices == nullptr) {
return;
}
*vertices = points_;
}
std::vector<Vec2d> Polygon2d::GetAllVertices() const { return points_; }
std::vector<LineSegment2d> Polygon2d::GetAllOverlaps(
const LineSegment2d &line_segment) const {
CHECK_GE(points_.size(), 3U);
if (line_segment.length() <= kMathEpsilon) {
std::vector<LineSegment2d> overlaps;
if (IsPointIn(line_segment.start())) {
overlaps.push_back(line_segment);
}
return overlaps;
}
std::vector<double> projections;
if (IsPointIn(line_segment.start())) {
projections.push_back(0.0);
}
if (IsPointIn(line_segment.end())) {
projections.push_back(line_segment.length());
}
for (const auto &poly_seg : line_segments_) {
Vec2d pt;
if (poly_seg.GetIntersect(line_segment, &pt)) {
projections.push_back(line_segment.ProjectOntoUnit(pt));
}
}
std::sort(projections.begin(), projections.end());
std::vector<std::pair<double, double>> overlaps;
for (size_t i = 0; i + 1 < projections.size(); ++i) {
const double start_proj = projections[i];
const double end_proj = projections[i + 1];
if (end_proj - start_proj <= kMathEpsilon) {
continue;
}
const Vec2d reference_point =
line_segment.start() +
(start_proj + end_proj) / 2.0 * line_segment.unit_direction();
if (!IsPointIn(reference_point)) {
continue;
}
if (overlaps.empty() ||
start_proj > overlaps.back().second + kMathEpsilon) {
overlaps.emplace_back(start_proj, end_proj);
} else {
overlaps.back().second = end_proj;
}
}
std::vector<LineSegment2d> overlap_line_segments;
for (const auto &overlap : overlaps) {
overlap_line_segments.emplace_back(
line_segment.start() + overlap.first * line_segment.unit_direction(),
line_segment.start() + overlap.second * line_segment.unit_direction());
}
return overlap_line_segments;
}
void Polygon2d::ExtremePoints(const double heading, Vec2d *const first,
Vec2d *const last) const {
CHECK_GE(points_.size(), 3U);
CHECK_NOTNULL(first);
CHECK_NOTNULL(last);
const Vec2d direction_vec = Vec2d::CreateUnitVec2d(heading);
double min_proj = std::numeric_limits<double>::infinity();
double max_proj = -std::numeric_limits<double>::infinity();
for (const auto &pt : points_) {
const double proj = pt.InnerProd(direction_vec);
if (proj < min_proj) {
min_proj = proj;
*first = pt;
}
if (proj > max_proj) {
max_proj = proj;
*last = pt;
}
}
}
AABox2d Polygon2d::AABoundingBox() const {
return AABox2d({min_x_, min_y_}, {max_x_, max_y_});
}
Box2d Polygon2d::BoundingBoxWithHeading(const double heading) const {
CHECK_GE(points_.size(), 3U);
const Vec2d direction_vec = Vec2d::CreateUnitVec2d(heading);
Vec2d px1;
Vec2d px2;
Vec2d py1;
Vec2d py2;
ExtremePoints(heading, &px1, &px2);
ExtremePoints(heading - M_PI_2, &py1, &py2);
const double x1 = px1.InnerProd(direction_vec);
const double x2 = px2.InnerProd(direction_vec);
const double y1 = py1.CrossProd(direction_vec);
const double y2 = py2.CrossProd(direction_vec);
return Box2d(
(x1 + x2) / 2.0 * direction_vec +
(y1 + y2) / 2.0 * Vec2d(direction_vec.y(), -direction_vec.x()),
heading, x2 - x1, y2 - y1);
}
Box2d Polygon2d::MinAreaBoundingBox() const {
CHECK_GE(points_.size(), 3U);
if (!is_convex_) {
Polygon2d convex_polygon;
ComputeConvexHull(points_, &convex_polygon);
ACHECK(convex_polygon.is_convex());
return convex_polygon.MinAreaBoundingBox();
}
double min_area = std::numeric_limits<double>::infinity();
double min_area_at_heading = 0.0;
int left_most = 0;
int right_most = 0;
int top_most = 0;
for (int i = 0; i < num_points_; ++i) {
const auto &line_segment = line_segments_[i];
double proj = 0.0;
double min_proj = line_segment.ProjectOntoUnit(points_[left_most]);
while ((proj = line_segment.ProjectOntoUnit(points_[Prev(left_most)])) <
min_proj) {
min_proj = proj;
left_most = Prev(left_most);
}
while ((proj = line_segment.ProjectOntoUnit(points_[Next(left_most)])) <
min_proj) {
min_proj = proj;
left_most = Next(left_most);
}
double max_proj = line_segment.ProjectOntoUnit(points_[right_most]);
while ((proj = line_segment.ProjectOntoUnit(points_[Prev(right_most)])) >
max_proj) {
max_proj = proj;
right_most = Prev(right_most);
}
while ((proj = line_segment.ProjectOntoUnit(points_[Next(right_most)])) >
max_proj) {
max_proj = proj;
right_most = Next(right_most);
}
double prod = 0.0;
double max_prod = line_segment.ProductOntoUnit(points_[top_most]);
while ((prod = line_segment.ProductOntoUnit(points_[Prev(top_most)])) >
max_prod) {
max_prod = prod;
top_most = Prev(top_most);
}
while ((prod = line_segment.ProductOntoUnit(points_[Next(top_most)])) >
max_prod) {
max_prod = prod;
top_most = Next(top_most);
}
const double area = max_prod * (max_proj - min_proj);
if (area < min_area) {
min_area = area;
min_area_at_heading = line_segment.heading();
}
}
return BoundingBoxWithHeading(min_area_at_heading);
}
Polygon2d Polygon2d::ExpandByDistance(const double distance) const {
if (!is_convex_) {
Polygon2d convex_polygon;
ComputeConvexHull(points_, &convex_polygon);
ACHECK(convex_polygon.is_convex());
return convex_polygon.ExpandByDistance(distance);
}
const double kMinAngle = 0.1;
std::vector<Vec2d> points;
for (int i = 0; i < num_points_; ++i) {
const double start_angle = line_segments_[Prev(i)].heading() - M_PI_2;
const double end_angle = line_segments_[i].heading() - M_PI_2;
const double diff = WrapAngle(end_angle - start_angle);
if (diff <= kMathEpsilon) {
points.push_back(points_[i] +
Vec2d::CreateUnitVec2d(start_angle) * distance);
} else {
const int count = static_cast<int>(diff / kMinAngle) + 1;
for (int k = 0; k <= count; ++k) {
const double angle = start_angle + diff * static_cast<double>(k) /
static_cast<double>(count);
points.push_back(points_[i] + Vec2d::CreateUnitVec2d(angle) * distance);
}
}
}
Polygon2d new_polygon;
ACHECK(ComputeConvexHull(points, &new_polygon));
return new_polygon;
}
std::string Polygon2d::DebugString() const {
return absl::StrCat("polygon2d ( num_points = ", num_points_, " points = (",
absl::StrJoin(points_, " ", util::DebugStringFormatter()),
" ) ", is_convex_ ? "convex" : "non-convex",
" area = ", area_, " )");
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/euler_angles_zxy.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Defines the EulerAnglesZXY class.
*/
#pragma once
// TODO(all): should use Angle class internally.
#include <cmath>
#include "Eigen/Geometry"
#include "modules/common/math/math_utils.h"
/**
* @namespace apollo::common::math
* @brief apollo::common::math
*/
namespace apollo {
namespace common {
namespace math {
/**
* @class EulerAnglesZXY
*
* Any orientation of a rigid body on a 3-D space can be achieved by
* composing three rotations about the axes of an orthogonal coordinate system.
* These rotations are said to be extrinsic if the axes are assumed to be
* motionless, and intrinsic otherwise. Here, we use an intrinsic referential,
* which is relative to the car's orientation.
* Our vehicle reference frame follows NovAtel's convention:
* Right/Forward/Up (RFU) respectively for the axes x/y/z.
* In particular, we describe the orientation of the car by three angles:
* 1) the pitch, in (-pi/2, pi/2), corresponds to a rotation around the x-axis;
* 2) the roll, in [-pi, pi), corresponds to a rotation around the y-axis;
* 3) the yaw, in [-pi, pi), corresponds to a rotation around the z-axis.
* The pitch is zero when the car is level and positive when the nose is up.
* The roll is zero when the car is level and positive when the left part is up.
* The yaw is zero when the car is facing North, and positive when facing West.
* In turn, in the world frame, the x/y/z axes point to East/North/Up (ENU).
* These angles represent the rotation from the world to the vehicle frames.
*
* @brief Implements a class of Euler angles (actually, Tait-Bryan angles),
* with intrinsic sequence ZXY.
*
* @param T Number type: double or float
*/
template <typename T>
class EulerAnglesZXY {
public:
/**
* @brief Constructs an identity rotation.
*/
EulerAnglesZXY() : roll_(0), pitch_(0), yaw_(0) {}
/**
* @brief Constructs a rotation using only yaw (i.e., around the z-axis).
*
* @param yaw The yaw of the car
*/
explicit EulerAnglesZXY(T yaw) : roll_(0), pitch_(0), yaw_(yaw) {}
/**
* @brief Constructs a rotation using arbitrary roll, pitch, and yaw.
*
* @param roll The roll of the car
* @param pitch The pitch of the car
* @param yaw The yaw of the car
*/
EulerAnglesZXY(T roll, T pitch, T yaw)
: roll_(roll), pitch_(pitch), yaw_(yaw) {}
/**
* @brief Constructs a rotation using components of a quaternion.
*
* @param qw Quaternion w-coordinate
* @param qx Quaternion x-coordinate
* @param qy Quaternion y-coordinate
* @param qz Quaternion z-coordinate
*/
EulerAnglesZXY(T qw, T qx, T qy, T qz)
: roll_(std::atan2(static_cast<T>(2.0) * (qw * qy - qx * qz),
static_cast<T>(2.0) * (Square<T>(qw) + Square<T>(qz)) -
static_cast<T>(1.0))),
pitch_(std::asin(static_cast<T>(2.0) * (qw * qx + qy * qz))),
yaw_(std::atan2(static_cast<T>(2.0) * (qw * qz - qx * qy),
static_cast<T>(2.0) * (Square<T>(qw) + Square<T>(qy)) -
static_cast<T>(1.0))) {}
/**
* @brief Constructs a rotation from quaternion.
* @param q Quaternion
*/
explicit EulerAnglesZXY(const Eigen::Quaternion<T> &q)
: EulerAnglesZXY(q.w(), q.x(), q.y(), q.z()) {}
/**
* @brief Getter for roll_
* @return The roll of the car
*/
T roll() const { return roll_; }
/**
* @brief Getter for pitch_
* @return The pitch of the car
*/
T pitch() const { return pitch_; }
/**
* @brief Getter for yaw_
* @return The yaw of the car
*/
T yaw() const { return yaw_; }
/**
* @brief Normalizes roll_, pitch_, and yaw_ to [-PI, PI).
*/
void Normalize() {
roll_ = NormalizeAngle(roll_);
pitch_ = NormalizeAngle(pitch_);
yaw_ = NormalizeAngle(yaw_);
}
/**
* @brief Verifies the validity of the specified rotation.
* @return True iff -PI/2 < pitch < PI/2
*/
bool IsValid() {
Normalize();
return pitch_ < M_PI_2 && pitch_ > -M_PI_2;
}
/**
* @brief Converts to a quaternion with a non-negative scalar part
* @return Quaternion encoding this rotation.
*/
Eigen::Quaternion<T> ToQuaternion() const {
T coeff = static_cast<T>(0.5);
T r = roll_ * coeff;
T p = pitch_ * coeff;
T y = yaw_ * coeff;
T sr = std::sin(r);
T sp = std::sin(p);
T sy = std::sin(y);
T cr = std::cos(r);
T cp = std::cos(p);
T cy = std::cos(y);
T qw = cr * cp * cy - sr * sp * sy;
T qx = cr * sp * cy - sr * cp * sy;
T qy = cr * sp * sy + sr * cp * cy;
T qz = cr * cp * sy + sr * sp * cy;
if (qw < 0.0) {
return {-qw, -qx, -qy, -qz};
}
return {qw, qx, qy, qz};
}
private:
T roll_;
T pitch_;
T yaw_;
};
using EulerAnglesZXYf = EulerAnglesZXY<float>;
using EulerAnglesZXYd = EulerAnglesZXY<double>;
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/aaboxkdtree2d.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Defines the templated AABoxKDTree2dNode class.
*/
#pragma once
#include <algorithm>
#include <limits>
#include <memory>
#include <vector>
#include "cyber/common/log.h"
#include "modules/common/math/aabox2d.h"
#include "modules/common/math/math_utils.h"
/**
* @namespace apollo::common::math
* @brief The math namespace deals with a number of useful mathematical objects.
*/
namespace apollo {
namespace common {
namespace math {
/**
* @class AABoxKDTreeParams
* @brief Contains parameters of axis-aligned bounding box.
*/
struct AABoxKDTreeParams {
/// The maximum depth of the kdtree.
int max_depth = -1;
/// The maximum number of items in one leaf node.
int max_leaf_size = -1;
/// The maximum dimension size of leaf node.
double max_leaf_dimension = -1.0;
};
/**
* @class AABoxKDTree2dNode
* @brief The class of KD-tree node of axis-aligned bounding box.
*/
template <class ObjectType>
class AABoxKDTree2dNode {
public:
using ObjectPtr = const ObjectType *;
/**
* @brief Constructor which takes a vector of objects,
* parameters and depth of the node.
* @param objects Objects to build the KD-tree node.
* @param params Parameters to build the KD-tree.
* @param depth Depth of the KD-tree node.
*/
AABoxKDTree2dNode(const std::vector<ObjectPtr> &objects,
const AABoxKDTreeParams ¶ms, int depth)
: depth_(depth) {
ACHECK(!objects.empty());
ComputeBoundary(objects);
ComputePartition();
if (SplitToSubNodes(objects, params)) {
std::vector<ObjectPtr> left_subnode_objects;
std::vector<ObjectPtr> right_subnode_objects;
PartitionObjects(objects, &left_subnode_objects, &right_subnode_objects);
// Split to sub-nodes.
if (!left_subnode_objects.empty()) {
left_subnode_.reset(new AABoxKDTree2dNode<ObjectType>(
left_subnode_objects, params, depth + 1));
}
if (!right_subnode_objects.empty()) {
right_subnode_.reset(new AABoxKDTree2dNode<ObjectType>(
right_subnode_objects, params, depth + 1));
}
} else {
InitObjects(objects);
}
}
/**
* @brief Get the nearest object to a target point by the KD-tree
* rooted at this node.
* @param point The target point. Search it's nearest object.
* @return The nearest object to the target point.
*/
ObjectPtr GetNearestObject(const Vec2d &point) const {
ObjectPtr nearest_object = nullptr;
double min_distance_sqr = std::numeric_limits<double>::infinity();
GetNearestObjectInternal(point, &min_distance_sqr, &nearest_object);
return nearest_object;
}
/**
* @brief Get objects within a distance to a point by the KD-tree
* rooted at this node.
* @param point The center point of the range to search objects.
* @param distance The radius of the range to search objects.
* @return All objects within the specified distance to the specified point.
*/
std::vector<ObjectPtr> GetObjects(const Vec2d &point,
const double distance) const {
std::vector<ObjectPtr> result_objects;
GetObjectsInternal(point, distance, Square(distance), &result_objects);
return result_objects;
}
/**
* @brief Get the axis-aligned bounding box of the objects.
* @return The axis-aligned bounding box of the objects.
*/
AABox2d GetBoundingBox() const {
return AABox2d({min_x_, min_y_}, {max_x_, max_y_});
}
private:
void InitObjects(const std::vector<ObjectPtr> &objects) {
num_objects_ = static_cast<int>(objects.size());
objects_sorted_by_min_ = objects;
objects_sorted_by_max_ = objects;
std::sort(objects_sorted_by_min_.begin(), objects_sorted_by_min_.end(),
[&](ObjectPtr obj1, ObjectPtr obj2) {
return partition_ == PARTITION_X
? obj1->aabox().min_x() < obj2->aabox().min_x()
: obj1->aabox().min_y() < obj2->aabox().min_y();
});
std::sort(objects_sorted_by_max_.begin(), objects_sorted_by_max_.end(),
[&](ObjectPtr obj1, ObjectPtr obj2) {
return partition_ == PARTITION_X
? obj1->aabox().max_x() > obj2->aabox().max_x()
: obj1->aabox().max_y() > obj2->aabox().max_y();
});
objects_sorted_by_min_bound_.reserve(num_objects_);
for (ObjectPtr object : objects_sorted_by_min_) {
objects_sorted_by_min_bound_.push_back(partition_ == PARTITION_X
? object->aabox().min_x()
: object->aabox().min_y());
}
objects_sorted_by_max_bound_.reserve(num_objects_);
for (ObjectPtr object : objects_sorted_by_max_) {
objects_sorted_by_max_bound_.push_back(partition_ == PARTITION_X
? object->aabox().max_x()
: object->aabox().max_y());
}
}
bool SplitToSubNodes(const std::vector<ObjectPtr> &objects,
const AABoxKDTreeParams ¶ms) {
if (params.max_depth >= 0 && depth_ >= params.max_depth) {
return false;
}
if (static_cast<int>(objects.size()) <= std::max(1, params.max_leaf_size)) {
return false;
}
if (params.max_leaf_dimension >= 0.0 &&
std::max(max_x_ - min_x_, max_y_ - min_y_) <=
params.max_leaf_dimension) {
return false;
}
return true;
}
double LowerDistanceSquareToPoint(const Vec2d &point) const {
double dx = 0.0;
if (point.x() < min_x_) {
dx = min_x_ - point.x();
} else if (point.x() > max_x_) {
dx = point.x() - max_x_;
}
double dy = 0.0;
if (point.y() < min_y_) {
dy = min_y_ - point.y();
} else if (point.y() > max_y_) {
dy = point.y() - max_y_;
}
return dx * dx + dy * dy;
}
double UpperDistanceSquareToPoint(const Vec2d &point) const {
const double dx =
(point.x() > mid_x_ ? (point.x() - min_x_) : (point.x() - max_x_));
const double dy =
(point.y() > mid_y_ ? (point.y() - min_y_) : (point.y() - max_y_));
return dx * dx + dy * dy;
}
void GetAllObjects(std::vector<ObjectPtr> *const result_objects) const {
result_objects->insert(result_objects->end(),
objects_sorted_by_min_.begin(),
objects_sorted_by_min_.end());
if (left_subnode_ != nullptr) {
left_subnode_->GetAllObjects(result_objects);
}
if (right_subnode_ != nullptr) {
right_subnode_->GetAllObjects(result_objects);
}
}
void GetObjectsInternal(const Vec2d &point, const double distance,
const double distance_sqr,
std::vector<ObjectPtr> *const result_objects) const {
if (LowerDistanceSquareToPoint(point) > distance_sqr) {
return;
}
if (UpperDistanceSquareToPoint(point) <= distance_sqr) {
GetAllObjects(result_objects);
return;
}
const double pvalue = (partition_ == PARTITION_X ? point.x() : point.y());
if (pvalue < partition_position_) {
const double limit = pvalue + distance;
for (int i = 0; i < num_objects_; ++i) {
if (objects_sorted_by_min_bound_[i] > limit) {
break;
}
ObjectPtr object = objects_sorted_by_min_[i];
if (object->DistanceSquareTo(point) <= distance_sqr) {
result_objects->push_back(object);
}
}
} else {
const double limit = pvalue - distance;
for (int i = 0; i < num_objects_; ++i) {
if (objects_sorted_by_max_bound_[i] < limit) {
break;
}
ObjectPtr object = objects_sorted_by_max_[i];
if (object->DistanceSquareTo(point) <= distance_sqr) {
result_objects->push_back(object);
}
}
}
if (left_subnode_ != nullptr) {
left_subnode_->GetObjectsInternal(point, distance, distance_sqr,
result_objects);
}
if (right_subnode_ != nullptr) {
right_subnode_->GetObjectsInternal(point, distance, distance_sqr,
result_objects);
}
}
void GetNearestObjectInternal(const Vec2d &point,
double *const min_distance_sqr,
ObjectPtr *const nearest_object) const {
if (LowerDistanceSquareToPoint(point) >= *min_distance_sqr - kMathEpsilon) {
return;
}
const double pvalue = (partition_ == PARTITION_X ? point.x() : point.y());
const bool search_left_first = (pvalue < partition_position_);
if (search_left_first) {
if (left_subnode_ != nullptr) {
left_subnode_->GetNearestObjectInternal(point, min_distance_sqr,
nearest_object);
}
} else {
if (right_subnode_ != nullptr) {
right_subnode_->GetNearestObjectInternal(point, min_distance_sqr,
nearest_object);
}
}
if (*min_distance_sqr <= kMathEpsilon) {
return;
}
if (search_left_first) {
for (int i = 0; i < num_objects_; ++i) {
const double bound = objects_sorted_by_min_bound_[i];
if (bound > pvalue && Square(bound - pvalue) > *min_distance_sqr) {
break;
}
ObjectPtr object = objects_sorted_by_min_[i];
const double distance_sqr = object->DistanceSquareTo(point);
if (distance_sqr < *min_distance_sqr) {
*min_distance_sqr = distance_sqr;
*nearest_object = object;
}
}
} else {
for (int i = 0; i < num_objects_; ++i) {
const double bound = objects_sorted_by_max_bound_[i];
if (bound < pvalue && Square(bound - pvalue) > *min_distance_sqr) {
break;
}
ObjectPtr object = objects_sorted_by_max_[i];
const double distance_sqr = object->DistanceSquareTo(point);
if (distance_sqr < *min_distance_sqr) {
*min_distance_sqr = distance_sqr;
*nearest_object = object;
}
}
}
if (*min_distance_sqr <= kMathEpsilon) {
return;
}
if (search_left_first) {
if (right_subnode_ != nullptr) {
right_subnode_->GetNearestObjectInternal(point, min_distance_sqr,
nearest_object);
}
} else {
if (left_subnode_ != nullptr) {
left_subnode_->GetNearestObjectInternal(point, min_distance_sqr,
nearest_object);
}
}
}
void ComputeBoundary(const std::vector<ObjectPtr> &objects) {
min_x_ = std::numeric_limits<double>::infinity();
min_y_ = std::numeric_limits<double>::infinity();
max_x_ = -std::numeric_limits<double>::infinity();
max_y_ = -std::numeric_limits<double>::infinity();
for (ObjectPtr object : objects) {
min_x_ = std::fmin(min_x_, object->aabox().min_x());
max_x_ = std::fmax(max_x_, object->aabox().max_x());
min_y_ = std::fmin(min_y_, object->aabox().min_y());
max_y_ = std::fmax(max_y_, object->aabox().max_y());
}
mid_x_ = (min_x_ + max_x_) / 2.0;
mid_y_ = (min_y_ + max_y_) / 2.0;
ACHECK(!std::isinf(max_x_) && !std::isinf(max_y_) && !std::isinf(min_x_) &&
!std::isinf(min_y_))
<< "the provided object box size is infinity";
}
void ComputePartition() {
if (max_x_ - min_x_ >= max_y_ - min_y_) {
partition_ = PARTITION_X;
partition_position_ = (min_x_ + max_x_) / 2.0;
} else {
partition_ = PARTITION_Y;
partition_position_ = (min_y_ + max_y_) / 2.0;
}
}
void PartitionObjects(const std::vector<ObjectPtr> &objects,
std::vector<ObjectPtr> *const left_subnode_objects,
std::vector<ObjectPtr> *const right_subnode_objects) {
left_subnode_objects->clear();
right_subnode_objects->clear();
std::vector<ObjectPtr> other_objects;
if (partition_ == PARTITION_X) {
for (ObjectPtr object : objects) {
if (object->aabox().max_x() <= partition_position_) {
left_subnode_objects->push_back(object);
} else if (object->aabox().min_x() >= partition_position_) {
right_subnode_objects->push_back(object);
} else {
other_objects.push_back(object);
}
}
} else {
for (ObjectPtr object : objects) {
if (object->aabox().max_y() <= partition_position_) {
left_subnode_objects->push_back(object);
} else if (object->aabox().min_y() >= partition_position_) {
right_subnode_objects->push_back(object);
} else {
other_objects.push_back(object);
}
}
}
InitObjects(other_objects);
}
private:
int num_objects_ = 0;
std::vector<ObjectPtr> objects_sorted_by_min_;
std::vector<ObjectPtr> objects_sorted_by_max_;
std::vector<double> objects_sorted_by_min_bound_;
std::vector<double> objects_sorted_by_max_bound_;
int depth_ = 0;
// Boundary
double min_x_ = 0.0;
double max_x_ = 0.0;
double min_y_ = 0.0;
double max_y_ = 0.0;
double mid_x_ = 0.0;
double mid_y_ = 0.0;
enum Partition {
PARTITION_X = 1,
PARTITION_Y = 2,
};
Partition partition_ = PARTITION_X;
double partition_position_ = 0.0;
std::unique_ptr<AABoxKDTree2dNode<ObjectType>> left_subnode_ = nullptr;
std::unique_ptr<AABoxKDTree2dNode<ObjectType>> right_subnode_ = nullptr;
};
/**
* @class AABoxKDTree2d
* @brief The class of KD-tree of Aligned Axis Bounding Box(AABox).
*/
template <class ObjectType>
class AABoxKDTree2d {
public:
using ObjectPtr = const ObjectType *;
/**
* @brief Constructor which takes a vector of objects and parameters.
* @param params Parameters to build the KD-tree.
*/
AABoxKDTree2d(const std::vector<ObjectType> &objects,
const AABoxKDTreeParams ¶ms) {
if (!objects.empty()) {
std::vector<ObjectPtr> object_ptrs;
for (const auto &object : objects) {
object_ptrs.push_back(&object);
}
root_.reset(new AABoxKDTree2dNode<ObjectType>(object_ptrs, params, 0));
}
}
/**
* @brief Get the nearest object to a target point.
* @param point The target point. Search it's nearest object.
* @return The nearest object to the target point.
*/
ObjectPtr GetNearestObject(const Vec2d &point) const {
return root_ == nullptr ? nullptr : root_->GetNearestObject(point);
}
/**
* @brief Get objects within a distance to a point.
* @param point The center point of the range to search objects.
* @param distance The radius of the range to search objects.
* @return All objects within the specified distance to the specified point.
*/
std::vector<ObjectPtr> GetObjects(const Vec2d &point,
const double distance) const {
if (root_ == nullptr) {
return {};
}
return root_->GetObjects(point, distance);
}
/**
* @brief Get the axis-aligned bounding box of the objects.
* @return The axis-aligned bounding box of the objects.
*/
AABox2d GetBoundingBox() const {
return root_ == nullptr ? AABox2d() : root_->GetBoundingBox();
}
private:
std::unique_ptr<AABoxKDTree2dNode<ObjectType>> root_ = nullptr;
};
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/linear_interpolation_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/linear_interpolation.h"
#include "Eigen/Dense"
#include "gtest/gtest.h"
namespace apollo {
namespace common {
namespace math {
TEST(LinearInterpolationTest, LerpOneDim) {
double t0 = 0.0;
double t1 = 1.0;
double x0 = 2.0;
double x1 = 4.0;
EXPECT_NEAR(lerp(x0, t0, x1, t1, 0.4), 2.8, 1e-6);
EXPECT_NEAR(lerp(x0, t0, x1, t1, 0.9), 3.8, 1e-6);
EXPECT_NEAR(lerp(x0, t0, x1, t1, 1.5), 5.0, 1e-6);
EXPECT_NEAR(lerp(x0, t0, x1, t1, -0.3), 1.4, 1e-6);
}
TEST(LinearInterpolationTest, LerpTwoDim) {
double t0 = 0.0;
double t1 = 1.0;
Eigen::Vector2d x0(2.0, 1.0);
Eigen::Vector2d x1(4.0, 5.0);
Eigen::Vector2d x = lerp(x0, t0, x1, t1, 0.4);
EXPECT_NEAR(x.x(), 2.8, 1e-6);
EXPECT_NEAR(x.y(), 2.6, 1e-6);
x = lerp(x0, t0, x1, t1, 1.2);
EXPECT_NEAR(x.x(), 4.4, 1e-6);
EXPECT_NEAR(x.y(), 5.8, 1e-6);
x = lerp(x0, t0, x1, t1, -0.5);
EXPECT_NEAR(x.x(), 1.0, 1e-6);
EXPECT_NEAR(x.y(), -1.0, 1e-6);
}
TEST(LinearInterpolationTest, SlerpCaseOne) {
double t0 = 0.0;
double t1 = 1.0;
double a0 = -2.0;
double a1 = 8.5;
EXPECT_NEAR(slerp(a0, t0, a1, t1, 0.4), -2.827, 1e-3);
}
TEST(LinearInterpolationTest, SlerpCaseTwo) {
double t0 = 0.0;
double t1 = 1.0;
double a0 = 3.00;
double a1 = -3.00;
EXPECT_NEAR(slerp(a0, t0, a1, t1, 0.5001), -3.1416, 1e-3);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/aaboxkdtree2d_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/aaboxkdtree2d.h"
#include <string>
#include "gtest/gtest.h"
#include "modules/common/math/line_segment2d.h"
#include "modules/common/math/math_utils.h"
namespace apollo {
namespace common {
namespace math {
namespace {
class Object {
public:
Object(const double x1, const double y1, const double x2, const double y2,
const int id)
: aabox_({x1, y1}, {x2, y2}),
line_segment_({x1, y1}, {x2, y2}),
id_(id) {}
const AABox2d &aabox() const { return aabox_; }
double DistanceTo(const Vec2d &point) const {
return line_segment_.DistanceTo(point);
}
double DistanceSquareTo(const Vec2d &point) const {
return line_segment_.DistanceSquareTo(point);
}
int id() const { return id_; }
private:
AABox2d aabox_;
LineSegment2d line_segment_;
int id_ = 0;
};
} // namespace
TEST(AABoxKDTree2dNode, OverallTests) {
const int kNumBoxes[4] = {1, 10, 50, 100};
const int kNumQueries = 1000;
const double kSize = 100;
const int kNumTrees = 4;
AABoxKDTreeParams kdtree_params[kNumTrees];
kdtree_params[1].max_depth = 2;
kdtree_params[2].max_leaf_dimension = kSize / 4.0;
kdtree_params[3].max_leaf_size = 20;
for (int num_boxes : kNumBoxes) {
std::vector<Object> objects;
for (int i = 0; i < num_boxes; ++i) {
const double cx = RandomDouble(-kSize, kSize);
const double cy = RandomDouble(-kSize, kSize);
const double dx = RandomDouble(-kSize / 10.0, kSize / 10.0);
const double dy = RandomDouble(-kSize / 10.0, kSize / 10.0);
objects.emplace_back(cx - dx, cy - dy, cx + dx, cy + dy, i);
}
std::unique_ptr<AABoxKDTree2d<Object>> kdtrees[kNumTrees];
for (int i = 0; i < kNumTrees; ++i) {
kdtrees[i].reset(new AABoxKDTree2d<Object>(objects, kdtree_params[i]));
}
for (int i = 0; i < kNumQueries; ++i) {
const Vec2d point(RandomDouble(-kSize * 1.5, kSize * 1.5),
RandomDouble(-kSize * 1.5, kSize * 1.5));
double expected_distance = std::numeric_limits<double>::infinity();
for (const auto &object : objects) {
expected_distance =
std::min(expected_distance, object.DistanceTo(point));
}
for (int k = 0; k < kNumTrees; ++k) {
const Object *nearest_object = kdtrees[k]->GetNearestObject(point);
const double actual_distance = nearest_object->DistanceTo(point);
EXPECT_NEAR(actual_distance, expected_distance, 1e-3);
}
}
for (int i = 0; i < kNumQueries; ++i) {
const Vec2d point(RandomDouble(-kSize * 1.5, kSize * 1.5),
RandomDouble(-kSize * 1.5, kSize * 1.5));
const double distance = RandomDouble(0, kSize * 2.0);
for (int k = 0; k < kNumTrees; ++k) {
std::vector<const Object *> result_objects =
kdtrees[k]->GetObjects(point, distance);
std::set<int> result_ids;
for (const Object *object : result_objects) {
result_ids.insert(object->id());
}
EXPECT_EQ(result_objects.size(), result_ids.size());
for (const auto &object : objects) {
const double d = object.DistanceTo(point);
if (std::abs(d - distance) <= 1e-3) {
continue;
}
if (d < distance) {
EXPECT_TRUE(result_ids.count(object.id()));
} else {
EXPECT_FALSE(result_ids.count(object.id()));
}
}
}
}
}
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/line_segment2d.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/line_segment2d.h"
#include <algorithm>
#include <cmath>
#include <utility>
#include "absl/strings/str_cat.h"
#include "cyber/common/log.h"
#include "modules/common/math/math_utils.h"
namespace apollo {
namespace common {
namespace math {
namespace {
bool IsWithin(double val, double bound1, double bound2) {
if (bound1 > bound2) {
std::swap(bound1, bound2);
}
return val >= bound1 - kMathEpsilon && val <= bound2 + kMathEpsilon;
}
} // namespace
LineSegment2d::LineSegment2d() { unit_direction_ = Vec2d(1, 0); }
LineSegment2d::LineSegment2d(const Vec2d &start, const Vec2d &end)
: start_(start), end_(end) {
const double dx = end_.x() - start_.x();
const double dy = end_.y() - start_.y();
length_ = hypot(dx, dy);
unit_direction_ =
(length_ <= kMathEpsilon ? Vec2d(0, 0)
: Vec2d(dx / length_, dy / length_));
heading_ = unit_direction_.Angle();
}
Vec2d LineSegment2d::rotate(const double angle) {
Vec2d diff_vec = end_ - start_;
diff_vec.SelfRotate(angle);
return start_ + diff_vec;
}
double LineSegment2d::length() const { return length_; }
double LineSegment2d::length_sqr() const { return length_ * length_; }
double LineSegment2d::DistanceTo(const Vec2d &point) const {
if (length_ <= kMathEpsilon) {
return point.DistanceTo(start_);
}
const double x0 = point.x() - start_.x();
const double y0 = point.y() - start_.y();
const double proj = x0 * unit_direction_.x() + y0 * unit_direction_.y();
if (proj <= 0.0) {
return hypot(x0, y0);
}
if (proj >= length_) {
return point.DistanceTo(end_);
}
return std::abs(x0 * unit_direction_.y() - y0 * unit_direction_.x());
}
double LineSegment2d::DistanceTo(const Vec2d &point,
Vec2d *const nearest_pt) const {
CHECK_NOTNULL(nearest_pt);
if (length_ <= kMathEpsilon) {
*nearest_pt = start_;
return point.DistanceTo(start_);
}
const double x0 = point.x() - start_.x();
const double y0 = point.y() - start_.y();
const double proj = x0 * unit_direction_.x() + y0 * unit_direction_.y();
if (proj < 0.0) {
*nearest_pt = start_;
return hypot(x0, y0);
}
if (proj > length_) {
*nearest_pt = end_;
return point.DistanceTo(end_);
}
*nearest_pt = start_ + unit_direction_ * proj;
return std::abs(x0 * unit_direction_.y() - y0 * unit_direction_.x());
}
double LineSegment2d::DistanceSquareTo(const Vec2d &point) const {
if (length_ <= kMathEpsilon) {
return point.DistanceSquareTo(start_);
}
const double x0 = point.x() - start_.x();
const double y0 = point.y() - start_.y();
const double proj = x0 * unit_direction_.x() + y0 * unit_direction_.y();
if (proj <= 0.0) {
return Square(x0) + Square(y0);
}
if (proj >= length_) {
return point.DistanceSquareTo(end_);
}
return Square(x0 * unit_direction_.y() - y0 * unit_direction_.x());
}
double LineSegment2d::DistanceSquareTo(const Vec2d &point,
Vec2d *const nearest_pt) const {
CHECK_NOTNULL(nearest_pt);
if (length_ <= kMathEpsilon) {
*nearest_pt = start_;
return point.DistanceSquareTo(start_);
}
const double x0 = point.x() - start_.x();
const double y0 = point.y() - start_.y();
const double proj = x0 * unit_direction_.x() + y0 * unit_direction_.y();
if (proj <= 0.0) {
*nearest_pt = start_;
return Square(x0) + Square(y0);
}
if (proj >= length_) {
*nearest_pt = end_;
return point.DistanceSquareTo(end_);
}
*nearest_pt = start_ + unit_direction_ * proj;
return Square(x0 * unit_direction_.y() - y0 * unit_direction_.x());
}
bool LineSegment2d::IsPointIn(const Vec2d &point) const {
if (length_ <= kMathEpsilon) {
return std::abs(point.x() - start_.x()) <= kMathEpsilon &&
std::abs(point.y() - start_.y()) <= kMathEpsilon;
}
const double prod = CrossProd(point, start_, end_);
if (std::abs(prod) > kMathEpsilon) {
return false;
}
return IsWithin(point.x(), start_.x(), end_.x()) &&
IsWithin(point.y(), start_.y(), end_.y());
}
double LineSegment2d::ProjectOntoUnit(const Vec2d &point) const {
return unit_direction_.InnerProd(point - start_);
}
double LineSegment2d::ProductOntoUnit(const Vec2d &point) const {
return unit_direction_.CrossProd(point - start_);
}
bool LineSegment2d::HasIntersect(const LineSegment2d &other_segment) const {
Vec2d point;
return GetIntersect(other_segment, &point);
}
bool LineSegment2d::GetIntersect(const LineSegment2d &other_segment,
Vec2d *const point) const {
CHECK_NOTNULL(point);
if (IsPointIn(other_segment.start())) {
*point = other_segment.start();
return true;
}
if (IsPointIn(other_segment.end())) {
*point = other_segment.end();
return true;
}
if (other_segment.IsPointIn(start_)) {
*point = start_;
return true;
}
if (other_segment.IsPointIn(end_)) {
*point = end_;
return true;
}
if (length_ <= kMathEpsilon || other_segment.length() <= kMathEpsilon) {
return false;
}
const double cc1 = CrossProd(start_, end_, other_segment.start());
const double cc2 = CrossProd(start_, end_, other_segment.end());
if (cc1 * cc2 >= -kMathEpsilon) {
return false;
}
const double cc3 =
CrossProd(other_segment.start(), other_segment.end(), start_);
const double cc4 =
CrossProd(other_segment.start(), other_segment.end(), end_);
if (cc3 * cc4 >= -kMathEpsilon) {
return false;
}
const double ratio = cc4 / (cc4 - cc3);
*point = Vec2d(start_.x() * ratio + end_.x() * (1.0 - ratio),
start_.y() * ratio + end_.y() * (1.0 - ratio));
return true;
}
// return distance with perpendicular foot point.
double LineSegment2d::GetPerpendicularFoot(const Vec2d &point,
Vec2d *const foot_point) const {
CHECK_NOTNULL(foot_point);
if (length_ <= kMathEpsilon) {
*foot_point = start_;
return point.DistanceTo(start_);
}
const double x0 = point.x() - start_.x();
const double y0 = point.y() - start_.y();
const double proj = x0 * unit_direction_.x() + y0 * unit_direction_.y();
*foot_point = start_ + unit_direction_ * proj;
return std::abs(x0 * unit_direction_.y() - y0 * unit_direction_.x());
}
std::string LineSegment2d::DebugString() const {
return absl::StrCat("segment2d ( start = ", start_.DebugString(),
" end = ", end_.DebugString(), " )");
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/mpc_osqp_test.cc | /******************************************************************************
* Copyright 2019 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/mpc_osqp.h"
#include <chrono>
#include <ctime>
#include <limits>
#include <utility>
#include <vector>
#include "cyber/common/log.h"
#include "gtest/gtest.h"
namespace apollo {
namespace common {
namespace math {
TEST(MPCOSQPSolverTest, ComputationTimeTest) {
const int states = 4;
const int controls = 2;
const int horizon = 3;
const int max_iter = 100;
const double eps = 0.001;
const double max = std::numeric_limits<double>::max();
Eigen::MatrixXd A(states, states);
A << 5., 6., 7., 8., 7., 8., 7., 8., 9., 10., 7., 8., 11., 4., 7., 8.;
Eigen::MatrixXd B(states, controls);
B << 2., 3, 2., 7, 2, 9, 3, 8;
Eigen::MatrixXd Q(states, states);
Q << 10., 0, 0, 0, 0, 10., 0, 0, 0, 0, 10.0, 0, 0, 0, 0, 10.0;
Eigen::MatrixXd R(controls, controls);
R << 0.1, 0, 0, 0.1;
Eigen::MatrixXd lower_control_bound(controls, 1);
lower_control_bound << 9.6 - 10.5916, 9.6 - 10.5916;
Eigen::MatrixXd upper_control_bound(controls, 1);
upper_control_bound << 13 - 10.5916, 13 - 10.5916;
Eigen::MatrixXd lower_state_bound(states, 1);
lower_state_bound << -M_PI / 6, -M_PI / 6, -1 * max, -1 * max;
Eigen::MatrixXd upper_state_bound(states, 1);
upper_state_bound << M_PI / 6, M_PI / 6, max, max;
Eigen::MatrixXd initial_state(states, 1);
initial_state << 0, 0, 0, 0;
std::vector<double> control_cmd(controls, 0);
Eigen::MatrixXd reference_state(states, 1);
reference_state << 0, 0, 1, 0;
std::vector<Eigen::MatrixXd> reference(horizon, reference_state);
// OSQP
MpcOsqp mpc_osqp_solver(A, B, Q, R, initial_state, lower_control_bound,
upper_control_bound, lower_state_bound,
upper_state_bound, reference_state, max_iter, horizon,
eps);
auto start_time_osqp = std::chrono::system_clock::now();
mpc_osqp_solver.Solve(&control_cmd);
auto end_time_osqp = std::chrono::system_clock::now();
std::chrono::duration<double> diff_OSQP = end_time_osqp - start_time_osqp;
AINFO << "OSQP used time: " << diff_OSQP.count() * 1000 << " ms.";
}
TEST(MPCOSQPSolverTest, NonFullRankMatrix) {
const int states = 2;
const int controls = 1;
const int horizon = 10;
const int max_iter = 100;
const double eps = 0.01;
const double max = std::numeric_limits<double>::max();
Eigen::MatrixXd A(states, states);
A << 0, 1, 0, 0;
Eigen::MatrixXd B(states, controls);
B << -1, 1;
Eigen::MatrixXd Q(states, states);
Q << 100, 0, 0, 0;
Eigen::MatrixXd R(controls, controls);
R << 0;
Eigen::MatrixXd lower_bound(controls, 1);
lower_bound << -5;
Eigen::MatrixXd upper_bound(controls, 1);
upper_bound << 5;
Eigen::MatrixXd initial_state(states, 1);
initial_state << 0, 5;
Eigen::MatrixXd reference_state(states, 1);
reference_state << 0, 0;
Eigen::MatrixXd state_lower_bound(states, 1);
state_lower_bound << -max, -max;
Eigen::MatrixXd state_upper_bound(states, 1);
state_upper_bound << max, max;
std::vector<double> control_cmd(controls, 0);
MpcOsqp mpc_osqp_solver(A, B, Q, R, initial_state, lower_bound, upper_bound,
state_lower_bound, state_upper_bound, reference_state,
max_iter, horizon, eps);
mpc_osqp_solver.Solve(&control_cmd);
EXPECT_FLOAT_EQ(upper_bound(0), control_cmd[0]);
}
TEST(MPCOSQPSolverTest, NullMatrix) {
const int states = 2;
const int controls = 1;
const int horizon = 10;
const int max_iter = 100;
const double eps = 0.01;
Eigen::MatrixXd A(states, states);
A << 0, 0, 0, 0;
Eigen::MatrixXd B(states, controls);
B << 0, 3;
Eigen::MatrixXd Q(states, states);
Q << 0, 0, 0, 10;
Eigen::MatrixXd R(controls, controls);
R << 0.1;
Eigen::MatrixXd lower_bound(controls, 1);
lower_bound << -10;
Eigen::MatrixXd upper_bound(controls, 1);
upper_bound << 10;
Eigen::MatrixXd initial_state(states, 1);
initial_state << 0, 0;
Eigen::MatrixXd reference_state(states, 1);
reference_state << 0, 0;
Eigen::MatrixXd state_lower_bound(states, 1);
state_lower_bound << -5, -5;
Eigen::MatrixXd state_upper_bound(states, 1);
state_upper_bound << 5, 5;
std::vector<double> control_cmd(controls, 0);
MpcOsqp mpc_osqp_solver(A, B, Q, R, initial_state, lower_bound, upper_bound,
state_lower_bound, state_upper_bound, reference_state,
max_iter, horizon, eps);
mpc_osqp_solver.Solve(&control_cmd);
EXPECT_NEAR(0.0, control_cmd[0], 1e-7);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/matrix_operations_test.cc | /******************************************************************************
* Copyright 2018 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/matrix_operations.h"
#include "gtest/gtest.h"
namespace apollo {
namespace common {
namespace math {
TEST(PseudoInverseTest, PseudoInverseI) {
const Eigen::Matrix<float, 2, 2> A = Eigen::MatrixXf::Identity(2, 2);
const double epsilon = 1.0e-6;
Eigen::Matrix<float, 2, 2> B = PseudoInverse<float, 2>(A, epsilon);
EXPECT_EQ(B(0, 0), 1);
EXPECT_EQ(B(0, 1), 0);
EXPECT_EQ(B(1, 0), 0);
EXPECT_EQ(B(1, 1), 1);
const Eigen::Matrix<float, 2, 2> C = Eigen::MatrixXf::Zero(2, 2);
Eigen::Matrix<float, 2, 2> D = PseudoInverse<float, 2>(C, epsilon);
EXPECT_EQ(D(0, 0), 0);
EXPECT_EQ(D(0, 1), 0);
EXPECT_EQ(D(1, 0), 0);
EXPECT_EQ(D(1, 1), 0);
}
TEST(PseudoInverseTest, PseudoInverseII) {
const Eigen::Matrix<float, 5, 1> A = Eigen::MatrixXf::Ones(5, 1);
const double epsilon = 1.0e-6;
Eigen::Matrix<float, 1, 5> B = PseudoInverse<float, 5, 1>(A, epsilon);
EXPECT_EQ(B.cols(), 5);
EXPECT_EQ(B.rows(), 1);
EXPECT_FLOAT_EQ(B(0, 0), 0.2);
EXPECT_FLOAT_EQ(B(0, 1), 0.2);
EXPECT_FLOAT_EQ(B(0, 2), 0.2);
EXPECT_FLOAT_EQ(B(0, 3), 0.2);
EXPECT_FLOAT_EQ(B(0, 4), 0.2);
const Eigen::Matrix<float, 5, 1> C = Eigen::MatrixXf::Zero(5, 1);
Eigen::Matrix<float, 1, 5> D = PseudoInverse<float, 5, 1>(C, epsilon);
EXPECT_EQ(D.cols(), 5);
EXPECT_EQ(D.rows(), 1);
EXPECT_FLOAT_EQ(D(0, 0), 0);
EXPECT_FLOAT_EQ(D(0, 1), 0);
EXPECT_FLOAT_EQ(D(0, 2), 0);
EXPECT_FLOAT_EQ(D(0, 3), 0);
EXPECT_FLOAT_EQ(D(0, 4), 0);
}
TEST(ContinuousToDiscreteTest, c2d_fixed_size) {
double ts = 0.0;
Eigen::Matrix<float, 2, 2> m_a = Eigen::MatrixXf::Identity(2, 2);
Eigen::Matrix<float, 2, 1> m_b = Eigen::MatrixXf::Ones(2, 1);
Eigen::Matrix<float, 1, 2> m_c = Eigen::MatrixXf::Ones(1, 2);
Eigen::Matrix<float, 1, 1> m_d = Eigen::MatrixXf::Identity(1, 1);
Eigen::Matrix<float, 2, 2> prt_a_d;
Eigen::Matrix<float, 2, 1> prt_b_d;
Eigen::Matrix<float, 1, 2> prt_c_d;
Eigen::Matrix<float, 1, 1> prt_d_d;
bool res = ContinuousToDiscrete<float, 2, 1, 1>(
m_a, m_b, m_c, m_d, ts, &prt_a_d, &prt_b_d, &prt_c_d, &prt_d_d);
EXPECT_FALSE(res);
ts = 1;
res = ContinuousToDiscrete<float, 2, 1, 1>(m_a, m_b, m_c, m_d, ts, &prt_a_d,
&prt_b_d, &prt_c_d, &prt_d_d);
EXPECT_TRUE(res);
EXPECT_FLOAT_EQ(prt_a_d(0, 0), 3);
EXPECT_FLOAT_EQ(prt_a_d(0, 1), 0);
EXPECT_FLOAT_EQ(prt_a_d(1, 0), 0);
EXPECT_FLOAT_EQ(prt_a_d(1, 1), 3);
EXPECT_FLOAT_EQ(prt_b_d(0, 0), 2);
EXPECT_FLOAT_EQ(prt_b_d(1, 0), 2);
EXPECT_FLOAT_EQ(prt_c_d(0, 0), 2);
EXPECT_FLOAT_EQ(prt_c_d(0, 1), 2);
EXPECT_FLOAT_EQ(prt_d_d(0, 0), 3);
ts = 0.1;
res = ContinuousToDiscrete<float, 2, 1, 1>(m_a, m_b, m_c, m_d, ts, &prt_a_d,
&prt_b_d, &prt_c_d, &prt_d_d);
EXPECT_TRUE(res);
EXPECT_FLOAT_EQ(prt_a_d(0, 0), 1.1052631);
EXPECT_FLOAT_EQ(prt_a_d(0, 1), 0);
EXPECT_FLOAT_EQ(prt_a_d(1, 0), 0);
EXPECT_FLOAT_EQ(prt_a_d(1, 1), 1.1052631);
EXPECT_FLOAT_EQ(prt_b_d(0, 0), 0.33287135);
EXPECT_FLOAT_EQ(prt_b_d(1, 0), 0.33287135);
EXPECT_FLOAT_EQ(prt_c_d(0, 0), 0.33287135);
EXPECT_FLOAT_EQ(prt_c_d(0, 1), 0.33287135);
EXPECT_FLOAT_EQ(prt_d_d(0, 0), 2.0526316);
ts = 0.01;
res = ContinuousToDiscrete<float, 2, 1, 1>(m_a, m_b, m_c, m_d, ts, &prt_a_d,
&prt_b_d, &prt_c_d, &prt_d_d);
EXPECT_TRUE(res);
EXPECT_FLOAT_EQ(prt_a_d(0, 0), 1.0100503);
EXPECT_FLOAT_EQ(prt_a_d(0, 1), 0);
EXPECT_FLOAT_EQ(prt_a_d(1, 0), 0);
EXPECT_FLOAT_EQ(prt_a_d(1, 1), 1.0100503);
EXPECT_FLOAT_EQ(prt_b_d(0, 0), 0.10050251);
EXPECT_FLOAT_EQ(prt_b_d(1, 0), 0.10050251);
EXPECT_FLOAT_EQ(prt_c_d(0, 0), 0.10050251);
EXPECT_FLOAT_EQ(prt_c_d(0, 1), 0.10050251);
EXPECT_FLOAT_EQ(prt_d_d(0, 0), 2.0050251);
}
TEST(ContinuousToDiscreteTest, c2d_dynamic_size) {
double ts = 0.0;
Eigen::MatrixXd m_a = Eigen::MatrixXd::Identity(2, 2);
Eigen::MatrixXd m_b = Eigen::MatrixXd::Ones(2, 1);
Eigen::MatrixXd m_c = Eigen::MatrixXd::Ones(1, 2);
Eigen::MatrixXd m_d = Eigen::MatrixXd::Identity(1, 1);
Eigen::MatrixXd prt_a_d;
Eigen::MatrixXd prt_b_d;
Eigen::MatrixXd prt_c_d;
Eigen::MatrixXd prt_d_d;
bool res = ContinuousToDiscrete(m_a, m_b, m_c, m_d, ts, &prt_a_d, &prt_b_d,
&prt_c_d, &prt_d_d);
EXPECT_FALSE(res);
ts = 1;
res = ContinuousToDiscrete(m_a, m_b, m_c, m_d, ts, &prt_a_d, &prt_b_d,
&prt_c_d, &prt_d_d);
EXPECT_TRUE(res);
EXPECT_FLOAT_EQ(prt_a_d(0, 0), 3);
EXPECT_FLOAT_EQ(prt_a_d(0, 1), 0);
EXPECT_FLOAT_EQ(prt_a_d(1, 0), 0);
EXPECT_FLOAT_EQ(prt_a_d(1, 1), 3);
EXPECT_FLOAT_EQ(prt_b_d(0, 0), 2);
EXPECT_FLOAT_EQ(prt_b_d(1, 0), 2);
EXPECT_FLOAT_EQ(prt_c_d(0, 0), 2);
EXPECT_FLOAT_EQ(prt_c_d(0, 1), 2);
EXPECT_FLOAT_EQ(prt_d_d(0, 0), 3);
ts = 0.1;
res = ContinuousToDiscrete(m_a, m_b, m_c, m_d, ts, &prt_a_d, &prt_b_d,
&prt_c_d, &prt_d_d);
EXPECT_TRUE(res);
EXPECT_FLOAT_EQ(prt_a_d(0, 0), 1.1052631);
EXPECT_FLOAT_EQ(prt_a_d(0, 1), 0);
EXPECT_FLOAT_EQ(prt_a_d(1, 0), 0);
EXPECT_FLOAT_EQ(prt_a_d(1, 1), 1.1052631);
EXPECT_FLOAT_EQ(prt_b_d(0, 0), 0.33287135);
EXPECT_FLOAT_EQ(prt_b_d(1, 0), 0.33287135);
EXPECT_FLOAT_EQ(prt_c_d(0, 0), 0.33287135);
EXPECT_FLOAT_EQ(prt_c_d(0, 1), 0.33287135);
EXPECT_FLOAT_EQ(prt_d_d(0, 0), 2.0526316);
ts = 0.01;
res = ContinuousToDiscrete(m_a, m_b, m_c, m_d, ts, &prt_a_d, &prt_b_d,
&prt_c_d, &prt_d_d);
EXPECT_TRUE(res);
EXPECT_FLOAT_EQ(prt_a_d(0, 0), 1.0100503);
EXPECT_FLOAT_EQ(prt_a_d(0, 1), 0);
EXPECT_FLOAT_EQ(prt_a_d(1, 0), 0);
EXPECT_FLOAT_EQ(prt_a_d(1, 1), 1.0100503);
EXPECT_FLOAT_EQ(prt_b_d(0, 0), 0.10050251);
EXPECT_FLOAT_EQ(prt_b_d(1, 0), 0.10050251);
EXPECT_FLOAT_EQ(prt_c_d(0, 0), 0.10050251);
EXPECT_FLOAT_EQ(prt_c_d(0, 1), 0.10050251);
EXPECT_FLOAT_EQ(prt_d_d(0, 0), 2.0050251);
}
TEST(DENSE_TO_CSC_MATRIX, dense_to_csc_matrix_test) {
{
std::vector<double> data;
std::vector<int> indices;
std::vector<int> indptr;
Eigen::MatrixXd dense_matrix(3, 3);
dense_matrix << 1.2, 0, 2.2, 0, 0, 3.1, 4.8, 5.4, 6.01;
DenseToCSCMatrix(dense_matrix, &data, &indices, &indptr);
std::vector<double> data_golden = {1.2, 4.8, 5.4, 2.2, 3.1, 6.01};
std::vector<int> indices_golden = {0, 2, 2, 0, 1, 2};
std::vector<int> indptr_golden = {0, 2, 3, 6};
EXPECT_EQ(data.size(), data_golden.size());
EXPECT_EQ(indices.size(), indices_golden.size());
EXPECT_EQ(indptr.size(), indptr_golden.size());
for (size_t i = 0; i < data.size(); ++i) {
EXPECT_DOUBLE_EQ(data[i], data_golden[i]);
}
for (size_t i = 0; i < indices.size(); ++i) {
EXPECT_EQ(indices[i], indices_golden[i]);
}
for (size_t i = 0; i < indptr.size(); ++i) {
EXPECT_EQ(indptr[i], indptr_golden[i]);
}
}
{
std::vector<double> data;
std::vector<int> indices;
std::vector<int> indptr;
Eigen::MatrixXd dense_matrix(2, 2);
dense_matrix << 4.0, 1.0, 1.0, 2.0;
DenseToCSCMatrix(dense_matrix, &data, &indices, &indptr);
std::vector<double> data_golden = {4.0, 1.0, 1.0, 2.0};
std::vector<int> indices_golden = {0, 1, 0, 1};
std::vector<int> indptr_golden = {0, 2, 4};
EXPECT_EQ(data.size(), data_golden.size());
EXPECT_EQ(indices.size(), indices_golden.size());
EXPECT_EQ(indptr.size(), indptr_golden.size());
for (size_t i = 0; i < data.size(); ++i) {
EXPECT_DOUBLE_EQ(data[i], data_golden[i]);
}
for (size_t i = 0; i < indices.size(); ++i) {
EXPECT_EQ(indices[i], indices_golden[i]);
}
for (size_t i = 0; i < indptr.size(); ++i) {
EXPECT_EQ(indptr[i], indptr_golden[i]);
}
}
{
std::vector<double> data;
std::vector<int> indices;
std::vector<int> indptr;
Eigen::MatrixXd dense_matrix(4, 6);
dense_matrix << 11, 0, 0, 14, 0, 16, 0, 22, 0, 0, 25, 26, 0, 0, 33, 34, 0,
36, 41, 0, 43, 44, 0, 46;
DenseToCSCMatrix(dense_matrix, &data, &indices, &indptr);
std::vector<double> data_golden = {11.0, 41.0, 22.0, 33.0, 43.0, 14.0, 34.0,
44.0, 25.0, 16.0, 26.0, 36.0, 46.0};
std::vector<int> indices_golden = {0, 3, 1, 2, 3, 0, 2, 3, 1, 0, 1, 2, 3};
std::vector<int> indptr_golden = {0, 2, 3, 5, 8, 9, 13};
EXPECT_EQ(data.size(), data_golden.size());
EXPECT_EQ(indices.size(), indices_golden.size());
EXPECT_EQ(indptr.size(), indptr_golden.size());
for (size_t i = 0; i < data.size(); ++i) {
EXPECT_DOUBLE_EQ(data[i], data_golden[i]);
}
for (size_t i = 0; i < indices.size(); ++i) {
EXPECT_EQ(indices[i], indices_golden[i]);
}
for (size_t i = 0; i < indptr.size(); ++i) {
EXPECT_EQ(indptr[i], indptr_golden[i]) << "i = " << i;
}
}
}
TEST(DENSE_TO_CSC_MATRIX, patterned_dense_to_csc_matrix_test) {
int N = 5;
Eigen::MatrixXd dense_matrix = Eigen::MatrixXd::Zero(N * 3, N * 3);
for (int i = 0; i < N; ++i) {
dense_matrix(i, i) = 1.0;
if (i + 1 < N) {
dense_matrix(i, i + 1) = 1.0;
}
if (i > 0) {
dense_matrix(i, i - 1) = 1.0;
}
}
for (int i = 0; i < N; ++i) {
dense_matrix(i + N, i + N) = 1.0;
}
for (int i = 0; i < N; ++i) {
dense_matrix(i + 2 * N, i + 2 * N) = 1.0;
if (i + 1 < N) {
dense_matrix(i + 2 * N, i + 2 * N + 1) = 1.0;
}
if (i > 0) {
dense_matrix(i + 2 * N, i + 2 * N - 1) = 1.0;
}
}
for (int i = 0; i < dense_matrix.rows(); ++i) {
for (int j = 0; j < dense_matrix.cols(); ++j) {
std::cout << dense_matrix(i, j) << ", ";
}
std::cout << std::endl;
}
std::cout << std::endl;
std::vector<double> data;
std::vector<int> indices;
std::vector<int> indptr;
DenseToCSCMatrix(dense_matrix, &data, &indices, &indptr);
EXPECT_EQ(data.size(), indices.size());
for (const auto ind : indices) {
std::cout << ind << ", ";
}
std::cout << std::endl;
for (const auto ipr : indptr) {
std::cout << ipr << ", ";
}
std::cout << std::endl;
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/aabox2d_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/aabox2d.h"
#include <string>
#include "gtest/gtest.h"
namespace apollo {
namespace common {
namespace math {
TEST(AABox2dTest, GetAllCorners) {
AABox2d box1({0, 0}, 4, 2);
std::vector<Vec2d> corners1;
box1.GetAllCorners(&corners1);
EXPECT_NEAR(corners1[0].x(), 2.0, 1e-5);
EXPECT_NEAR(corners1[0].y(), -1.0, 1e-5);
EXPECT_NEAR(corners1[1].x(), 2.0, 1e-5);
EXPECT_NEAR(corners1[1].y(), 1.0, 1e-5);
EXPECT_NEAR(corners1[2].x(), -2.0, 1e-5);
EXPECT_NEAR(corners1[2].y(), 1.0, 1e-5);
EXPECT_NEAR(corners1[3].x(), -2.0, 1e-5);
EXPECT_NEAR(corners1[3].y(), -1.0, 1e-5);
EXPECT_EQ(
box1.DebugString(),
"aabox2d ( center = vec2d ( x = 0 y = 0 ) length = 4 width = 2 )");
std::vector<Vec2d> corners2;
AABox2d box2({3, 1}, {7, 3});
box2.GetAllCorners(&corners2);
EXPECT_NEAR(corners2[0].x(), 7.0, 1e-5);
EXPECT_NEAR(corners2[0].y(), 1.0, 1e-5);
EXPECT_NEAR(corners2[1].x(), 7.0, 1e-5);
EXPECT_NEAR(corners2[1].y(), 3.0, 1e-5);
EXPECT_NEAR(corners2[2].x(), 3.0, 1e-5);
EXPECT_NEAR(corners2[2].y(), 3.0, 1e-5);
EXPECT_NEAR(corners2[3].x(), 3.0, 1e-5);
EXPECT_NEAR(corners2[3].y(), 1.0, 1e-5);
EXPECT_EQ(
box2.DebugString(),
"aabox2d ( center = vec2d ( x = 5 y = 2 ) length = 4 width = 2 )");
}
TEST(AABox2dTest, CenterAndLengths) {
AABox2d box1({0, 0}, 10, 10);
EXPECT_NEAR(box1.center_x(), 0.0, 1e-5);
EXPECT_NEAR(box1.center_y(), 0.0, 1e-5);
EXPECT_NEAR(box1.length(), 10.0, 1e-5);
EXPECT_NEAR(box1.width(), 10.0, 1e-5);
EXPECT_NEAR(box1.half_length(), 5.0, 1e-5);
EXPECT_NEAR(box1.half_width(), 5.0, 1e-5);
AABox2d box2({{0, 2}, {0, -6}, {3, 0}, {1, 0}});
EXPECT_NEAR(box2.center_x(), 1.5, 1e-5);
EXPECT_NEAR(box2.center_y(), -2.0, 1e-5);
EXPECT_NEAR(box2.length(), 3.0, 1e-5);
EXPECT_NEAR(box2.width(), 8.0, 1e-5);
EXPECT_NEAR(box2.half_length(), 1.5, 1e-5);
EXPECT_NEAR(box2.half_width(), 4.0, 1e-5);
}
TEST(AABox2dTest, HasOverlap) {
AABox2d box1({0, 0}, 4, 2);
AABox2d box2({3, 1}, {7, 3});
AABox2d box3({0, 0}, 10, 10);
EXPECT_FALSE(box1.HasOverlap(box2));
EXPECT_TRUE(box1.HasOverlap(box3));
EXPECT_TRUE(box2.HasOverlap(box3));
}
TEST(AABox2dTest, DistanceTo) {
AABox2d box({0, 0}, 4, 2);
EXPECT_NEAR(box.DistanceTo({3, 0}), 1.0, 1e-5);
EXPECT_NEAR(box.DistanceTo({-3, 0}), 1.0, 1e-5);
EXPECT_NEAR(box.DistanceTo({0, 2}), 1.0, 1e-5);
EXPECT_NEAR(box.DistanceTo({0, -2}), 1.0, 1e-5);
EXPECT_NEAR(box.DistanceTo({0, 0}), 0.0, 1e-5);
EXPECT_NEAR(box.DistanceTo({0, 1}), 0.0, 1e-5);
EXPECT_NEAR(box.DistanceTo({1, 0}), 0.0, 1e-5);
EXPECT_NEAR(box.DistanceTo({0, -1}), 0.0, 1e-5);
EXPECT_NEAR(box.DistanceTo({-1, 0}), 0.0, 1e-5);
}
TEST(AABox2dTest, IsPointIn) {
AABox2d box({0, 0}, 4, 2);
EXPECT_TRUE(box.IsPointIn({0, 0}));
EXPECT_TRUE(box.IsPointIn({1, 0.5}));
EXPECT_TRUE(box.IsPointIn({-0.5, -1}));
EXPECT_TRUE(box.IsPointIn({2, 1}));
EXPECT_FALSE(box.IsPointIn({-3, 0}));
EXPECT_FALSE(box.IsPointIn({0, 2}));
EXPECT_FALSE(box.IsPointIn({-4, -2}));
}
TEST(AABox2dTest, IsPointOnBoundary) {
AABox2d box({0, 0}, 4, 2);
EXPECT_FALSE(box.IsPointOnBoundary({0, 0}));
EXPECT_FALSE(box.IsPointOnBoundary({1, 0.5}));
EXPECT_TRUE(box.IsPointOnBoundary({-0.5, -1}));
EXPECT_TRUE(box.IsPointOnBoundary({2, 0.5}));
EXPECT_TRUE(box.IsPointOnBoundary({-2, 1}));
EXPECT_FALSE(box.IsPointOnBoundary({-3, 0}));
EXPECT_FALSE(box.IsPointOnBoundary({0, 2}));
EXPECT_FALSE(box.IsPointOnBoundary({-4, -2}));
}
TEST(AABox2dTest, MinMax) {
AABox2d box1({0, 0}, 4, 2);
EXPECT_NEAR(box1.min_x(), -2, 1e-5);
EXPECT_NEAR(box1.max_x(), 2, 1e-5);
EXPECT_NEAR(box1.min_y(), -1, 1e-5);
EXPECT_NEAR(box1.max_y(), 1, 1e-5);
AABox2d box2({3, 1}, {7, 3});
EXPECT_NEAR(box2.min_x(), 3, 1e-5);
EXPECT_NEAR(box2.max_x(), 7, 1e-5);
EXPECT_NEAR(box2.min_y(), 1, 1e-5);
EXPECT_NEAR(box2.max_y(), 3, 1e-5);
}
TEST(AABox2dTest, Shift) {
AABox2d box({0, 0}, 4, 2);
box.Shift({30, 40});
std::vector<Vec2d> corners;
box.GetAllCorners(&corners);
EXPECT_NEAR(corners[0].x(), 32.0, 1e-5);
EXPECT_NEAR(corners[0].y(), 39.0, 1e-5);
EXPECT_NEAR(corners[1].x(), 32.0, 1e-5);
EXPECT_NEAR(corners[1].y(), 41.0, 1e-5);
EXPECT_NEAR(corners[2].x(), 28.0, 1e-5);
EXPECT_NEAR(corners[2].y(), 41.0, 1e-5);
EXPECT_NEAR(corners[3].x(), 28.0, 1e-5);
EXPECT_NEAR(corners[3].y(), 39.0, 1e-5);
}
TEST(AABox2dTest, MergeFrom) {
AABox2d box({3, 1}, {7, 3});
box.MergeFrom(AABox2d({5, -1}, {10, 7}));
EXPECT_NEAR(box.center_x(), 6.5, 1e-5);
EXPECT_NEAR(box.center_y(), 3, 1e-5);
EXPECT_NEAR(box.length(), 7, 1e-5);
EXPECT_NEAR(box.width(), 8, 1e-5);
EXPECT_NEAR(box.half_length(), 3.5, 1e-5);
EXPECT_NEAR(box.half_width(), 4, 1e-5);
box.MergeFrom({6, 6});
EXPECT_NEAR(box.center_x(), 6.5, 1e-5);
EXPECT_NEAR(box.center_y(), 3, 1e-5);
EXPECT_NEAR(box.length(), 7, 1e-5);
EXPECT_NEAR(box.width(), 8, 1e-5);
EXPECT_NEAR(box.half_length(), 3.5, 1e-5);
EXPECT_NEAR(box.half_width(), 4, 1e-5);
box.MergeFrom({-5, 20});
EXPECT_NEAR(box.center_x(), 2.5, 1e-5);
EXPECT_NEAR(box.center_y(), 9.5, 1e-5);
EXPECT_NEAR(box.length(), 15, 1e-5);
EXPECT_NEAR(box.width(), 21, 1e-5);
EXPECT_NEAR(box.half_length(), 7.5, 1e-5);
EXPECT_NEAR(box.half_width(), 10.5, 1e-5);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/path_matcher.h | /******************************************************************************
* Copyright 2018 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
**/
#pragma once
#include <utility>
#include <vector>
#include "modules/common_msgs/basic_msgs/pnc_point.pb.h"
namespace apollo {
namespace common {
namespace math {
class PathMatcher {
public:
PathMatcher() = delete;
static PathPoint MatchToPath(const std::vector<PathPoint>& reference_line,
const double x, const double y);
static std::pair<double, double> GetPathFrenetCoordinate(
const std::vector<PathPoint>& reference_line, const double x,
const double y);
static PathPoint MatchToPath(const std::vector<PathPoint>& reference_line,
const double s);
private:
static PathPoint FindProjectionPoint(const PathPoint& p0, const PathPoint& p1,
const double x, const double y);
};
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/linear_quadratic_regulator.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include <limits>
#include "Eigen/Dense"
#include "cyber/common/log.h"
#include "modules/common/math/linear_quadratic_regulator.h"
namespace apollo {
namespace common {
namespace math {
using Matrix = Eigen::MatrixXd;
// solver with cross term
void SolveLQRProblem(const Matrix &A, const Matrix &B, const Matrix &Q,
const Matrix &R, const Matrix &M, const double tolerance,
const uint max_num_iteration, Matrix *ptr_K) {
if (A.rows() != A.cols() || B.rows() != A.rows() || Q.rows() != Q.cols() ||
Q.rows() != A.rows() || R.rows() != R.cols() || R.rows() != B.cols() ||
M.rows() != Q.rows() || M.cols() != R.cols()) {
AERROR << "LQR solver: one or more matrices have incompatible dimensions.";
return;
}
Matrix AT = A.transpose();
Matrix BT = B.transpose();
Matrix MT = M.transpose();
// Solves a discrete-time Algebraic Riccati equation (DARE)
// Calculate Matrix Difference Riccati Equation, initialize P and Q
Matrix P = Q;
uint num_iteration = 0;
double diff = std::numeric_limits<double>::max();
while (num_iteration++ < max_num_iteration && diff > tolerance) {
Matrix P_next =
AT * P * A -
(AT * P * B + M) * (R + BT * P * B).inverse() * (BT * P * A + MT) + Q;
// check the difference between P and P_next
diff = fabs((P_next - P).maxCoeff());
P = P_next;
}
if (num_iteration >= max_num_iteration) {
ADEBUG << "LQR solver cannot converge to a solution, "
"last consecutive result diff is: "
<< diff;
} else {
ADEBUG << "LQR solver converged at iteration: " << num_iteration
<< ", max consecutive result diff.: " << diff;
}
*ptr_K = (R + BT * P * B).inverse() * (BT * P * A + MT);
}
void SolveLQRProblem(const Matrix &A, const Matrix &B, const Matrix &Q,
const Matrix &R, const double tolerance,
const uint max_num_iteration, Matrix *ptr_K) {
// create M as zero matrix of the right size:
// M.rows() == Q.rows() && M.cols() == R.cols()
Matrix M = Matrix::Zero(Q.rows(), R.cols());
SolveLQRProblem(A, B, Q, R, M, tolerance, max_num_iteration, ptr_K);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/angle_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/angle.h"
#include <cmath>
#include "gtest/gtest.h"
#include "modules/common/math/sin_table.h"
namespace apollo {
namespace common {
namespace math {
TEST(Angle, SIN_TABLE) {
EXPECT_FLOAT_EQ(0.0f, SIN_TABLE[0]);
EXPECT_FLOAT_EQ(1.0f, SIN_TABLE[16384]);
}
TEST(Angle, Angle8) {
auto a = Angle8::from_deg(90.0);
EXPECT_DOUBLE_EQ(90.0, a.to_deg());
EXPECT_DOUBLE_EQ(M_PI_2, a.to_rad());
EXPECT_FLOAT_EQ(1.0f, sin(a));
EXPECT_FLOAT_EQ(0.0f, cos(a));
}
TEST(Angle, Angle16) {
auto a = Angle16(1);
EXPECT_DOUBLE_EQ(180.0 / 32768, a.to_deg());
a = Angle16::from_deg(-150.0 - 360.0);
EXPECT_NEAR(-0.5f, sin(a), 1e-4);
EXPECT_NEAR(-0.5 * sqrt(3), cos(a), 1e-4);
}
TEST(Angle, Angle32) {
auto a = Angle32::from_rad(1.0);
EXPECT_NEAR(180 / M_PI, a.to_deg(), 1e-7);
EXPECT_NEAR(1.0, a.to_rad(), 1e-9);
}
TEST(Angle, operators) {
auto a = Angle16::from_deg(100.0);
auto b = a;
a += b;
a *= 0.5;
a = 7 * (a + b * 0.7);
a /= 1.1;
EXPECT_DOUBLE_EQ(-63.65478515625, a.to_deg());
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/linear_interpolation.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/linear_interpolation.h"
#include <cmath>
#include "cyber/common/log.h"
#include "modules/common/math/math_utils.h"
namespace apollo {
namespace common {
namespace math {
double slerp(const double a0, const double t0, const double a1, const double t1,
const double t) {
if (std::abs(t1 - t0) <= kMathEpsilon) {
ADEBUG << "input time difference is too small";
return NormalizeAngle(a0);
}
const double a0_n = NormalizeAngle(a0);
const double a1_n = NormalizeAngle(a1);
double d = a1_n - a0_n;
if (d > M_PI) {
d = d - 2 * M_PI;
} else if (d < -M_PI) {
d = d + 2 * M_PI;
}
const double r = (t - t0) / (t1 - t0);
const double a = a0_n + d * r;
return NormalizeAngle(a);
}
SLPoint InterpolateUsingLinearApproximation(const SLPoint &p0,
const SLPoint &p1, const double w) {
CHECK_GE(w, 0.0);
SLPoint p;
p.set_s((1 - w) * p0.s() + w * p1.s());
p.set_l((1 - w) * p0.l() + w * p1.l());
return p;
}
PathPoint InterpolateUsingLinearApproximation(const PathPoint &p0,
const PathPoint &p1,
const double s) {
double s0 = p0.s();
double s1 = p1.s();
PathPoint path_point;
double weight = (s - s0) / (s1 - s0);
double x = (1 - weight) * p0.x() + weight * p1.x();
double y = (1 - weight) * p0.y() + weight * p1.y();
double theta = slerp(p0.theta(), p0.s(), p1.theta(), p1.s(), s);
double kappa = (1 - weight) * p0.kappa() + weight * p1.kappa();
double dkappa = (1 - weight) * p0.dkappa() + weight * p1.dkappa();
double ddkappa = (1 - weight) * p0.ddkappa() + weight * p1.ddkappa();
path_point.set_x(x);
path_point.set_y(y);
path_point.set_theta(theta);
path_point.set_kappa(kappa);
path_point.set_dkappa(dkappa);
path_point.set_ddkappa(ddkappa);
path_point.set_s(s);
return path_point;
}
TrajectoryPoint InterpolateUsingLinearApproximation(const TrajectoryPoint &tp0,
const TrajectoryPoint &tp1,
const double t) {
if (!tp0.has_path_point() || !tp1.has_path_point()) {
TrajectoryPoint p;
p.mutable_path_point()->CopyFrom(PathPoint());
return p;
}
const PathPoint pp0 = tp0.path_point();
const PathPoint pp1 = tp1.path_point();
double t0 = tp0.relative_time();
double t1 = tp1.relative_time();
TrajectoryPoint tp;
tp.set_v(lerp(tp0.v(), t0, tp1.v(), t1, t));
tp.set_a(lerp(tp0.a(), t0, tp1.a(), t1, t));
tp.set_relative_time(t);
tp.set_steer(slerp(tp0.steer(), t0, tp1.steer(), t1, t));
PathPoint *path_point = tp.mutable_path_point();
path_point->set_x(lerp(pp0.x(), t0, pp1.x(), t1, t));
path_point->set_y(lerp(pp0.y(), t0, pp1.y(), t1, t));
path_point->set_theta(slerp(pp0.theta(), t0, pp1.theta(), t1, t));
path_point->set_kappa(lerp(pp0.kappa(), t0, pp1.kappa(), t1, t));
path_point->set_dkappa(lerp(pp0.dkappa(), t0, pp1.dkappa(), t1, t));
path_point->set_ddkappa(lerp(pp0.ddkappa(), t0, pp1.ddkappa(), t1, t));
path_point->set_s(lerp(pp0.s(), t0, pp1.s(), t1, t));
return tp;
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/matrix_operations.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Defines some useful matrix operations.
*/
#pragma once
#include <cmath>
#include <utility>
#include <vector>
#include "Eigen/Dense"
#include "Eigen/SVD"
#include "cyber/common/log.h"
/**
* @namespace apollo::common::math
* @brief The math namespace deals with a number of useful mathematical objects.
*/
namespace apollo {
namespace common {
namespace math {
/**
* @brief Computes the Moore-Penrose pseudo-inverse of a given square matrix,
* rounding all eigenvalues with absolute value bounded by epsilon to zero.
*
* @param m The square matrix to be pseudo-inverted
* @param epsilon A small positive real number (optional; default is 1.0e-6).
*
* @return Moore-Penrose pseudo-inverse of the given matrix.
*/
template <typename T, unsigned int N>
Eigen::Matrix<T, N, N> PseudoInverse(const Eigen::Matrix<T, N, N> &m,
const double epsilon = 1.0e-6) {
Eigen::JacobiSVD<Eigen::Matrix<T, N, N>> svd(
m, Eigen::ComputeFullU | Eigen::ComputeFullV);
return static_cast<Eigen::Matrix<T, N, N>>(
svd.matrixV() *
(svd.singularValues().array().abs() > epsilon)
.select(svd.singularValues().array().inverse(), 0)
.matrix()
.asDiagonal() *
svd.matrixU().adjoint());
}
/**
* @brief Computes the Moore-Penrose pseudo-inverse of a given matrix,
* rounding all eigenvalues with absolute value bounded by epsilon to zero.
*
* @param m The matrix to be pseudo-inverted
* @param epsilon A small positive real number (optional; default is 1.0e-6).
*
* @return Moore-Penrose pseudo-inverse of the given matrix.
*/
template <typename T, unsigned int M, unsigned int N>
Eigen::Matrix<T, N, M> PseudoInverse(const Eigen::Matrix<T, M, N> &m,
const double epsilon = 1.0e-6) {
Eigen::Matrix<T, M, M> t = m * m.transpose();
return static_cast<Eigen::Matrix<T, N, M>>(m.transpose() *
PseudoInverse<T, M>(t));
}
/**
* @brief Computes bilinear transformation of the continuous to discrete form
for state space representation
* This assumes equation format of
*
* dot_x = Ax + Bu
* y = Cx + Du
*
*
*
* @param m_a, m_b, m_c, m_d are the state space matrix control matrix
*
* @return true or false.
*/
template <typename T, unsigned int L, unsigned int N, unsigned int O>
bool ContinuousToDiscrete(const Eigen::Matrix<T, L, L> &m_a,
const Eigen::Matrix<T, L, N> &m_b,
const Eigen::Matrix<T, O, L> &m_c,
const Eigen::Matrix<T, O, N> &m_d, const double ts,
Eigen::Matrix<T, L, L> *ptr_a_d,
Eigen::Matrix<T, L, N> *ptr_b_d,
Eigen::Matrix<T, O, L> *ptr_c_d,
Eigen::Matrix<T, O, N> *ptr_d_d) {
if (ts <= 0.0) {
AERROR << "ContinuousToDiscrete : ts is less than or equal to zero";
return false;
}
// Only matrix_a is mandatory to be non-zeros in matrix
// conversion.
if (m_a.rows() == 0) {
AERROR << "ContinuousToDiscrete: matrix_a size 0 ";
return false;
}
Eigen::Matrix<T, L, L> m_identity = Eigen::Matrix<T, L, L>::Identity();
*ptr_a_d = PseudoInverse<T, L>(m_identity - ts * 0.5 * m_a) *
(m_identity + ts * 0.5 * m_a);
*ptr_b_d =
std::sqrt(ts) * PseudoInverse<T, L>(m_identity - ts * 0.5 * m_a) * m_b;
*ptr_c_d =
std::sqrt(ts) * m_c * PseudoInverse<T, L>(m_identity - ts * 0.5 * m_a);
*ptr_d_d =
0.5 * m_c * PseudoInverse<T, L>(m_identity - ts * 0.5 * m_a) * m_b + m_d;
return true;
}
bool ContinuousToDiscrete(const Eigen::MatrixXd &m_a,
const Eigen::MatrixXd &m_b,
const Eigen::MatrixXd &m_c,
const Eigen::MatrixXd &m_d, const double ts,
Eigen::MatrixXd *ptr_a_d, Eigen::MatrixXd *ptr_b_d,
Eigen::MatrixXd *ptr_c_d, Eigen::MatrixXd *ptr_d_d);
template <typename T, int M, int N, typename D>
void DenseToCSCMatrix(const Eigen::Matrix<T, M, N> &dense_matrix,
std::vector<T> *data, std::vector<D> *indices,
std::vector<D> *indptr) {
static constexpr double epsilon = 1e-9;
int data_count = 0;
for (int c = 0; c < dense_matrix.cols(); ++c) {
indptr->emplace_back(data_count);
for (int r = 0; r < dense_matrix.rows(); ++r) {
if (std::fabs(dense_matrix(r, c)) < epsilon) {
continue;
}
data->emplace_back(dense_matrix(r, c));
++data_count;
indices->emplace_back(r);
}
}
indptr->emplace_back(data_count);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/math_utils_test.cc | /******************************************************************************
* Copyright 2018 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/math_utils.h"
#include "gtest/gtest.h"
#include "osqp/osqp.h"
namespace apollo {
namespace common {
namespace math {
TEST(MathUtilsTest, CrossProd) {
EXPECT_NEAR(CrossProd({0, 0}, {0, 1}, {1, 0}), -1.0, 1e-5);
EXPECT_NEAR(CrossProd({0, 0}, {1, 0}, {0, 1}), 1.0, 1e-5);
EXPECT_NEAR(CrossProd({0, 1}, {0, 0}, {1, 0}), 1.0, 1e-5);
EXPECT_NEAR(CrossProd({1, 2}, {3, 4}, {5, 6}), 0.0, 1e-5);
EXPECT_NEAR(CrossProd({1, 2}, {3, 4}, {6, 5}), -4.0, 1e-5);
EXPECT_NEAR(CrossProd({2, 2}, {7, 5}, {3, 4}), 7.0, 1e-5);
}
TEST(MathUtilsTest, InnerProd) {
EXPECT_NEAR(InnerProd({0, 0}, {0, 1}, {1, 0}), 0.0, 1e-5);
EXPECT_NEAR(InnerProd({0, 0}, {1, 0}, {0, 1}), 0.0, 1e-5);
EXPECT_NEAR(InnerProd({0, 1}, {0, 0}, {1, 0}), 1.0, 1e-5);
EXPECT_NEAR(InnerProd({1, 2}, {3, 4}, {5, 6}), 16.0, 1e-5);
EXPECT_NEAR(InnerProd({1, 2}, {3, 4}, {6, 5}), 16.0, 1e-5);
EXPECT_NEAR(InnerProd({2, 2}, {7, 5}, {3, 4}), 11.0, 1e-5);
EXPECT_NEAR(InnerProd({2, 2}, {0, 0}, {3, 4}), -6.0, 1e-5);
}
TEST(MathUtilsTest, WrapAngle) {
EXPECT_NEAR(WrapAngle(-1.2), -1.2 + M_PI * 2.0, 1e-6);
EXPECT_NEAR(WrapAngle(3.4), 3.4, 1e-6);
EXPECT_NEAR(WrapAngle(5.6), 5.6, 1e-6);
EXPECT_NEAR(WrapAngle(7.8), 7.8 - M_PI * 2.0, 1e-6);
EXPECT_NEAR(WrapAngle(12.4), std::fmod(12.4, M_PI * 2.0), 1e-6);
EXPECT_NEAR(WrapAngle(-12.4), std::fmod(-12.4, M_PI * 2.0) + M_PI * 2.0,
1e-6);
}
TEST(MathUtilsTest, NormalizeAngle) {
EXPECT_DOUBLE_EQ(1.5, NormalizeAngle(1.5));
EXPECT_DOUBLE_EQ(1.5 - M_PI, NormalizeAngle(1.5 + M_PI));
EXPECT_DOUBLE_EQ(1.5, NormalizeAngle(1.5 + M_PI * 2));
EXPECT_DOUBLE_EQ(1.5, NormalizeAngle(1.5 - M_PI * 2));
EXPECT_DOUBLE_EQ(-1.5, NormalizeAngle(-1.5));
EXPECT_DOUBLE_EQ(-9.0 + M_PI * 2, NormalizeAngle(-9.0));
EXPECT_DOUBLE_EQ(-M_PI, NormalizeAngle(-M_PI));
EXPECT_DOUBLE_EQ(-M_PI, NormalizeAngle(M_PI));
EXPECT_DOUBLE_EQ(-M_PI, NormalizeAngle(-M_PI * 3));
EXPECT_DOUBLE_EQ(-M_PI, NormalizeAngle(M_PI * 3));
EXPECT_DOUBLE_EQ(0.0, NormalizeAngle(M_PI * 4));
}
TEST(MathUtilsTest, Square) {
EXPECT_DOUBLE_EQ(121.0, Square(11.0));
EXPECT_FLOAT_EQ(144.0f, Square(-12.0f));
EXPECT_EQ(169, Square(-13));
EXPECT_EQ(2147395600, Square(46340));
EXPECT_EQ(-2147479015, Square(46341)); // Overflow!
}
TEST(MathUtilsTest, Sqr) {
EXPECT_DOUBLE_EQ(121.0, Sqr(11.0));
EXPECT_DOUBLE_EQ(0.25, Sqr(0.5));
EXPECT_DOUBLE_EQ(169.0, Sqr(-13.0));
}
TEST(MathUtilsTest, Sigmoid) { EXPECT_DOUBLE_EQ(0.5, Sigmoid(0.0)); }
TEST(MathUtilsTest, Clamp) {
EXPECT_EQ(1, Clamp(1, 0, 6));
EXPECT_EQ(6, Clamp(7, 0, 6));
EXPECT_EQ(0, Clamp(-1, 0, 6));
EXPECT_EQ(0, Clamp(0, 0, 6)); // test lower bound as input
EXPECT_EQ(6, Clamp(6, 0, 6)); // test upper bound as input
}
TEST(MathUtilsTest, RotateVector2d) {
double expected_x = 0.0;
double expected_y = std::sqrt(2.0);
Eigen::Vector2d result = RotateVector2d({1.0, 1.0}, M_PI / 4);
auto tol = 1.0e-10;
EXPECT_NEAR(expected_x, result.x(), tol);
EXPECT_NEAR(expected_y, result.y(), tol);
expected_x = -1.0;
expected_y = 0.0;
result = RotateVector2d({0.0, 1.0}, M_PI / 2);
EXPECT_NEAR(expected_x, result.x(), tol);
EXPECT_NEAR(expected_y, result.y(), tol);
expected_x = -1.0;
expected_y = 0.0;
result = RotateVector2d({1.0, 0.0}, M_PI);
EXPECT_NEAR(expected_x, result.x(), tol);
EXPECT_NEAR(expected_y, result.y(), tol);
}
TEST(MathUtilsTest, AlmostEqualTest) {
double x = 2.0;
double x_root = std::sqrt(x);
double y = Square(x_root);
EXPECT_TRUE(almost_equal(x, y, 2));
EXPECT_FALSE(almost_equal(y, 2.0001, 2));
}
TEST(MathUtilsTest, QPSTTest) {
// Load problem data
c_float P_x[4] = {
4.00000000000000000000,
1.00000000000000000000,
1.00000000000000000000,
2.00000000000000000000,
};
c_int P_nnz = 4;
c_int P_i[4] = {
0,
1,
0,
1,
};
c_int P_p[3] = {
0,
2,
4,
};
c_float q[2] = {
1.00000000000000000000,
1.00000000000000000000,
};
c_float A_x[4] = {
1.00000000000000000000,
1.00000000000000000000,
1.00000000000000000000,
1.00000000000000000000,
};
c_int A_nnz = 4;
c_int A_i[4] = {
0,
1,
0,
2,
};
c_int A_p[3] = {
0,
2,
4,
};
c_float l[3] = {
1.00000000000000000000,
0.00000000000000000000,
0.00000000000000000000,
};
c_float u[3] = {
1.00000000000000000000,
0.69999999999999995559,
0.69999999999999995559,
};
c_int n = 2;
c_int m = 3;
// Problem settings
OSQPSettings *settings =
reinterpret_cast<OSQPSettings *>(c_malloc(sizeof(OSQPSettings)));
// Structures
OSQPWorkspace *work = NULL; // Workspace
OSQPData *data; // OSQPData
// Populate data
data = reinterpret_cast<OSQPData *>(c_malloc(sizeof(OSQPData)));
data->n = n;
data->m = m;
data->P = csc_matrix(data->n, data->n, P_nnz, P_x, P_i, P_p);
data->q = q;
data->A = csc_matrix(data->m, data->n, A_nnz, A_x, A_i, A_p);
data->l = l;
data->u = u;
// Define Solver settings as default
osqp_set_default_settings(settings);
// Setup workspace
work = osqp_setup(data, settings);
// osqp_setup(&work, data, settings);
// Solve Problem
osqp_solve(work);
// Clean workspace
osqp_cleanup(work);
c_free(data->A);
c_free(data->P);
c_free(data);
c_free(settings);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/linear_interpolation.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Linear interpolation functions.
*/
#pragma once
#include <cmath>
#include "cyber/common/log.h"
#include "modules/common_msgs/basic_msgs/pnc_point.pb.h"
/**
* @namespace apollo::common::math
* @brief apollo::common::math
*/
namespace apollo {
namespace common {
namespace math {
/**
* @brief Linear interpolation between two points of type T.
* @param x0 The coordinate of the first point.
* @param t0 The interpolation parameter of the first point.
* @param x1 The coordinate of the second point.
* @param t1 The interpolation parameter of the second point.
* @param t The interpolation parameter for interpolation.
* @param x The coordinate of the interpolated point.
* @return Interpolated point.
*/
template <typename T>
T lerp(const T &x0, const double t0, const T &x1, const double t1,
const double t) {
if (std::abs(t1 - t0) <= 1.0e-6) {
AERROR << "input time difference is too small";
return x0;
}
const double r = (t - t0) / (t1 - t0);
const T x = x0 + r * (x1 - x0);
return x;
}
/**
* @brief Spherical linear interpolation between two angles.
* The two angles are within range [-M_PI, M_PI).
* @param a0 The value of the first angle.
* @param t0 The interpolation parameter of the first angle.
* @param a1 The value of the second angle.
* @param t1 The interpolation parameter of the second angle.
* @param t The interpolation parameter for interpolation.
* @param a The value of the spherically interpolated angle.
* @return Interpolated angle.
*/
double slerp(const double a0, const double t0, const double a1, const double t1,
const double t);
SLPoint InterpolateUsingLinearApproximation(const SLPoint &p0,
const SLPoint &p1, const double w);
PathPoint InterpolateUsingLinearApproximation(const PathPoint &p0,
const PathPoint &p1,
const double s);
TrajectoryPoint InterpolateUsingLinearApproximation(const TrajectoryPoint &tp0,
const TrajectoryPoint &tp1,
const double t);
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/hermite_spline.h | /******************************************************************************
* Copyright 2018 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
**/
#pragma once
#include <array>
#include <utility>
#include "cyber/common/log.h"
namespace apollo {
namespace common {
namespace math {
// Hermite spline implementation that works for 1d and 2d space interpolation.
// Valid input type T: double, Eigen::Vector2d
template <typename T, std::size_t N>
class HermiteSpline {
public:
HermiteSpline(std::array<T, (N + 1) / 2> x0, std::array<T, (N + 1) / 2> x1,
const double z0 = 0.0, const double z1 = 1.0);
virtual ~HermiteSpline() = default;
virtual T Evaluate(const std::uint32_t order, const double z) const;
private:
std::array<T, (N + 1) / 2> x0_;
std::array<T, (N + 1) / 2> x1_;
double z0_ = 0.0;
double delta_z_ = 0.0;
};
template <typename T, std::size_t N>
inline HermiteSpline<T, N>::HermiteSpline(std::array<T, (N + 1) / 2> x0,
std::array<T, (N + 1) / 2> x1,
const double z0, const double z1)
: x0_(std::move(x0)), x1_(std::move(x1)), z0_(z0), delta_z_(z1 - z0) {
ACHECK(N == 3 || N == 5)
<< "Error: currently we only support cubic and quintic hermite splines!";
}
template <typename T, std::size_t N>
inline T HermiteSpline<T, N>::Evaluate(const std::uint32_t order,
const double z) const {
CHECK_LE(z0_, z);
CHECK_LE(z, z0_ + delta_z_);
// if N == 3, cubic hermite spline, N == 5, quintic hermite spline
if (N == 3) {
const T& p0 = x0_[0];
const T& v0 = x0_[1];
const T& p1 = x1_[0];
const T& v1 = x1_[1];
switch (order) {
case 0: {
const double t = (z - z0_) / delta_z_;
const double t2 = t * t;
const double t3 = t2 * t;
return (2.0 * t3 - 3.0 * t2 + 1.0) * p0 + (t3 - 2 * t2 + t) * v0 +
(-2.0 * t3 + 3.0 * t2) * p1 + (t3 - t2) * v1;
}
case 1: {
const double t = (z - z0_) / delta_z_;
const double t2 = t * t;
return (6.0 * t2 - 6.0 * t) * p0 + (3.0 * t2 - 4 * t + 1.0) * v0 +
(-6.0 * t2 + 6.0 * t) * p1 + (3.0 * t2 - 2.0 * t) * v1;
}
case 2: {
const double t = (z - z0_) / delta_z_;
return (12.0 * t - 6.0) * p0 + (6.0 * t - 4.0) * v0 +
(-12.0 * t + 6.0) * p1 + (6.0 * t - 2.0) * v1;
}
case 3: {
return 12.0 * p0 + 6.0 * v0 - 12.0 * p1 + 6.0 * v1;
}
default: { break; }
}
} else {
CHECK_EQ(5, N);
const T& p0 = x0_[0];
const T& v0 = x0_[1];
const T& a0 = x0_[2];
const T& p1 = x1_[0];
const T& v1 = x1_[1];
const T& a1 = x1_[2];
switch (order) {
case 0: {
const double t = (z - z0_) / delta_z_;
const double t2 = t * t;
const double t3 = t * t2;
const double t4 = t2 * t2;
const double t5 = t2 * t3;
const double det0 = t3 - t4;
const double det1 = t4 - t5;
const double h0 = 1.0 - 10.0 * t3 + 15.0 * t4 - 6.0 * t5;
const double h1 = t - 6.0 * t3 + 8.0 * t4 - 3.0 * t5;
const double h2 = 0.5 * (t2 - t5) - 1.5 * det0;
const double h3 = 10.0 * t3 - 15.0 * t4 + 6.0 * t5;
const double h4 = -4.0 * det0 + 3.0 * det1;
const double h5 = 0.5 * (det0 - det1);
return h0 * p0 + h1 * v0 + h2 * a0 + h3 * p1 + h4 * v1 + h5 * a1;
}
case 1: {
const double t = (z - z0_) / delta_z_;
const double t2 = t * t;
const double t3 = t * t2;
const double t4 = t2 * t2;
const double det0 = t2 - t3;
const double det1 = t3 - t4;
const double dh0 = -30.0 * det0 + 30.0 * det1;
const double dh1 = 1 - 18.0 * t2 + 32.0 * t3 - 15.0 * t4;
const double dh2 = t - 4.5 * t2 + 6.0 * t3 - 2.5 * t4;
const double dh3 = 30.0 * det0 - 30.0 * det1;
const double dh4 = -12.0 * t2 + 28.0 * t3 - 15.0 * t4;
const double dh5 = 1.5 * det0 - 2.5 * det1;
return dh0 * p0 + dh1 * v0 + dh2 * a0 + dh3 * p1 + dh4 * v1 + dh5 * a1;
}
case 2: {
const double t = (z - z0_) / delta_z_;
const double t2 = t * t;
const double t3 = t * t2;
const double det0 = t - t2;
const double det1 = t2 - t3;
const double ddh0 = -60.0 * det0 + 120.0 * det1;
const double ddh1 = -36.0 * det0 + 60.0 * det1;
const double ddh2 = 1.0 - 9.0 * t + 18.0 * t2 - 10.0 * t3;
const double ddh3 = 60.0 * det0 - 120.0 * det1;
const double ddh4 = -24.0 * det0 + 60.0 * det1;
const double ddh5 = 3.0 * t - 12.0 * t2 + 10.0 * t3;
return ddh0 * p0 + ddh1 * v0 + ddh2 * a0 + ddh3 * p1 + ddh4 * v1 +
ddh5 * a1;
}
case 3: {
const double t = (z - z0_) / delta_z_;
const double t2 = t * t;
const double det = t - t2;
const double dddh0 = -60.0 + 360.0 * det;
const double dddh1 = -36.0 + 192.0 * t - 180.0 * t2;
const double dddh2 = -9.0 + 36.0 * t - 30.0 * t2;
const double dddh3 = 60.0 - 360.0 * det;
const double dddh4 = -24.0 + 168.0 * t - 180.0 * t2;
const double dddh5 = 3.0 - 24.0 * t + 30.0 * t2;
return dddh0 * p0 + dddh1 * v0 + dddh2 * a0 + dddh3 * p1 + dddh4 * v1 +
dddh5 * a1;
}
case 4: {
const double t = (z - z0_) / delta_z_;
const double d4h0 = 360.0 - 720.0 * t;
const double d4h1 = 192.0 - 360.0 * t;
const double d4h2 = 36.0 - 60.0 * t;
const double d4h3 = -360.0 + 720.0 * t;
const double d4h4 = 168.0 - 360.0 * t;
const double d4h5 = -24.0 + 60.0 * t;
return d4h0 * p0 + d4h1 * v0 + d4h2 * a0 + d4h3 * p1 + d4h4 * v1 +
d4h5 * a1;
}
case 5: {
const double d5h0 = -720.0;
const double d5h1 = -360.0;
const double d5h2 = -60.0;
const double d5h3 = 720.0;
const double d5h4 = -360.0;
const double d5h5 = 60.0;
return d5h0 * p0 + d5h1 * v0 + d5h2 * a0 + d5h3 * p1 + d5h4 * v1 +
d5h5 * a1;
}
default: { break; }
}
}
return T();
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/integral_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/integral.h"
#include <cmath>
#include "gtest/gtest.h"
namespace apollo {
namespace common {
namespace math {
namespace {
double LinearFunc(double x) { return 2.0 * x; }
double SquareFunc(double x) { return x * x; }
double CubicFunc(double x) { return x * x * x; }
double SinFunc(double x) { return std::sin(x); }
} // namespace
TEST(IntegralTest, Integration) {
double linear_integral = IntegrateByGaussLegendre<5>(LinearFunc, 0.0, 1.0);
EXPECT_NEAR(linear_integral, 1.0, 1e-5);
double square_integral = IntegrateByGaussLegendre<5>(SquareFunc, 0.0, 1.0);
EXPECT_NEAR(square_integral, 1.0 / 3.0, 1e-5);
double cubic_integral = IntegrateByGaussLegendre<5>(CubicFunc, 0.0, 1.0);
EXPECT_NEAR(cubic_integral, 1.0 / 4.0, 1e-5);
double sin_integral = IntegrateByGaussLegendre<5>(SinFunc, 0.0, 0.5 * M_PI);
EXPECT_NEAR(sin_integral, 1.0, 1e-5);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/polygon2d_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/polygon2d.h"
#include <algorithm>
#include <string>
#include "gtest/gtest.h"
#include "modules/common/math/box2d.h"
#include "modules/common/math/line_segment2d.h"
#include "modules/common/math/math_utils.h"
namespace apollo {
namespace common {
namespace math {
namespace {
bool ProjectByXSlow(const std::vector<Vec2d> &points, double x,
double *const min_y, double *const max_y) {
*min_y = std::numeric_limits<double>::infinity();
*max_y = -std::numeric_limits<double>::infinity();
for (const Vec2d &p1 : points) {
if (p1.x() < x) {
for (const Vec2d &p2 : points) {
if (p2.x() > x) {
const double y = ((p2.x() - x) * p1.y() + (x - p1.x()) * p2.y()) /
(p2.x() - p1.x());
*min_y = std::min(*min_y, y);
*max_y = std::max(*max_y, y);
}
}
}
}
return *min_y <= *max_y;
}
} // namespace
TEST(Polygon2dTest, polygon_IsPointIn) {
const Polygon2d poly1(Box2d::CreateAABox({0, 0}, {1, 1}));
EXPECT_EQ(poly1.DebugString(),
"polygon2d ( num_points = 4 points = (vec2d ( x = 1 y = 0 ) "
"vec2d ( x = 1 y = 1 ) vec2d ( x = 0 y = 1 ) vec2d ( x = 0 y = "
"0 ) ) convex area = 1 )");
EXPECT_TRUE(poly1.IsPointIn({0.5, 0.5}));
EXPECT_TRUE(poly1.IsPointIn({0.2, 0.2}));
EXPECT_TRUE(poly1.IsPointIn({0.2, 0.8}));
EXPECT_TRUE(poly1.IsPointIn({0.8, 0.2}));
EXPECT_TRUE(poly1.IsPointIn({0.8, 0.8}));
EXPECT_TRUE(poly1.IsPointOnBoundary({0.0, 0.0}));
EXPECT_TRUE(poly1.IsPointIn({0.0, 0.0}));
EXPECT_TRUE(poly1.IsPointOnBoundary({0.0, 0.5}));
EXPECT_TRUE(poly1.IsPointIn({0.0, 0.5}));
EXPECT_TRUE(poly1.IsPointOnBoundary({1.0, 0.5}));
EXPECT_TRUE(poly1.IsPointIn({1.0, 0.5}));
EXPECT_FALSE(poly1.IsPointIn({-0.2, 0.5}));
EXPECT_FALSE(poly1.IsPointIn({1.2, 0.5}));
EXPECT_FALSE(poly1.IsPointIn({0.5, -0.2}));
EXPECT_FALSE(poly1.IsPointIn({0.5, 1.2}));
EXPECT_FALSE(poly1.IsPointIn({0, -0.1}));
EXPECT_FALSE(poly1.IsPointIn({-0.1, 0}));
EXPECT_FALSE(poly1.IsPointIn({1.0, -0.1}));
EXPECT_FALSE(poly1.IsPointIn({-0.1, 1.0}));
EXPECT_FALSE(poly1.IsPointIn({0, 1.1}));
EXPECT_FALSE(poly1.IsPointIn({1.1, 0}));
EXPECT_FALSE(poly1.IsPointIn({1.0, 1.1}));
EXPECT_FALSE(poly1.IsPointIn({1.1, 1.0}));
const Polygon2d poly2({{0, 1}, {1, 0}, {0, -1}, {-1, 0}});
EXPECT_TRUE(poly2.IsPointIn({0, 0}));
EXPECT_TRUE(poly2.IsPointIn({0, 0.9}));
EXPECT_TRUE(poly2.IsPointIn({0.9, 0}));
EXPECT_TRUE(poly2.IsPointIn({0, -0.9}));
EXPECT_TRUE(poly2.IsPointIn({-0.9, 0}));
EXPECT_FALSE(poly2.IsPointIn({0, 1.1}));
EXPECT_FALSE(poly2.IsPointIn({1.1, 0}));
EXPECT_FALSE(poly2.IsPointIn({0, -1.1}));
EXPECT_FALSE(poly2.IsPointIn({-1.1, 0}));
const Polygon2d poly3({{4, 4}, {5, 6}, {6, 6}});
EXPECT_FALSE(poly3.IsPointIn({5, 4.5}));
EXPECT_FALSE(poly3.IsPointOnBoundary({5, 4.5}));
EXPECT_TRUE(poly3.IsPointIn({5, 5}));
EXPECT_TRUE(poly3.IsPointOnBoundary({5, 5}));
EXPECT_TRUE(poly3.IsPointIn({5, 5.5}));
EXPECT_FALSE(poly3.IsPointOnBoundary({5, 5.5}));
EXPECT_TRUE(poly3.IsPointIn({5, 6}));
EXPECT_TRUE(poly3.IsPointOnBoundary({5, 6}));
EXPECT_FALSE(poly3.IsPointIn({5, 6.5}));
EXPECT_FALSE(poly3.IsPointOnBoundary({5, 6.5}));
// Concave polygons.
const Polygon2d poly4({{0, 0}, {2, 0}, {2, 2}, {1, 1}, {0, 2}});
EXPECT_TRUE(poly4.IsPointIn({0.5, 1.5}));
EXPECT_TRUE(poly4.IsPointOnBoundary({0.5, 1.5}));
EXPECT_FALSE(poly4.IsPointIn({1.0, 1.5}));
EXPECT_TRUE(poly4.IsPointIn({1.5, 1.5}));
EXPECT_TRUE(poly4.IsPointOnBoundary({1.5, 1.5}));
const Polygon2d poly5(
{{0, 0}, {4, 0}, {4, 2}, {3, 2}, {2, 1}, {1, 2}, {0, 2}});
EXPECT_FALSE(poly5.IsPointIn({-0.5, 2.0}));
EXPECT_TRUE(poly5.IsPointIn({0.5, 2.0}));
EXPECT_FALSE(poly5.IsPointIn({1.5, 2.0}));
EXPECT_FALSE(poly5.IsPointIn({2.0, 2.0}));
EXPECT_FALSE(poly5.IsPointIn({2.5, 2.0}));
EXPECT_TRUE(poly5.IsPointIn({3.5, 2.0}));
EXPECT_FALSE(poly5.IsPointIn({4.5, 2.0}));
}
TEST(Polygon2dTest, DistanceToPoint) {
const Box2d box1(Box2d::CreateAABox({0, 0}, {1, 1}));
const Polygon2d poly1(box1);
EXPECT_NEAR(poly1.DistanceTo({0.5, 0.5}), 0.0, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({-0.2, 0.5}), 0.2, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({1.2, 0.5}), 0.2, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({0.5, -0.2}), 0.2, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({0.5, 1.2}), 0.2, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({0, -0.1}), 0.1, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({-0.1, 0}), 0.1, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({1.0, -0.1}), 0.1, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({-0.1, 1.0}), 0.1, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({0, 1.1}), 0.1, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({1.1, 0}), 0.1, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({1.0, 1.1}), 0.1, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({1.1, 1.0}), 0.1, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({-0.1, -0.1}), 0.1 * sqrt(2.0), 1e-5);
EXPECT_NEAR(poly1.DistanceTo({-0.1, 1.1}), 0.1 * sqrt(2.0), 1e-5);
EXPECT_NEAR(poly1.DistanceTo({1.1, -0.1}), 0.1 * sqrt(2.0), 1e-5);
EXPECT_NEAR(poly1.DistanceTo({1.1, 1.1}), 0.1 * sqrt(2.0), 1e-5);
for (int iter = 0; iter < 10000; ++iter) {
const double x = RandomDouble(-10, 10);
const double y = RandomDouble(-10, 10);
EXPECT_NEAR(poly1.DistanceTo({x, y}), box1.DistanceTo({x, y}), 1e-5);
}
for (int iter = 0; iter < 100; ++iter) {
const double center_x = RandomDouble(-10, 10);
const double center_y = RandomDouble(-10, 10);
const double heading = RandomDouble(0, M_PI * 2.0);
const double length = RandomDouble(1, 5);
const double width = RandomDouble(1, 5);
const Box2d box({center_x, center_y}, heading, length, width);
const Polygon2d polygon(box);
for (int iter2 = 0; iter2 < 100; ++iter2) {
const double x = RandomDouble(-20, 20);
const double y = RandomDouble(-20, 20);
EXPECT_NEAR(polygon.DistanceTo({x, y}), box.DistanceTo({x, y}), 1e-5);
}
}
const Polygon2d poly2({{0, 1}, {1, 0}, {0, -1}, {-1, 0}});
EXPECT_NEAR(poly2.DistanceTo({0, 0}), 0.0, 1e-5);
EXPECT_NEAR(poly2.DistanceTo({0, 1.1}), 0.1, 1e-5);
EXPECT_NEAR(poly2.DistanceTo({1.1, 0}), 0.1, 1e-5);
EXPECT_NEAR(poly2.DistanceTo({0, -1.1}), 0.1, 1e-5);
EXPECT_NEAR(poly2.DistanceTo({-1.1, 0}), 0.1, 1e-5);
EXPECT_NEAR(poly2.DistanceTo({0.5, 0.5}), 0.0, 1e-5);
EXPECT_NEAR(poly2.DistanceTo({0.6, 0.6}), 0.1 * sqrt(2.0), 1e-5);
const Polygon2d poly3(
{{0, 0}, {4, 0}, {4, 2}, {3, 2}, {2, 1}, {1, 2}, {0, 2}});
EXPECT_NEAR(poly3.DistanceTo({-0.5, 2.0}), 0.5, 1e-5);
EXPECT_NEAR(poly3.DistanceTo({0.5, 2.0}), 0.0, 1e-5);
EXPECT_NEAR(poly3.DistanceTo({1.5, 2.0}), 0.5 / sqrt(2.0), 1e-5);
EXPECT_NEAR(poly3.DistanceTo({2.0, 2.0}), 1.0 / sqrt(2.0), 1e-5);
EXPECT_NEAR(poly3.DistanceTo({2.5, 2.0}), 0.5 / sqrt(2.0), 1e-5);
EXPECT_NEAR(poly3.DistanceTo({3.5, 2.0}), 0.0, 1e-5);
EXPECT_NEAR(poly3.DistanceTo({4.5, 2.0}), 0.5, 1e-5);
EXPECT_NEAR(poly3.DistanceTo({-0.5, 1.0}), 0.5, 1e-5);
EXPECT_NEAR(poly3.DistanceTo({2.0, 1.0}), 0.0, 1e-5);
EXPECT_NEAR(poly3.DistanceTo({4.5, 1.0}), 0.5, 1e-5);
}
TEST(Polygon2dTest, DistanceToLineSegment) {
const Polygon2d poly1(Box2d::CreateAABox({0, 0}, {1, 1}));
EXPECT_NEAR(poly1.DistanceTo({{0.5, 0.5}, {1.0, 1.0}}), 0.0, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({{-0.2, 0.5}, {1.2, 0.5}}), 0.0, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({{-2.0, -2.0}, {2.0, 2.0}}), 0.0, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({{-0.2, 0.5}, {-0.2, 0.8}}), 0.2, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({{1.2, 0.5}, {1.2, 0.3}}), 0.2, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({{0.5, -0.2}, {0.8, -0.2}}), 0.2, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({{0.5, 1.2}, {0.3, 1.2}}), 0.2, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({{-0.3, 0.5}, {-0.2, 0.8}}), 0.2, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({{1.2, 0.5}, {1.3, 0.3}}), 0.2, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({{0.5, -0.3}, {0.8, -0.2}}), 0.2, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({{0.5, 1.2}, {0.3, 1.3}}), 0.2, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({{0, -0.1}, {-0.1, 0}}), 0.1 / sqrt(2.0), 1e-5);
EXPECT_NEAR(poly1.DistanceTo({{1.0, 1.1}, {1.1, 1.0}}), 0.1 / sqrt(2.0),
1e-5);
EXPECT_NEAR(poly1.DistanceTo({{-10.0, 0.5}, {2.0, 0.5}}), 0.0, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({{-1.0, 0.5}, {10.0, 0.5}}), 0.0, 1e-5);
EXPECT_NEAR(poly1.DistanceTo({{-1.0, 2.0}, {-1.0, 2.0}}), sqrt(2.0), 1e-5);
EXPECT_NEAR(poly1.DistanceTo({{0.5, 0.5}, {0.5, 0.5}}), 0.0, 1e-5);
const Polygon2d poly2({{0, 1}, {1, 0}, {0, -1}, {-1, 0}});
EXPECT_NEAR(poly2.DistanceTo({{-2, 0}, {2, 0}}), 0.0, 1e-5);
EXPECT_NEAR(poly2.DistanceTo({{0, -2}, {0, 2}}), 0.0, 1e-5);
EXPECT_NEAR(poly2.DistanceTo({{0, 1.1}, {1.1, 0}}), 0.1 / sqrt(2.0), 1e-5);
EXPECT_NEAR(poly2.DistanceTo({{0, 1.1}, {-1.1, 0}}), 0.1 / sqrt(2.0), 1e-5);
EXPECT_NEAR(poly2.DistanceTo({{0, -1.1}, {1.1, 0}}), 0.1 / sqrt(2.0), 1e-5);
EXPECT_NEAR(poly2.DistanceTo({{0, -1.1}, {-1.1, 0}}), 0.1 / sqrt(2.0), 1e-5);
EXPECT_NEAR(poly2.DistanceTo({{0.6, 0.6}, {0.7, 0.7}}), 0.1 * sqrt(2.0),
1e-5);
EXPECT_NEAR(poly2.DistanceTo({{-0.6, -0.6}, {-0.7, -0.7}}), 0.1 * sqrt(2.0),
1e-5);
EXPECT_NEAR(poly2.DistanceTo({{-0.6, -0.6}, {0.7, 0.7}}), 0.0, 1e-5);
const Polygon2d poly3({{0, 0}, {2, 0}, {2, 2}, {1, 1}, {0, 2}});
EXPECT_NEAR(poly3.DistanceTo({{-2, 0}, {2, 0}}), 0.0, 1e-5);
EXPECT_NEAR(poly3.DistanceTo({{0.7, 2.0}, {1.2, 2.0}}), 0.7 / sqrt(2.0),
1e-5);
EXPECT_NEAR(poly3.DistanceTo({{0.7, 2.0}, {1.4, 2.0}}), 0.6 / sqrt(2.0),
1e-5);
EXPECT_NEAR(poly3.DistanceTo({{0.7, 1.5}, {1.6, 1.5}}), 0.0, 1e-5);
}
TEST(Polygon2dTest, DistanceToPolygon) {
const Polygon2d poly1(Box2d::CreateAABox({0, 0}, {1, 1}));
const Polygon2d poly2({{0, 1}, {1, 0}, {0, -1}, {-1, 0}});
const Polygon2d poly3(Box2d::CreateAABox({2, 2}, {3, 3}));
const Polygon2d poly4(Box2d::CreateAABox({-10, -10}, {10, 10}));
EXPECT_NEAR(poly1.DistanceTo(poly2), 0.0, 1e-5);
EXPECT_NEAR(poly1.DistanceTo(poly3), sqrt(2.0), 1e-5);
EXPECT_NEAR(poly2.DistanceTo(poly3), 1.5 * sqrt(2.0), 1e-5);
EXPECT_NEAR(poly4.DistanceTo(poly1), 0.0, 1e-5);
EXPECT_NEAR(poly4.DistanceTo(poly2), 0.0, 1e-5);
EXPECT_NEAR(poly4.DistanceTo(poly3), 0.0, 1e-5);
}
TEST(Polygon2dTest, ContainPolygon) {
const Polygon2d poly1(Box2d::CreateAABox({0, 0}, {3, 3}));
const Polygon2d poly2(Box2d::CreateAABox({1, 1}, {2, 2}));
const Polygon2d poly3(Box2d::CreateAABox({1.5, 1.5}, {4, 4}));
const Polygon2d poly4(Box2d::CreateAABox({-10, -10}, {10, 10}));
EXPECT_TRUE(poly1.Contains(poly2));
EXPECT_FALSE(poly2.Contains(poly1));
EXPECT_FALSE(poly1.Contains(poly3));
EXPECT_FALSE(poly2.Contains(poly3));
EXPECT_FALSE(poly3.Contains(poly1));
EXPECT_FALSE(poly3.Contains(poly2));
EXPECT_TRUE(poly4.Contains(poly1));
EXPECT_TRUE(poly4.Contains(poly2));
EXPECT_TRUE(poly4.Contains(poly3));
const Polygon2d poly5(
{{0, 0}, {4, 0}, {4, 2}, {3, 2}, {2, 1}, {1, 2}, {0, 2}});
const Polygon2d poly6({{0, 1}, {4, 1}, {4, 2}, {0, 2}});
const Polygon2d poly7({{0, 1}, {1, 1}, {1, 2}, {0, 2}});
const Polygon2d poly8({{3, 1}, {4, 1}, {4, 2}, {3, 2}});
const Polygon2d poly9({{0, 0}, {4, 0}, {4, 1}, {0, 1}});
EXPECT_FALSE(poly5.Contains(poly6));
EXPECT_TRUE(poly5.Contains(poly7));
EXPECT_TRUE(poly5.Contains(poly8));
EXPECT_TRUE(poly5.Contains(poly9));
}
TEST(Polygon2dTest, ConvexHull) {
Polygon2d polygon;
EXPECT_FALSE(Polygon2d::ComputeConvexHull({}, &polygon));
EXPECT_FALSE(Polygon2d::ComputeConvexHull({{1, 2}}, &polygon));
EXPECT_FALSE(Polygon2d::ComputeConvexHull({{3, 4}, {5, 6}}, &polygon));
EXPECT_FALSE(
Polygon2d::ComputeConvexHull({{3, 4}, {3, 4}, {5, 6}, {5, 6}}, &polygon));
EXPECT_TRUE(Polygon2d::ComputeConvexHull({{0, 0}, {0, 4}, {3, 0}}, &polygon));
EXPECT_TRUE(polygon.is_convex());
EXPECT_NEAR(6.0, polygon.area(), 1e-5);
EXPECT_TRUE(
Polygon2d::ComputeConvexHull({{0, 0}, {0, 4}, {3, 0}, {3, 4}}, &polygon));
EXPECT_TRUE(polygon.is_convex());
EXPECT_NEAR(12.0, polygon.area(), 1e-5);
EXPECT_TRUE(Polygon2d::ComputeConvexHull(
{{0, 0}, {2, 2}, {1, 1}, {0, 4}, {3, 0}, {3, 4}}, &polygon));
EXPECT_TRUE(polygon.is_convex());
EXPECT_NEAR(12.0, polygon.area(), 1e-5);
EXPECT_TRUE(Polygon2d::ComputeConvexHull(
{{0, 0}, {0, 4}, {0, 1}, {0, 3}, {0, 2}, {1, 0}, {3, 0}, {2, 0}},
&polygon));
EXPECT_TRUE(polygon.is_convex());
EXPECT_NEAR(6.0, polygon.area(), 1e-5);
for (int iter = 0; iter < 10000; ++iter) {
const int kRange = 10;
const int n = RandomInt(3, 10);
std::vector<Vec2d> points;
for (int i = 0; i < n; ++i) {
points.emplace_back(RandomInt(0, kRange), RandomInt(0, kRange));
}
double area = 0;
for (int x0 = 0; x0 < kRange; ++x0) {
double min_y = 0.0;
double max_y = 0.0;
if (ProjectByXSlow(points, x0 + 0.5, &min_y, &max_y)) {
area += max_y - min_y;
}
}
Polygon2d polygon;
if (area < 1e-3) {
EXPECT_FALSE(Polygon2d::ComputeConvexHull(points, &polygon));
} else {
EXPECT_TRUE(Polygon2d::ComputeConvexHull(points, &polygon));
EXPECT_NEAR(area, polygon.area(), 1e-5);
}
}
}
TEST(Polygon2dTest, Overlap) {
const Polygon2d poly1(Box2d::CreateAABox({0, 0}, {2, 2}));
const Polygon2d poly2(Box2d::CreateAABox({1, 1}, {3, 3}));
const Polygon2d poly3(Box2d::CreateAABox({2, 0}, {4, 2}));
const Polygon2d poly4(Box2d({2, 2}, M_PI_4, sqrt(2.0), sqrt(2.0)));
Polygon2d overlap_polygon;
EXPECT_TRUE(poly1.ComputeOverlap(poly2, &overlap_polygon));
EXPECT_NEAR(overlap_polygon.area(), 1.0, 1e-5);
EXPECT_TRUE(poly2.ComputeOverlap(poly1, &overlap_polygon));
EXPECT_NEAR(overlap_polygon.area(), 1.0, 1e-5);
EXPECT_TRUE(poly2.ComputeOverlap(poly3, &overlap_polygon));
EXPECT_NEAR(overlap_polygon.area(), 1.0, 1e-5);
EXPECT_TRUE(poly3.ComputeOverlap(poly2, &overlap_polygon));
EXPECT_NEAR(overlap_polygon.area(), 1.0, 1e-5);
EXPECT_FALSE(poly1.ComputeOverlap(poly3, &overlap_polygon));
EXPECT_FALSE(poly3.ComputeOverlap(poly1, &overlap_polygon));
EXPECT_TRUE(poly1.ComputeOverlap(poly4, &overlap_polygon));
EXPECT_NEAR(overlap_polygon.area(), 0.5, 1e-5);
EXPECT_TRUE(poly4.ComputeOverlap(poly1, &overlap_polygon));
EXPECT_NEAR(overlap_polygon.area(), 0.5, 1e-5);
EXPECT_TRUE(poly2.ComputeOverlap(poly4, &overlap_polygon));
EXPECT_NEAR(overlap_polygon.area(), 2.0, 1e-5);
EXPECT_TRUE(poly4.ComputeOverlap(poly2, &overlap_polygon));
EXPECT_NEAR(overlap_polygon.area(), 2.0, 1e-5);
EXPECT_TRUE(poly3.ComputeOverlap(poly4, &overlap_polygon));
EXPECT_NEAR(overlap_polygon.area(), 0.5, 1e-5);
EXPECT_TRUE(poly4.ComputeOverlap(poly3, &overlap_polygon));
EXPECT_NEAR(overlap_polygon.area(), 0.5, 1e-5);
EXPECT_NEAR(poly1.ComputeIoU(poly2), 0.1428, 1e-4);
EXPECT_NEAR(poly2.ComputeIoU(poly1), 0.1428, 1e-4);
EXPECT_NEAR(poly1.ComputeIoU(poly3), 0.0, 1e-4);
EXPECT_NEAR(poly3.ComputeIoU(poly1), 0.0, 1e-4);
EXPECT_NEAR(poly1.ComputeIoU(poly4), 0.0909, 1e-4);
EXPECT_NEAR(poly4.ComputeIoU(poly1), 0.0909, 1e-4);
EXPECT_NEAR(poly2.ComputeIoU(poly3), 0.1428, 1e-4);
EXPECT_NEAR(poly3.ComputeIoU(poly2), 0.1428, 1e-4);
EXPECT_NEAR(poly2.ComputeIoU(poly4), 0.5, 1e-4);
EXPECT_NEAR(poly4.ComputeIoU(poly2), 0.5, 1e-4);
EXPECT_NEAR(poly3.ComputeIoU(poly4), 0.0909, 1e-4);
EXPECT_NEAR(poly4.ComputeIoU(poly3), 0.0909, 1e-4);
Vec2d first_intersect;
Vec2d last_intersect;
EXPECT_FALSE(poly1.GetOverlap(LineSegment2d({-1, 0}, {-1, 2}),
&first_intersect, &last_intersect));
EXPECT_FALSE(poly1.GetOverlap(LineSegment2d({-1, 1}, {-3, 1}),
&first_intersect, &last_intersect));
EXPECT_FALSE(poly1.GetOverlap(LineSegment2d({1, 3}, {1, 5}), &first_intersect,
&last_intersect));
EXPECT_TRUE(poly1.GetOverlap(LineSegment2d({1, -1}, {1, 3}), &first_intersect,
&last_intersect));
EXPECT_NEAR(1.0, first_intersect.x(), 1e-5);
EXPECT_NEAR(0.0, first_intersect.y(), 1e-5);
EXPECT_NEAR(1.0, last_intersect.x(), 1e-5);
EXPECT_NEAR(2.0, last_intersect.y(), 1e-5);
EXPECT_TRUE(poly1.GetOverlap(LineSegment2d({1, 1}, {1, 3}), &first_intersect,
&last_intersect));
EXPECT_NEAR(1.0, first_intersect.x(), 1e-5);
EXPECT_NEAR(1.0, first_intersect.y(), 1e-5);
EXPECT_NEAR(1.0, last_intersect.x(), 1e-5);
EXPECT_NEAR(2.0, last_intersect.y(), 1e-5);
EXPECT_TRUE(poly1.GetOverlap(LineSegment2d({1, -1}, {1, 1}), &first_intersect,
&last_intersect));
EXPECT_NEAR(1.0, first_intersect.x(), 1e-5);
EXPECT_NEAR(0.0, first_intersect.y(), 1e-5);
EXPECT_NEAR(1.0, last_intersect.x(), 1e-5);
EXPECT_NEAR(1.0, last_intersect.y(), 1e-5);
EXPECT_TRUE(poly1.GetOverlap(LineSegment2d({1, 3}, {3, 1}), &first_intersect,
&last_intersect));
EXPECT_NEAR(2.0, first_intersect.x(), 1e-5);
EXPECT_NEAR(2.0, first_intersect.y(), 1e-5);
EXPECT_NEAR(2.0, last_intersect.x(), 1e-5);
EXPECT_NEAR(2.0, last_intersect.y(), 1e-5);
EXPECT_FALSE(poly1.GetOverlap(LineSegment2d({4, 3}, {4, 3}), &first_intersect,
&last_intersect));
EXPECT_TRUE(poly1.GetOverlap(LineSegment2d({1, 1}, {1, 1}), &first_intersect,
&last_intersect));
EXPECT_NEAR(1.0, first_intersect.x(), 1e-5);
EXPECT_NEAR(1.0, first_intersect.y(), 1e-5);
EXPECT_NEAR(1.0, last_intersect.x(), 1e-5);
EXPECT_NEAR(1.0, last_intersect.y(), 1e-5);
const Polygon2d poly5(
{{0, 0}, {4, 0}, {4, 2}, {3, 2}, {2, 1}, {1, 2}, {0, 2}});
std::vector<LineSegment2d> overlap_line_segments =
poly5.GetAllOverlaps(LineSegment2d({-10, 1.5}, {10, 1.5}));
EXPECT_EQ(2, overlap_line_segments.size());
EXPECT_NEAR(0.0, overlap_line_segments[0].start().x(), 1e-5);
EXPECT_NEAR(1.5, overlap_line_segments[0].start().y(), 1e-5);
EXPECT_NEAR(1.5, overlap_line_segments[0].end().x(), 1e-5);
EXPECT_NEAR(1.5, overlap_line_segments[0].end().y(), 1e-5);
EXPECT_NEAR(2.5, overlap_line_segments[1].start().x(), 1e-5);
EXPECT_NEAR(1.5, overlap_line_segments[1].start().y(), 1e-5);
EXPECT_NEAR(4.0, overlap_line_segments[1].end().x(), 1e-5);
EXPECT_NEAR(1.5, overlap_line_segments[1].end().y(), 1e-5);
overlap_line_segments =
poly5.GetAllOverlaps(LineSegment2d({-10, 1}, {10, 1}));
EXPECT_EQ(1, overlap_line_segments.size());
EXPECT_NEAR(0.0, overlap_line_segments[0].start().x(), 1e-5);
EXPECT_NEAR(1.0, overlap_line_segments[0].start().y(), 1e-5);
EXPECT_NEAR(4.0, overlap_line_segments[0].end().x(), 1e-5);
EXPECT_NEAR(1.0, overlap_line_segments[0].end().y(), 1e-5);
overlap_line_segments =
poly5.GetAllOverlaps(LineSegment2d({-10, 0.5}, {10, 0.5}));
EXPECT_EQ(1, overlap_line_segments.size());
EXPECT_NEAR(0.0, overlap_line_segments[0].start().x(), 1e-5);
EXPECT_NEAR(0.5, overlap_line_segments[0].start().y(), 1e-5);
EXPECT_NEAR(4.0, overlap_line_segments[0].end().x(), 1e-5);
EXPECT_NEAR(0.5, overlap_line_segments[0].end().y(), 1e-5);
overlap_line_segments =
poly5.GetAllOverlaps(LineSegment2d({-10, -0.5}, {10, -0.5}));
EXPECT_EQ(0, overlap_line_segments.size());
overlap_line_segments =
poly5.GetAllOverlaps(LineSegment2d({-10, 2.5}, {10, 2.5}));
EXPECT_EQ(0, overlap_line_segments.size());
overlap_line_segments =
poly5.GetAllOverlaps(LineSegment2d({2, 0.5}, {2, 0.5}));
EXPECT_EQ(1, overlap_line_segments.size());
EXPECT_NEAR(2.0, overlap_line_segments[0].start().x(), 1e-5);
EXPECT_NEAR(0.5, overlap_line_segments[0].start().y(), 1e-5);
EXPECT_NEAR(2.0, overlap_line_segments[0].end().x(), 1e-5);
EXPECT_NEAR(0.5, overlap_line_segments[0].end().y(), 1e-5);
overlap_line_segments =
poly5.GetAllOverlaps(LineSegment2d({5, 0.5}, {5, 0.5}));
EXPECT_EQ(0, overlap_line_segments.size());
EXPECT_TRUE(Polygon2d({{0, 0}, {0, 4}, {4, 0}})
.ComputeOverlap(Polygon2d({{1, 1}, {1, 3}, {3, 1}}),
&overlap_polygon));
EXPECT_NEAR(overlap_polygon.area(), 2.0, 1e-5);
EXPECT_TRUE(Polygon2d({{0, 0}, {0, 4}, {4, 0}})
.ComputeOverlap(Polygon2d({{1, 1}, {-1, 1}, {1, 3}}),
&overlap_polygon));
EXPECT_NEAR(overlap_polygon.area(), 1.5, 1e-5);
EXPECT_TRUE(Polygon2d({{0, 0}, {0, 4}, {4, 0}})
.ComputeOverlap(Polygon2d({{2, 1}, {-1, 1}, {2, 4}}),
&overlap_polygon));
EXPECT_NEAR(overlap_polygon.area(), 3.0, 1e-5);
EXPECT_TRUE(Polygon2d({{0, 0}, {0, 4}, {4, 0}})
.ComputeOverlap(Polygon2d({{3, 1}, {-1, 1}, {3, 5}}),
&overlap_polygon));
EXPECT_NEAR(overlap_polygon.area(), 3.5, 1e-5);
EXPECT_TRUE(Polygon2d({{0, 0}, {0, 4}, {4, 0}})
.ComputeOverlap(Polygon2d({{4, 1}, {-1, 1}, {4, 6}}),
&overlap_polygon));
EXPECT_NEAR(overlap_polygon.area(), 3.5, 1e-5);
for (int iter = 0; iter < 10000; ++iter) {
const double x1 = RandomDouble(-10, 10);
const double y1 = RandomDouble(-10, 10);
const double x2 = RandomDouble(-10, 10);
const double y2 = RandomDouble(-10, 10);
const double heading1 = RandomDouble(0, M_PI * 2.0);
const double heading2 = RandomDouble(0, M_PI * 2.0);
const double l1 = RandomDouble(1, 5);
const double l2 = RandomDouble(1, 5);
const double w1 = RandomDouble(1, 5);
const double w2 = RandomDouble(1, 5);
Box2d box1({x1, y1}, heading1, l1, w1);
Box2d box2({x2, y2}, heading2, l2, w2);
Box2d shrinked_box2({x2, y2}, heading2, l2 - 0.2, w2 - 0.2);
Box2d extended_box2({x2, y2}, heading2, l2 + 0.2, w2 + 0.2);
if (!box1.HasOverlap(extended_box2)) {
EXPECT_FALSE(
Polygon2d(box1).ComputeOverlap(Polygon2d(box2), &overlap_polygon));
} else if (box1.HasOverlap(shrinked_box2)) {
EXPECT_TRUE(
Polygon2d(box1).ComputeOverlap(Polygon2d(box2), &overlap_polygon));
}
}
for (int iter = 0; iter < 10000; ++iter) {
const int kRange = 10;
const int n1 = RandomInt(3, 10);
const int n2 = RandomInt(3, 10);
std::vector<Vec2d> points1, points2;
for (int i = 0; i < n1; ++i) {
points1.emplace_back(RandomInt(0, kRange), RandomInt(0, kRange));
}
for (int i = 0; i < n2; ++i) {
points2.emplace_back(RandomInt(0, kRange), RandomInt(0, kRange));
}
Polygon2d polygon1;
Polygon2d polygon2;
if (!Polygon2d::ComputeConvexHull(points1, &polygon1) ||
!Polygon2d::ComputeConvexHull(points2, &polygon2)) {
continue;
}
std::vector<double> key_points;
for (int x0 = 0; x0 <= kRange; ++x0) {
key_points.push_back(x0);
}
for (const auto &line_segment1 : polygon1.line_segments()) {
for (const auto &line_segment2 : polygon2.line_segments()) {
Vec2d pt;
if (line_segment1.GetIntersect(line_segment2, &pt)) {
key_points.push_back(pt.x());
}
}
}
double area = 0;
std::sort(key_points.begin(), key_points.end());
for (size_t i = 0; i + 1 < key_points.size(); ++i) {
const double width = key_points[i + 1] - key_points[i];
if (width < 1e-6) {
continue;
}
const double x = (key_points[i] + key_points[i + 1]) / 2.0;
double min_y1 = 0.0;
double max_y1 = 0.0;
double min_y2 = 0.0;
double max_y2 = 0.0;
if (ProjectByXSlow(points1, x, &min_y1, &max_y1) &&
ProjectByXSlow(points2, x, &min_y2, &max_y2)) {
area +=
std::max(0.0, std::min(max_y1, max_y2) - std::max(min_y1, min_y2)) *
width;
}
}
Polygon2d overlap_polygon;
if (area < 1e-3) {
EXPECT_FALSE(polygon1.ComputeOverlap(polygon2, &overlap_polygon));
} else {
EXPECT_TRUE(Polygon2d::ComputeConvexHull(points1, &polygon1));
EXPECT_TRUE(Polygon2d::ComputeConvexHull(points2, &polygon2));
EXPECT_TRUE(polygon1.ComputeOverlap(polygon2, &overlap_polygon));
EXPECT_NEAR(area, overlap_polygon.area(), 1e-5);
}
}
}
TEST(Polygon2dTest, BoundingBox) {
Polygon2d poly1(Box2d::CreateAABox({0, 0}, {2, 2}));
Box2d box = poly1.BoundingBoxWithHeading(0.0);
EXPECT_NEAR(1.0, box.center().x(), 1e-5);
EXPECT_NEAR(1.0, box.center().y(), 1e-5);
EXPECT_NEAR(4.0, box.area(), 1e-5);
EXPECT_TRUE(Polygon2d(box).Contains(poly1));
AABox2d aabox = poly1.AABoundingBox();
EXPECT_NEAR(1.0, aabox.center().x(), 1e-5);
EXPECT_NEAR(1.0, aabox.center().y(), 1e-5);
EXPECT_NEAR(4.0, aabox.area(), 1e-5);
EXPECT_NEAR(2.0, aabox.length(), 1e-5);
EXPECT_NEAR(2.0, aabox.width(), 1e-5);
box = poly1.BoundingBoxWithHeading(M_PI_4);
EXPECT_NEAR(1.0, box.center().x(), 1e-5);
EXPECT_NEAR(1.0, box.center().y(), 1e-5);
EXPECT_NEAR(8.0, box.area(), 1e-5);
EXPECT_TRUE(Polygon2d(box).Contains(poly1));
box = poly1.MinAreaBoundingBox();
EXPECT_NEAR(1.0, box.center().x(), 1e-5);
EXPECT_NEAR(1.0, box.center().y(), 1e-5);
EXPECT_NEAR(4.0, box.area(), 1e-5);
EXPECT_TRUE(Polygon2d(box).Contains(poly1));
Polygon2d poly2({{1, 0}, {0, 1}, {-1, 0}, {0, -1}});
box = poly2.BoundingBoxWithHeading(0.0);
EXPECT_NEAR(0.0, box.center().x(), 1e-5);
EXPECT_NEAR(0.0, box.center().y(), 1e-5);
EXPECT_NEAR(4.0, box.area(), 1e-5);
EXPECT_TRUE(Polygon2d(box).Contains(poly2));
aabox = poly2.AABoundingBox();
EXPECT_NEAR(0.0, aabox.center().x(), 1e-5);
EXPECT_NEAR(0.0, aabox.center().y(), 1e-5);
EXPECT_NEAR(4.0, aabox.area(), 1e-5);
EXPECT_NEAR(2.0, aabox.length(), 1e-5);
EXPECT_NEAR(2.0, aabox.width(), 1e-5);
box = poly2.BoundingBoxWithHeading(M_PI_4);
EXPECT_NEAR(0.0, box.center().x(), 1e-5);
EXPECT_NEAR(0.0, box.center().y(), 1e-5);
EXPECT_NEAR(2.0, box.area(), 1e-5);
EXPECT_TRUE(Polygon2d(box).Contains(poly2));
box = poly2.MinAreaBoundingBox();
EXPECT_NEAR(0.0, box.center().x(), 1e-5);
EXPECT_NEAR(0.0, box.center().y(), 1e-5);
EXPECT_NEAR(2.0, box.area(), 1e-5);
EXPECT_TRUE(Polygon2d(box).Contains(poly2));
for (int iter = 0; iter < 1000; ++iter) {
const int num_sample_points = RandomInt(3, 10);
std::vector<Vec2d> points;
for (int i = 0; i < num_sample_points; ++i) {
const double x = RandomInt(-10, 10);
const double y = RandomInt(-10, 10);
points.emplace_back(x, y);
}
Polygon2d polygon;
if (!Polygon2d::ComputeConvexHull(points, &polygon)) {
continue;
}
double min_area = std::numeric_limits<double>::infinity();
for (int iter2 = 0; iter2 < 10; ++iter2) {
const double heading = RandomDouble(0, M_PI * 2.0);
box = polygon.BoundingBoxWithHeading(heading);
EXPECT_TRUE(Polygon2d(box).Contains(polygon));
min_area = std::min(min_area, box.area());
}
box = polygon.MinAreaBoundingBox();
EXPECT_TRUE(Polygon2d(box).Contains(polygon));
EXPECT_LE(box.area(), min_area + 1e-5);
}
}
TEST(Polygon2dTest, Expand) {
{
const Polygon2d poly(Box2d::CreateAABox({0, 0}, {2, 2}));
const Polygon2d exp_poly = poly.ExpandByDistance(1.0);
EXPECT_TRUE(exp_poly.is_convex());
const Box2d box = exp_poly.BoundingBoxWithHeading(0.0);
EXPECT_NEAR(box.center().x(), 1.0, 1e-6);
EXPECT_NEAR(box.center().y(), 1.0, 1e-6);
EXPECT_NEAR(box.width(), 4.0, 1e-6);
EXPECT_NEAR(box.length(), 4.0, 1e-6);
EXPECT_NEAR(exp_poly.area(), 12 + M_PI, 0.1);
}
{
const std::vector<Vec2d> points{{0, 0}, {2, 0}, {2, 2}, {0, 2}, {1, 1}};
const Polygon2d poly(points);
const Polygon2d exp_poly = poly.ExpandByDistance(1.0);
EXPECT_TRUE(exp_poly.is_convex());
const Box2d box = exp_poly.BoundingBoxWithHeading(0.0);
EXPECT_NEAR(box.center().x(), 1.0, 1e-6);
EXPECT_NEAR(box.center().y(), 1.0, 1e-6);
EXPECT_NEAR(box.width(), 4.0, 1e-6);
EXPECT_NEAR(box.length(), 4.0, 1e-6);
EXPECT_NEAR(exp_poly.area(), 12 + M_PI, 0.1);
}
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/matrix_operations.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Defines some useful matrix operations.
*/
#include <cmath>
#include <utility>
#include "Eigen/Dense"
#include "Eigen/SVD"
#include "modules/common/math/matrix_operations.h"
/**
* @namespace apollo::common::math
* @brief The math namespace deals with a number of useful mathematical objects.
*/
namespace apollo {
namespace common {
namespace math {
bool ContinuousToDiscrete(const Eigen::MatrixXd &m_a,
const Eigen::MatrixXd &m_b,
const Eigen::MatrixXd &m_c,
const Eigen::MatrixXd &m_d, const double ts,
Eigen::MatrixXd *ptr_a_d, Eigen::MatrixXd *ptr_b_d,
Eigen::MatrixXd *ptr_c_d, Eigen::MatrixXd *ptr_d_d) {
if (ts <= 0.0) {
AERROR << "ContinuousToDiscrete : ts is less than or equal to zero";
return false;
}
// Only matrix_a is mandatory to be non-zeros in matrix
// conversion.
if (m_a.rows() == 0) {
AERROR << "ContinuousToDiscrete: matrix_a size 0 ";
return false;
}
if (m_a.cols() != m_b.rows() || m_b.cols() != m_d.cols() ||
m_c.rows() != m_d.rows() || m_a.cols() != m_c.cols()) {
AERROR << "ContinuousToDiscrete: matrix dimensions mismatch";
return false;
}
Eigen::MatrixXd m_identity =
Eigen::MatrixXd::Identity(m_a.cols(), m_a.rows());
*ptr_a_d =
(m_identity - ts * 0.5 * m_a).inverse() * (m_identity + ts * 0.5 * m_a);
*ptr_b_d = std::sqrt(ts) * (m_identity - ts * 0.5 * m_a).inverse() * m_b;
*ptr_c_d = std::sqrt(ts) * m_c * (m_identity - ts * 0.5 * m_a).inverse();
*ptr_d_d = 0.5 * m_c * (m_identity - ts * 0.5 * m_a).inverse() * m_b + m_d;
return true;
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/vec2d.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Defines the Vec2d class.
*/
#pragma once
#include <cmath>
#include <string>
/**
* @namespace apollo::common::math
* @brief apollo::common::math
*/
namespace apollo {
namespace common {
namespace math {
constexpr double kMathEpsilon = 1e-10;
/**
* @class Vec2d
*
* @brief Implements a class of 2-dimensional vectors.
*/
class Vec2d {
public:
//! Constructor which takes x- and y-coordinates.
constexpr Vec2d(const double x, const double y) noexcept : x_(x), y_(y) {}
//! Constructor returning the zero vector.
constexpr Vec2d() noexcept : Vec2d(0, 0) {}
//! Creates a unit-vector with a given angle to the positive x semi-axis
static Vec2d CreateUnitVec2d(const double angle);
//! Getter for x component
double x() const { return x_; }
//! Getter for y component
double y() const { return y_; }
//! Setter for x component
void set_x(const double x) { x_ = x; }
//! Setter for y component
void set_y(const double y) { y_ = y; }
//! Gets the length of the vector
double Length() const;
//! Gets the squared length of the vector
double LengthSquare() const;
//! Gets the angle between the vector and the positive x semi-axis
double Angle() const;
//! Returns the unit vector that is co-linear with this vector
void Normalize();
//! Returns the distance to the given vector
double DistanceTo(const Vec2d &other) const;
//! Returns the squared distance to the given vector
double DistanceSquareTo(const Vec2d &other) const;
//! Returns the "cross" product between these two Vec2d (non-standard).
double CrossProd(const Vec2d &other) const;
//! Returns the inner product between these two Vec2d.
double InnerProd(const Vec2d &other) const;
//! rotate the vector by angle.
Vec2d rotate(const double angle) const;
//! rotate the vector itself by angle.
void SelfRotate(const double angle);
//! Sums two Vec2d
Vec2d operator+(const Vec2d &other) const;
//! Subtracts two Vec2d
Vec2d operator-(const Vec2d &other) const;
//! Multiplies Vec2d by a scalar
Vec2d operator*(const double ratio) const;
//! Divides Vec2d by a scalar
Vec2d operator/(const double ratio) const;
//! Sums another Vec2d to the current one
Vec2d &operator+=(const Vec2d &other);
//! Subtracts another Vec2d to the current one
Vec2d &operator-=(const Vec2d &other);
//! Multiplies this Vec2d by a scalar
Vec2d &operator*=(const double ratio);
//! Divides this Vec2d by a scalar
Vec2d &operator/=(const double ratio);
//! Compares two Vec2d
bool operator==(const Vec2d &other) const;
//! Returns a human-readable string representing this object
std::string DebugString() const;
protected:
double x_ = 0.0;
double y_ = 0.0;
};
//! Multiplies the given Vec2d by a given scalar
Vec2d operator*(const double ratio, const Vec2d &vec);
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/box2d.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief The class of Box2d. Here, the x/y axes are respectively Forward/Left,
* as opposed to what happens in euler_angles_zxy.h (Right/Forward).
*/
#pragma once
#include <limits>
#include <string>
#include <vector>
#include "modules/common/math/aabox2d.h"
#include "modules/common/math/line_segment2d.h"
#include "modules/common/math/vec2d.h"
/**
* @namespace apollo::common::math
* @brief apollo::common::math
*/
namespace apollo {
namespace common {
namespace math {
/**
* @class Box2d
* @brief Rectangular (undirected) bounding box in 2-D.
*
* This class is referential-agnostic, although our convention on the use of
* the word "heading" in this project (permanently set to be 0 at East)
* forces us to assume that the X/Y frame here is East/North.
* For disambiguation, we call the axis of the rectangle parallel to the
* heading direction the "heading-axis". The size of the heading-axis is
* called "length", and the size of the axis perpendicular to it "width".
*/
class Box2d {
public:
Box2d() = default;
/**
* @brief Constructor which takes the center, heading, length and width.
* @param center The center of the rectangular bounding box.
* @param heading The angle between the x-axis and the heading-axis,
* measured counter-clockwise.
* @param length The size of the heading-axis.
* @param width The size of the axis perpendicular to the heading-axis.
*/
Box2d(const Vec2d ¢er, const double heading, const double length,
const double width);
/**
* @brief Constructor which takes the heading-axis and the width of the box
* @param axis The heading-axis
* @param width The width of the box, which is taken perpendicularly
* to the heading direction.
*/
Box2d(const LineSegment2d &axis, const double width);
/**
* @brief Constructor which takes an AABox2d (axes-aligned box).
* @param aabox The input AABox2d.
*/
explicit Box2d(const AABox2d &aabox);
/**
* @brief Creates an axes-aligned Box2d from two opposite corners
* @param one_corner One of the corners
* @param opposite_corner The opposite corner to the first one
* @return An axes-aligned Box2d
*/
static Box2d CreateAABox(const Vec2d &one_corner,
const Vec2d &opposite_corner);
/**
* @brief Getter of the center of the box
* @return The center of the box
*/
const Vec2d ¢er() const { return center_; }
/**
* @brief Getter of the x-coordinate of the center of the box
* @return The x-coordinate of the center of the box
*/
double center_x() const { return center_.x(); }
/**
* @brief Getter of the y-coordinate of the center of the box
* @return The y-coordinate of the center of the box
*/
double center_y() const { return center_.y(); }
/**
* @brief Getter of the length
* @return The length of the heading-axis
*/
double length() const { return length_; }
/**
* @brief Getter of the width
* @return The width of the box taken perpendicularly to the heading
*/
double width() const { return width_; }
/**
* @brief Getter of half the length
* @return Half the length of the heading-axis
*/
double half_length() const { return half_length_; }
/**
* @brief Getter of half the width
* @return Half the width of the box taken perpendicularly to the heading
*/
double half_width() const { return half_width_; }
/**
* @brief Getter of the heading
* @return The counter-clockwise angle between the x-axis and the heading-axis
*/
double heading() const { return heading_; }
/**
* @brief Getter of the cosine of the heading
* @return The cosine of the heading
*/
double cos_heading() const { return cos_heading_; }
/**
* @brief Getter of the sine of the heading
* @return The sine of the heading
*/
double sin_heading() const { return sin_heading_; }
/**
* @brief Getter of the area of the box
* @return The product of its length and width
*/
double area() const { return length_ * width_; }
/**
* @brief Getter of the size of the diagonal of the box
* @return The diagonal size of the box
*/
double diagonal() const { return std::hypot(length_, width_); }
/**
* @brief Getter of the corners of the box
* @param corners The vector where the corners are listed
*/
void GetAllCorners(std::vector<Vec2d> *const corners) const;
/**
* @brief Getter of the corners of the box
* @param corners The vector where the corners are listed
*/
std::vector<Vec2d> GetAllCorners() const;
/**
* @brief Tests points for membership in the box
* @param point A point that we wish to test for membership in the box
* @return True iff the point is contained in the box
*/
bool IsPointIn(const Vec2d &point) const;
/**
* @brief Tests points for membership in the boundary of the box
* @param point A point that we wish to test for membership in the boundary
* @return True iff the point is a boundary point of the box
*/
bool IsPointOnBoundary(const Vec2d &point) const;
/**
* @brief Determines the distance between the box and a given point
* @param point The point whose distance to the box we wish to compute
* @return A distance
*/
double DistanceTo(const Vec2d &point) const;
/**
* @brief Determines the distance between the box and a given line segment
* @param line_segment The line segment whose distance to the box we compute
* @return A distance
*/
double DistanceTo(const LineSegment2d &line_segment) const;
/**
* @brief Determines the distance between two boxes
* @param box The box whose distance to this box we want to compute
* @return A distance
*/
double DistanceTo(const Box2d &box) const;
/**
* @brief Determines whether this box overlaps a given line segment
* @param line_segment The line-segment
* @return True if they overlap
*/
bool HasOverlap(const LineSegment2d &line_segment) const;
/**
* @brief Determines whether these two boxes overlap
* @param line_segment The other box
* @return True if they overlap
*/
bool HasOverlap(const Box2d &box) const;
/**
* @brief Gets the smallest axes-aligned box containing the current one
* @return An axes-aligned box
*/
AABox2d GetAABox() const;
/**
* @brief Rotate from center.
* @param rotate_angle Angle to rotate.
*/
void RotateFromCenter(const double rotate_angle);
/**
* @brief Shifts this box by a given vector
* @param shift_vec The vector determining the shift
*/
void Shift(const Vec2d &shift_vec);
/**
* @brief Extend the box longitudinally
* @param extension_length the length to extend
*/
void LongitudinalExtend(const double extension_length);
void LateralExtend(const double extension_length);
/**
* @brief Gets a human-readable description of the box
* @return A debug-string
*/
std::string DebugString() const;
void InitCorners();
double max_x() const { return max_x_; }
double min_x() const { return min_x_; }
double max_y() const { return max_y_; }
double min_y() const { return min_y_; }
private:
Vec2d center_;
double length_ = 0.0;
double width_ = 0.0;
double half_length_ = 0.0;
double half_width_ = 0.0;
double heading_ = 0.0;
double cos_heading_ = 1.0;
double sin_heading_ = 0.0;
std::vector<Vec2d> corners_;
double max_x_ = std::numeric_limits<double>::lowest();
double min_x_ = std::numeric_limits<double>::max();
double max_y_ = std::numeric_limits<double>::lowest();
double min_y_ = std::numeric_limits<double>::max();
};
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/quaternion.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Contains a number of helper functions related to quaternions.
* The reader should refer to euler_angles_zxy.h for clarifications.
* However, although the vehicle frame defined therein might change,
* the definition of the heading of the car, used below, is permanently fixed:
* 0 at East, pi/2 at North, -pi/2 at South.
*/
#pragma once
#include <cmath>
#include "Eigen/Dense"
#include "Eigen/Geometry"
#include "modules/common/math/euler_angles_zxy.h"
#include "modules/common/math/math_utils.h"
#include "modules/common_msgs/basic_msgs/geometry.pb.h"
/**
* @namespace apollo::common::math
* @brief apollo::common::math
*/
namespace apollo {
namespace common {
namespace math {
/*
* @brief Returns heading (in radians) in [-PI, PI), with 0 being East.
* Note that x/y/z is East/North/Up.
*
* @param qw Quaternion w-coordinate
* @param qx Quaternion x-coordinate
* @param qy Quaternion y-coordinate
* @param qz Quaternion z-coordinate
*
* @return Heading encoded by given quaternion
*/
inline double QuaternionToHeading(const double qw, const double qx,
const double qy, const double qz) {
EulerAnglesZXYd euler_angles(qw, qx, qy, qz);
// euler_angles.yaw() is zero when the car is pointing North, but
// the heading is zero when the car is pointing East.
return NormalizeAngle(euler_angles.yaw() + M_PI_2);
}
/*
* @brief Returns heading (in radians) in [-PI, PI), with 0 being East.
* Note that x/y/z is East/North/Up.
*
* @param q Eigen::Quaternion
*
* @return Heading encoded by given quaternion
*/
template <typename T>
inline T QuaternionToHeading(const Eigen::Quaternion<T> &q) {
return static_cast<T>(QuaternionToHeading(q.w(), q.x(), q.y(), q.z()));
}
/*
* @brief Returns a quaternion encoding a rotation with zero roll, zero pitch,
* and the specified heading/yaw.
* Note that heading is zero at East and yaw is zero at North.
* Satisfies QuaternionToHeading(HeadingToQuaternion(h)) = h.
*
* @param heading The heading to encode in the rotation
*
* @return Quaternion encoding rotation by given heading
*/
template <typename T>
inline Eigen::Quaternion<T> HeadingToQuaternion(T heading) {
// Note that heading is zero at East and yaw is zero at North.
EulerAnglesZXY<T> euler_angles(heading - M_PI_2);
return euler_angles.ToQuaternion();
}
/*
* @brief Applies the rotation defined by a quaternion to a given vector.
* Note that x/y/z is East/North/Up.
*
* @param orientation Quaternion
* @param original Vector (in East-North-Up frame)
*
* @return Rotated vector
*/
inline Eigen::Vector3d QuaternionRotate(const Quaternion &orientation,
const Eigen::Vector3d &original) {
Eigen::Quaternion<double> quaternion(orientation.qw(), orientation.qx(),
orientation.qy(), orientation.qz());
return static_cast<Eigen::Vector3d>(quaternion.toRotationMatrix() * original);
}
inline Eigen::Vector3d InverseQuaternionRotate(const Quaternion &orientation,
const Eigen::Vector3d &rotated) {
Eigen::Quaternion<double> quaternion(orientation.qw(), orientation.qx(),
orientation.qy(), orientation.qz());
return static_cast<Eigen::Vector3d>(quaternion.toRotationMatrix().inverse() *
rotated);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/search_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/search.h"
#include <cmath>
#include "gtest/gtest.h"
namespace apollo {
namespace common {
namespace math {
namespace {
double LinearFunc(double x) { return 2.0 * x; }
double SquareFunc(double x) { return x * x; }
double CubicFunc(double x) { return (x - 1.0) * (x - 2.0) * (x - 3.0); }
double SinFunc(double x) { return std::sin(x); }
} // namespace
TEST(SearchTest, GoldenSectionSearch) {
double linear_argmin = GoldenSectionSearch(LinearFunc, 0.0, 1.0, 1e-6);
EXPECT_NEAR(linear_argmin, 0.0, 1e-5);
double square_argmin = GoldenSectionSearch(SquareFunc, -1.0, 2.0, 1e-6);
EXPECT_NEAR(square_argmin, 0.0, 1e-5);
double cubic_argmin_1 = GoldenSectionSearch(CubicFunc, 0.0, 1.5, 1e-6);
EXPECT_NEAR(cubic_argmin_1, 0.0, 1e-5);
double cubic_argmin_2 = GoldenSectionSearch(CubicFunc, 1.0, 1.8, 1e-6);
EXPECT_NEAR(cubic_argmin_2, 1.0, 1e-5);
double cubic_argmin_3 = GoldenSectionSearch(CubicFunc, 2.0, 3.0, 1e-6);
EXPECT_NEAR(cubic_argmin_3, 2.0 + 1.0 / std::sqrt(3.0), 1e-5);
double sin_argmin = GoldenSectionSearch(SinFunc, 0.0, 2 * M_PI, 1e-6);
EXPECT_NEAR(sin_argmin, 1.5 * M_PI, 1e-5);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/search.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/search.h"
#include <cmath>
namespace apollo {
namespace common {
namespace math {
double GoldenSectionSearch(const std::function<double(double)> &func,
const double lower_bound, const double upper_bound,
const double tol) {
static constexpr double gr = 1.618033989; // (sqrt(5) + 1) / 2
double a = lower_bound;
double b = upper_bound;
double t = (b - a) / gr;
double c = b - t;
double d = a + t;
while (std::abs(c - d) > tol) {
if (func(c) < func(d)) {
b = d;
} else {
a = c;
}
t = (b - a) / gr;
c = b - t;
d = a + t;
}
return (a + b) * 0.5;
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/aabox2d.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Defines the AABox2d class.
*/
#pragma once
#include <string>
#include <vector>
#include "modules/common/math/vec2d.h"
/**
* @namespace apollo::common::math
* @brief apollo::common::math
*/
namespace apollo {
namespace common {
namespace math {
/**
* @class AABox2d
* @brief Implements a class of (undirected) axes-aligned bounding boxes in 2-D.
* This class is referential-agnostic.
*/
class AABox2d {
public:
/**
* @brief Default constructor.
* Creates an axes-aligned box with zero length and width at the origin.
*/
AABox2d() = default;
/**
* @brief Parameterized constructor.
* Creates an axes-aligned box with given center, length, and width.
* @param center The center of the box
* @param length The size of the box along the x-axis
* @param width The size of the box along the y-axis
*/
AABox2d(const Vec2d ¢er, const double length, const double width);
/**
* @brief Parameterized constructor.
* Creates an axes-aligned box from two opposite corners.
* @param one_corner One corner of the box
* @param opposite_corner The opposite corner to the first one
*/
AABox2d(const Vec2d &one_corner, const Vec2d &opposite_corner);
/**
* @brief Parameterized constructor.
* Creates an axes-aligned box containing all points in a given vector.
* @param points Vector of points to be included inside the box.
*/
explicit AABox2d(const std::vector<Vec2d> &points);
/**
* @brief Getter of center_
* @return Center of the box
*/
const Vec2d ¢er() const { return center_; }
/**
* @brief Getter of x-component of center_
* @return x-component of the center of the box
*/
double center_x() const { return center_.x(); }
/**
* @brief Getter of y-component of center_
* @return y-component of the center of the box
*/
double center_y() const { return center_.y(); }
/**
* @brief Getter of length_
* @return The length of the box
*/
double length() const { return length_; }
/**
* @brief Getter of width_
* @return The width of the box
*/
double width() const { return width_; }
/**
* @brief Getter of half_length_
* @return Half of the length of the box
*/
double half_length() const { return half_length_; }
/**
* @brief Getter of half_width_
* @return Half of the width of the box
*/
double half_width() const { return half_width_; }
/**
* @brief Getter of length_*width_
* @return The area of the box
*/
double area() const { return length_ * width_; }
/**
* @brief Returns the minimum x-coordinate of the box
*
* @return x-coordinate
*/
double min_x() const { return center_.x() - half_length_; }
/**
* @brief Returns the maximum x-coordinate of the box
*
* @return x-coordinate
*/
double max_x() const { return center_.x() + half_length_; }
/**
* @brief Returns the minimum y-coordinate of the box
*
* @return y-coordinate
*/
double min_y() const { return center_.y() - half_width_; }
/**
* @brief Returns the maximum y-coordinate of the box
*
* @return y-coordinate
*/
double max_y() const { return center_.y() + half_width_; }
/**
* @brief Gets all corners in counter clockwise order.
*
* @param corners Output where the corners are written
*/
void GetAllCorners(std::vector<Vec2d> *const corners) const;
/**
* @brief Determines whether a given point is in the box.
*
* @param point The point we wish to test for containment in the box
*/
bool IsPointIn(const Vec2d &point) const;
/**
* @brief Determines whether a given point is on the boundary of the box.
*
* @param point The point we wish to test for boundary membership
*/
bool IsPointOnBoundary(const Vec2d &point) const;
/**
* @brief Determines the distance between a point and the box.
*
* @param point The point whose distance to the box we wish to determine.
*/
double DistanceTo(const Vec2d &point) const;
/**
* @brief Determines the distance between two boxes.
*
* @param box Another box.
*/
double DistanceTo(const AABox2d &box) const;
/**
* @brief Determines whether two boxes overlap.
*
* @param box Another box
*/
bool HasOverlap(const AABox2d &box) const;
/**
* @brief Shift the center of AABox by the input vector.
*
* @param shift_vec The vector by which we wish to shift the box
*/
void Shift(const Vec2d &shift_vec);
/**
* @brief Changes box to include another given box, as well as the current
* one.
*
* @param other_box Another box
*/
void MergeFrom(const AABox2d &other_box);
/**
* @brief Changes box to include a given point, as well as the current box.
*
* @param other_point Another point
*/
void MergeFrom(const Vec2d &other_point);
/**
* @brief Gets a human-readable debug string
*
* @return A string
*/
std::string DebugString() const;
private:
Vec2d center_;
double length_ = 0.0;
double width_ = 0.0;
double half_length_ = 0.0;
double half_width_ = 0.0;
};
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/angle.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Defines the templated Angle class.
*/
#pragma once
#include <cmath>
#include <cstdint>
#include <limits>
/**
* @namespace apollo::common::math
* @brief apollo::common::math
*/
namespace apollo {
namespace common {
namespace math {
/**
* @class Angle
* @brief The Angle class uses an integer to represent an angle, and supports
* commonly-used operations such as addition and subtraction,
* as well as the use of trigonometric functions.
*
* Having a specialized Angle class prevents code repetition, namely for tasks
* such as computing angle differences or finding equivalent angles in some
* specified interval, typically [-pi, pi).
* Representing angles by integers has the following advantages:
* 1) Finer level of precision control (< means "less precise than"):
* Angle8 < Angle16 < float < Angle32 < double < Angle64.
* 2) Angle8 and Angle16 allow super fast trigonometric functions
* via a 64-KiB lookup table.
* 3) Higher precision with the same representation size.
* The use of the Angle class is encouraged.
* In particular, Angle32 should be used for latitude/longitude (<1cm error).
* Angle16 is precise enough for localization/object detection.
* @param T signed integer type
*/
template <typename T>
class Angle {
public:
static_assert(std::numeric_limits<T>::is_integer &&
std::numeric_limits<T>::is_signed,
"T must be a signed integer type");
/**
* @brief Constructs an Angle object from an angle in degrees (factory).
* @param value Angle in degrees
* @return Angle object
*/
static Angle from_deg(const double value) {
return Angle(static_cast<T>(std::lround(value * DEG_TO_RAW)));
}
/**
* @brief Constructs an Angle object from an angle in radians (factory).
* @param value Angle in radians
* @return Angle object
*/
static Angle from_rad(const double value) {
return Angle(static_cast<T>(std::lround(value * RAD_TO_RAW)));
}
/**
* @brief Constructs an Angle object from raw internal value.
* @param value Angle in degrees
* @return Angle object
*/
explicit Angle(const T value = 0) : value_(value) {}
/// Internal representation of pi
static constexpr T RAW_PI = std::numeric_limits<T>::min();
/// Internal representation of pi/2
static constexpr T RAW_PI_2 =
static_cast<T>(-(std::numeric_limits<T>::min() >> 1));
/// Used for converting angle units
static constexpr double DEG_TO_RAW = RAW_PI / -180.0;
/// Used for converting angle units
static constexpr double RAD_TO_RAW = RAW_PI * -M_1_PI;
/// Used for converting angle units
static constexpr double RAW_TO_DEG = -180.0 / RAW_PI;
/// Used for converting angle units
static constexpr double RAW_TO_RAD = -M_PI / RAW_PI;
/**
* @brief Getter of value_.
* @return Internal unsigned integer representation of angle
*/
T raw() const { return value_; }
/**
* @brief Converts the internal representation to degrees.
* @return angle in degrees
*/
double to_deg() const { return value_ * RAW_TO_DEG; }
/**
* @brief Converts the internal representation to radians.
* @return angle in radians
*/
double to_rad() const { return value_ * RAW_TO_RAD; }
/**
* @brief Sums another angle to the current one.
* @param other Another Angle object
* @return Result of sum
*/
Angle operator+=(Angle other) {
value_ = static_cast<T>(value_ + other.value_);
return *this;
}
/**
* @brief Subtracts another angle from the current one.
* @param other Another Angle object
* @return Result of subtraction
*/
Angle operator-=(Angle other) {
value_ = static_cast<T>(value_ - other.value_);
return *this;
}
/**
* @brief Multiplies angle by scalar
* @param s A scalar
* @return Result of multiplication
*/
template <typename Scalar>
Angle operator*=(Scalar s) {
value_ = static_cast<T>(std::lround(value_ * s));
return *this;
}
/**
* @brief Divides angle by scalar
* @param s A scalar
* @return Result of division
*/
template <typename Scalar>
Angle operator/=(Scalar s) {
value_ = static_cast<T>(std::lround(value_ / s));
return *this;
}
private:
T value_;
};
using Angle8 = Angle<int8_t>;
using Angle16 = Angle<int16_t>;
using Angle32 = Angle<int32_t>;
using Angle64 = Angle<int64_t>;
/**
* @brief Sums two angles
* @param lhs An Angle object
* @param rhs An Angle object
* @return Result of addition
*/
template <typename T>
Angle<T> operator+(Angle<T> lhs, Angle<T> rhs) {
lhs += rhs;
return lhs;
}
/**
* @brief Subtracts two angles
* @param lhs An Angle object
* @param rhs An Angle object
* @return Result of subtraction
*/
template <typename T>
Angle<T> operator-(Angle<T> lhs, Angle<T> rhs) {
lhs -= rhs;
return lhs;
}
/**
* @brief Multiplies an Angle by a scalar
* @param lhs An Angle object
* @param rhs A scalar
* @return Result of multiplication
*/
template <typename T, typename Scalar>
Angle<T> operator*(Angle<T> lhs, Scalar rhs) {
lhs *= rhs;
return lhs;
}
/**
* @brief Multiplies an Angle by a scalar
* @param lhs An Angle object
* @param rhs A scalar
* @return Result of multiplication
*/
template <typename T, typename Scalar>
Angle<T> operator*(Scalar lhs, Angle<T> rhs) {
rhs *= lhs;
return rhs;
}
/**
* @brief Divides an Angle by a scalar
* @param lhs An Angle object
* @param rhs A scalar
* @return Result of division
*/
template <typename T, typename Scalar>
Angle<T> operator/(Angle<T> lhs, Scalar rhs) {
lhs /= rhs;
return lhs;
}
/**
* @brief Divides an Angle by a scalar
* @param lhs An Angle object
* @param rhs A scalar
* @return Result of division
*/
template <typename T>
double operator/(Angle<T> lhs, Angle<T> rhs) {
return static_cast<double>(lhs.raw()) / rhs.raw();
}
/**
* @brief Tests two Angle objects for equality
* @param lhs An Angle object
* @param rhs An Angle object
* @return lhs == rhs
*/
template <typename T>
bool operator==(Angle<T> lhs, Angle<T> rhs) {
return lhs.raw() == rhs.raw();
}
/**
* @brief Tests two Angle objects for inequality
* @param lhs An Angle object
* @param rhs An Angle object
* @return lhs != rhs
*/
template <typename T>
bool operator!=(Angle<T> lhs, Angle<T> rhs) {
return !(lhs == rhs);
}
// Fast trigonometric functions. Single precision is sufficient for Angle16 and
// Angle8.
float sin(Angle16 a);
float cos(Angle16 a);
float tan(Angle16 a);
float sin(Angle8 a);
float cos(Angle8 a);
float tan(Angle8 a);
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/angle.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/angle.h"
#include "modules/common/math/sin_table.h"
namespace apollo {
namespace common {
namespace math {
float sin(Angle16 a) {
int16_t idx = a.raw();
if (idx < -Angle16::RAW_PI_2) {
idx = static_cast<int16_t>(idx + Angle16::RAW_PI);
return -SIN_TABLE[idx % SIN_TABLE_SIZE];
}
if (idx < 0) {
return -SIN_TABLE[(-idx) % SIN_TABLE_SIZE];
}
if (idx < Angle16::RAW_PI_2) {
return SIN_TABLE[idx % SIN_TABLE_SIZE];
}
idx = static_cast<int16_t>(Angle16::RAW_PI - idx);
return SIN_TABLE[idx % SIN_TABLE_SIZE];
}
float cos(Angle16 a) {
Angle16 b(static_cast<int16_t>(Angle16::RAW_PI_2 - a.raw()));
return sin(b);
}
float tan(Angle16 a) { return sin(a) / cos(a); }
float sin(Angle8 a) {
Angle16 b(static_cast<int16_t>(a.raw() << 8));
return sin(b);
}
float cos(Angle8 a) {
Angle16 b(static_cast<int16_t>(a.raw() << 8));
return cos(b);
}
float tan(Angle8 a) {
Angle16 b(static_cast<int16_t>(a.raw() << 8));
return tan(b);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/math_utils.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Math-related util functions.
*/
#pragma once
#include <cmath>
#include <limits>
#include <type_traits>
#include <utility>
#include "Eigen/Dense"
#include "modules/common/math/vec2d.h"
/**
* @namespace apollo::common::math
* @brief apollo::common::math
*/
namespace apollo {
namespace common {
namespace math {
double Sqr(const double x);
/**
* @brief Cross product between two 2-D vectors from the common start point,
* and end at two other points.
* @param start_point The common start point of two vectors in 2-D.
* @param end_point_1 The end point of the first vector.
* @param end_point_2 The end point of the second vector.
*
* @return The cross product result.
*/
double CrossProd(const Vec2d &start_point, const Vec2d &end_point_1,
const Vec2d &end_point_2);
/**
* @brief Inner product between two 2-D vectors from the common start point,
* and end at two other points.
* @param start_point The common start point of two vectors in 2-D.
* @param end_point_1 The end point of the first vector.
* @param end_point_2 The end point of the second vector.
*
* @return The inner product result.
*/
double InnerProd(const Vec2d &start_point, const Vec2d &end_point_1,
const Vec2d &end_point_2);
/**
* @brief Cross product between two vectors.
* One vector is formed by 1st and 2nd parameters of the function.
* The other vector is formed by 3rd and 4th parameters of the function.
* @param x0 The x coordinate of the first vector.
* @param y0 The y coordinate of the first vector.
* @param x1 The x coordinate of the second vector.
* @param y1 The y coordinate of the second vector.
*
* @return The cross product result.
*/
double CrossProd(const double x0, const double y0, const double x1,
const double y1);
/**
* @brief Inner product between two vectors.
* One vector is formed by 1st and 2nd parameters of the function.
* The other vector is formed by 3rd and 4th parameters of the function.
* @param x0 The x coordinate of the first vector.
* @param y0 The y coordinate of the first vector.
* @param x1 The x coordinate of the second vector.
* @param y1 The y coordinate of the second vector.
*
* @return The inner product result.
*/
double InnerProd(const double x0, const double y0, const double x1,
const double y1);
/**
* @brief Wrap angle to [0, 2 * PI).
* @param angle the original value of the angle.
* @return The wrapped value of the angle.
*/
double WrapAngle(const double angle);
/**
* @brief Normalize angle to [-PI, PI).
* @param angle the original value of the angle.
* @return The normalized value of the angle.
*/
double NormalizeAngle(const double angle);
/**
* @brief Calculate the difference between angle from and to
* @param from the start angle
* @param from the end angle
* @return The difference between from and to. The range is between [-PI, PI).
*/
double AngleDiff(const double from, const double to);
/**
* @brief Get a random integer between two integer values by a random seed.
* @param s The lower bound of the random integer.
* @param t The upper bound of the random integer.
* @param random_seed The random seed.
* @return A random integer between s and t based on the input random_seed.
*/
int RandomInt(const int s, const int t, unsigned int rand_seed = 1);
/**
* @brief Get a random double between two integer values by a random seed.
* @param s The lower bound of the random double.
* @param t The upper bound of the random double.
* @param random_seed The random seed.
* @return A random double between s and t based on the input random_seed.
*/
double RandomDouble(const double s, const double t, unsigned int rand_seed = 1);
/**
* @brief Compute squared value.
* @param value The target value to get its squared value.
* @return Squared value of the input value.
*/
template <typename T>
inline T Square(const T value) {
return value * value;
}
/**
* @brief Clamp a value between two bounds.
* If the value goes beyond the bounds, return one of the bounds,
* otherwise, return the original value.
* @param value The original value to be clamped.
* @param bound1 One bound to clamp the value.
* @param bound2 The other bound to clamp the value.
* @return The clamped value.
*/
template <typename T>
T Clamp(const T value, T bound1, T bound2) {
if (bound1 > bound2) {
std::swap(bound1, bound2);
}
if (value < bound1) {
return bound1;
} else if (value > bound2) {
return bound2;
}
return value;
}
// Gaussian
double Gaussian(const double u, const double std, const double x);
inline double Sigmoid(const double x) { return 1.0 / (1.0 + std::exp(-x)); }
// Rotate a 2d vector counter-clockwise by theta
Eigen::Vector2d RotateVector2d(const Eigen::Vector2d &v_in, const double theta);
inline std::pair<double, double> RFUToFLU(const double x, const double y) {
return std::make_pair(y, -x);
}
inline std::pair<double, double> FLUToRFU(const double x, const double y) {
return std::make_pair(-y, x);
}
inline void L2Norm(int feat_dim, float *feat_data) {
if (feat_dim == 0) {
return;
}
// feature normalization
float l2norm = 0.0f;
for (int i = 0; i < feat_dim; ++i) {
l2norm += feat_data[i] * feat_data[i];
}
if (l2norm == 0) {
float val = 1.f / std::sqrt(static_cast<float>(feat_dim));
for (int i = 0; i < feat_dim; ++i) {
feat_data[i] = val;
}
} else {
l2norm = std::sqrt(l2norm);
for (int i = 0; i < feat_dim; ++i) {
feat_data[i] /= l2norm;
}
}
}
// Cartesian coordinates to Polar coordinates
std::pair<double, double> Cartesian2Polar(double x, double y);
template <class T>
typename std::enable_if<!std::numeric_limits<T>::is_integer, bool>::type
almost_equal(T x, T y, int ulp) {
// the machine epsilon has to be scaled to the magnitude of the values used
// and multiplied by the desired precision in ULPs (units in the last place)
// unless the result is subnormal
return std::fabs(x - y) <=
std::numeric_limits<T>::epsilon() * std::fabs(x + y) * ulp ||
std::fabs(x - y) < std::numeric_limits<T>::min();
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/integral.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/integral.h"
#include <array>
#include "cyber/common/log.h"
namespace apollo {
namespace common {
namespace math {
double IntegrateBySimpson(const std::vector<double>& func, const double dx,
const std::size_t nsteps) {
CHECK_EQ(1U, nsteps & 1);
double sum1 = 0.0;
double sum2 = 0.0;
for (std::size_t i = 1; i + 1 < nsteps; ++i) {
if ((i & 1) != 0) {
sum1 += func[i];
} else {
sum2 += func[i];
}
}
return dx / 3.0 * (4.0 * sum1 + 2.0 * sum2 + func[0] + func[nsteps - 1]);
}
double IntegrateByTrapezoidal(const std::vector<double>& func, const double dx,
const std::size_t nsteps) {
double sum = 0;
for (std::size_t i = 1; i + 1 < nsteps; ++i) {
sum += func[i];
}
return dx * sum + 0.5 * dx * (func[0] + func[nsteps - 1]);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/cartesian_frenet_conversion.h | /******************************************************************************
* Copyright 2018 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
**/
#pragma once
#include <array>
#include "modules/common/math/vec2d.h"
namespace apollo {
namespace common {
namespace math {
// Notations:
// s_condition = [s, s_dot, s_ddot]
// s: longitudinal coordinate w.r.t reference line.
// s_dot: ds / dt
// s_ddot: d(s_dot) / dt
// d_condition = [d, d_prime, d_pprime]
// d: lateral coordinate w.r.t. reference line
// d_prime: dd / ds
// d_pprime: d(d_prime) / ds
// l: the same as d.
class CartesianFrenetConverter {
public:
CartesianFrenetConverter() = delete;
/**
* Convert a vehicle state in Cartesian frame to Frenet frame.
* Decouple a 2d movement to two independent 1d movement w.r.t. reference
* line.
* The lateral movement is a function of longitudinal accumulated distance s
* to achieve better satisfaction of nonholonomic constraints.
*/
static void cartesian_to_frenet(const double rs, const double rx,
const double ry, const double rtheta,
const double rkappa, const double rdkappa,
const double x, const double y,
const double v, const double a,
const double theta, const double kappa,
std::array<double, 3>* const ptr_s_condition,
std::array<double, 3>* const ptr_d_condition);
static void cartesian_to_frenet(const double rs, const double rx,
const double ry, const double rtheta,
const double x, const double y, double* ptr_s,
double* ptr_d);
/**
* Convert a vehicle state in Frenet frame to Cartesian frame.
* Combine two independent 1d movement w.r.t. reference line to a 2d movement.
*/
static void frenet_to_cartesian(const double rs, const double rx,
const double ry, const double rtheta,
const double rkappa, const double rdkappa,
const std::array<double, 3>& s_condition,
const std::array<double, 3>& d_condition,
double* const ptr_x, double* const ptr_y,
double* const ptr_theta,
double* const ptr_kappa, double* const ptr_v,
double* const ptr_a);
// given sl point extract x, y, theta, kappa
static double CalculateTheta(const double rtheta, const double rkappa,
const double l, const double dl);
static double CalculateKappa(const double rkappa, const double rdkappa,
const double l, const double dl,
const double ddl);
static Vec2d CalculateCartesianPoint(const double rtheta, const Vec2d& rpoint,
const double l);
/**
* @brief: given sl, theta, and road's theta, kappa, extract derivative l,
*second order derivative l:
*/
static double CalculateLateralDerivative(const double theta_ref,
const double theta, const double l,
const double kappa_ref);
// given sl, theta, and road's theta, kappa, extract second order derivative
static double CalculateSecondOrderLateralDerivative(
const double theta_ref, const double theta, const double kappa_ref,
const double kappa, const double dkappa_ref, const double l);
};
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/mpc_osqp.h | /******************************************************************************
* Copyright 2019 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#pragma once
#include <algorithm>
#include <limits>
#include <memory>
#include <utility>
#include <vector>
#include "Eigen/Eigen"
#include "osqp/osqp.h"
#include "cyber/common/log.h"
namespace apollo {
namespace common {
namespace math {
class MpcOsqp {
public:
/**
* @brief Solver for discrete-time model predictive control problem.
* @param matrix_a The system dynamic matrix
* @param matrix_b The control matrix
* @param matrix_q The cost matrix for control state
* @param matrix_lower The lower bound control constrain matrix
* @param matrix_upper The upper bound control constrain matrix
* @param matrix_initial_state The initial state matrix
* @param max_iter The maximum iterations
*/
MpcOsqp(const Eigen::MatrixXd &matrix_a, const Eigen::MatrixXd &matrix_b,
const Eigen::MatrixXd &matrix_q, const Eigen::MatrixXd &matrix_r,
const Eigen::MatrixXd &matrix_initial_x,
const Eigen::MatrixXd &matrix_u_lower,
const Eigen::MatrixXd &matrix_u_upper,
const Eigen::MatrixXd &matrix_x_lower,
const Eigen::MatrixXd &matrix_x_upper,
const Eigen::MatrixXd &matrix_x_ref, const int max_iter,
const int horizon, const double eps_abs);
// control vector
bool Solve(std::vector<double> *control_cmd);
private:
void CalculateKernel(std::vector<c_float> *P_data,
std::vector<c_int> *P_indices,
std::vector<c_int> *P_indptr);
void CalculateEqualityConstraint(std::vector<c_float> *A_data,
std::vector<c_int> *A_indices,
std::vector<c_int> *A_indptr);
void CalculateGradient();
void CalculateConstraintVectors();
OSQPSettings *Settings();
OSQPData *Data();
void FreeData(OSQPData *data);
template <typename T>
T *CopyData(const std::vector<T> &vec) {
T *data = new T[vec.size()];
memcpy(data, vec.data(), sizeof(T) * vec.size());
return data;
}
private:
Eigen::MatrixXd matrix_a_;
Eigen::MatrixXd matrix_b_;
Eigen::MatrixXd matrix_q_;
Eigen::MatrixXd matrix_r_;
Eigen::MatrixXd matrix_initial_x_;
const Eigen::MatrixXd matrix_u_lower_;
const Eigen::MatrixXd matrix_u_upper_;
const Eigen::MatrixXd matrix_x_lower_;
const Eigen::MatrixXd matrix_x_upper_;
const Eigen::MatrixXd matrix_x_ref_;
int max_iteration_;
size_t horizon_;
double eps_abs_;
size_t state_dim_;
size_t control_dim_;
size_t num_param_;
int num_constraint_;
Eigen::VectorXd gradient_;
Eigen::VectorXd lowerBound_;
Eigen::VectorXd upperBound_;
};
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/path_matcher.cc | /******************************************************************************
* Copyright 2018 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
**/
#include "modules/common/math/path_matcher.h"
#include <algorithm>
#include <cmath>
#include <vector>
#include "glog/logging.h"
#include "modules/common/math/linear_interpolation.h"
namespace apollo {
namespace common {
namespace math {
PathPoint PathMatcher::MatchToPath(const std::vector<PathPoint>& reference_line,
const double x, const double y) {
CHECK_GT(reference_line.size(), 0U);
auto func_distance_square = [](const PathPoint& point, const double x,
const double y) {
double dx = point.x() - x;
double dy = point.y() - y;
return dx * dx + dy * dy;
};
double distance_min = func_distance_square(reference_line.front(), x, y);
std::size_t index_min = 0;
for (std::size_t i = 1; i < reference_line.size(); ++i) {
double distance_temp = func_distance_square(reference_line[i], x, y);
if (distance_temp < distance_min) {
distance_min = distance_temp;
index_min = i;
}
}
std::size_t index_start = (index_min == 0) ? index_min : index_min - 1;
std::size_t index_end =
(index_min + 1 == reference_line.size()) ? index_min : index_min + 1;
if (index_start == index_end) {
return reference_line[index_start];
}
return FindProjectionPoint(reference_line[index_start],
reference_line[index_end], x, y);
}
std::pair<double, double> PathMatcher::GetPathFrenetCoordinate(
const std::vector<PathPoint>& reference_line, const double x,
const double y) {
auto matched_path_point = MatchToPath(reference_line, x, y);
double rtheta = matched_path_point.theta();
double rx = matched_path_point.x();
double ry = matched_path_point.y();
double delta_x = x - rx;
double delta_y = y - ry;
double side = std::cos(rtheta) * delta_y - std::sin(rtheta) * delta_x;
std::pair<double, double> relative_coordinate;
relative_coordinate.first = matched_path_point.s();
relative_coordinate.second =
std::copysign(std::hypot(delta_x, delta_y), side);
return relative_coordinate;
}
PathPoint PathMatcher::MatchToPath(const std::vector<PathPoint>& reference_line,
const double s) {
auto comp = [](const PathPoint& point, const double s) {
return point.s() < s;
};
auto it_lower =
std::lower_bound(reference_line.begin(), reference_line.end(), s, comp);
if (it_lower == reference_line.begin()) {
return reference_line.front();
} else if (it_lower == reference_line.end()) {
return reference_line.back();
}
// interpolate between it_lower - 1 and it_lower
// return interpolate(*(it_lower - 1), *it_lower, s);
return InterpolateUsingLinearApproximation(*(it_lower - 1), *it_lower, s);
}
PathPoint PathMatcher::FindProjectionPoint(const PathPoint& p0,
const PathPoint& p1, const double x,
const double y) {
double v0x = x - p0.x();
double v0y = y - p0.y();
double v1x = p1.x() - p0.x();
double v1y = p1.y() - p0.y();
double v1_norm = std::sqrt(v1x * v1x + v1y * v1y);
double dot = v0x * v1x + v0y * v1y;
double delta_s = dot / v1_norm;
return InterpolateUsingLinearApproximation(p0, p1, p0.s() + delta_s);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/aabox2d.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/aabox2d.h"
#include <algorithm>
#include <cmath>
#include "absl/strings/str_cat.h"
#include "cyber/common/log.h"
#include "modules/common/math/math_utils.h"
namespace apollo {
namespace common {
namespace math {
AABox2d::AABox2d(const Vec2d ¢er, const double length, const double width)
: center_(center),
length_(length),
width_(width),
half_length_(length / 2.0),
half_width_(width / 2.0) {
CHECK_GT(length_, -kMathEpsilon);
CHECK_GT(width_, -kMathEpsilon);
}
AABox2d::AABox2d(const Vec2d &one_corner, const Vec2d &opposite_corner)
: AABox2d((one_corner + opposite_corner) / 2.0,
std::abs(one_corner.x() - opposite_corner.x()),
std::abs(one_corner.y() - opposite_corner.y())) {}
AABox2d::AABox2d(const std::vector<Vec2d> &points) {
ACHECK(!points.empty());
double min_x = points[0].x();
double max_x = points[0].x();
double min_y = points[0].y();
double max_y = points[0].y();
for (const auto &point : points) {
min_x = std::min(min_x, point.x());
max_x = std::max(max_x, point.x());
min_y = std::min(min_y, point.y());
max_y = std::max(max_y, point.y());
}
center_ = {(min_x + max_x) / 2.0, (min_y + max_y) / 2.0};
length_ = max_x - min_x;
width_ = max_y - min_y;
half_length_ = length_ / 2.0;
half_width_ = width_ / 2.0;
}
void AABox2d::GetAllCorners(std::vector<Vec2d> *const corners) const {
CHECK_NOTNULL(corners)->clear();
corners->reserve(4);
corners->emplace_back(center_.x() + half_length_, center_.y() - half_width_);
corners->emplace_back(center_.x() + half_length_, center_.y() + half_width_);
corners->emplace_back(center_.x() - half_length_, center_.y() + half_width_);
corners->emplace_back(center_.x() - half_length_, center_.y() - half_width_);
}
bool AABox2d::IsPointIn(const Vec2d &point) const {
return std::abs(point.x() - center_.x()) <= half_length_ + kMathEpsilon &&
std::abs(point.y() - center_.y()) <= half_width_ + kMathEpsilon;
}
bool AABox2d::IsPointOnBoundary(const Vec2d &point) const {
const double dx = std::abs(point.x() - center_.x());
const double dy = std::abs(point.y() - center_.y());
return (std::abs(dx - half_length_) <= kMathEpsilon &&
dy <= half_width_ + kMathEpsilon) ||
(std::abs(dy - half_width_) <= kMathEpsilon &&
dx <= half_length_ + kMathEpsilon);
}
double AABox2d::DistanceTo(const Vec2d &point) const {
const double dx = std::abs(point.x() - center_.x()) - half_length_;
const double dy = std::abs(point.y() - center_.y()) - half_width_;
if (dx <= 0.0) {
return std::max(0.0, dy);
}
if (dy <= 0.0) {
return dx;
}
return hypot(dx, dy);
}
double AABox2d::DistanceTo(const AABox2d &box) const {
const double dx =
std::abs(box.center_x() - center_.x()) - box.half_length() - half_length_;
const double dy =
std::abs(box.center_y() - center_.y()) - box.half_width() - half_width_;
if (dx <= 0.0) {
return std::max(0.0, dy);
}
if (dy <= 0.0) {
return dx;
}
return hypot(dx, dy);
}
bool AABox2d::HasOverlap(const AABox2d &box) const {
return std::abs(box.center_x() - center_.x()) <=
box.half_length() + half_length_ &&
std::abs(box.center_y() - center_.y()) <=
box.half_width() + half_width_;
}
void AABox2d::Shift(const Vec2d &shift_vec) { center_ += shift_vec; }
void AABox2d::MergeFrom(const AABox2d &other_box) {
const double x1 = std::min(min_x(), other_box.min_x());
const double x2 = std::max(max_x(), other_box.max_x());
const double y1 = std::min(min_y(), other_box.min_y());
const double y2 = std::max(max_y(), other_box.max_y());
center_ = Vec2d((x1 + x2) / 2.0, (y1 + y2) / 2.0);
length_ = x2 - x1;
width_ = y2 - y1;
half_length_ = length_ / 2.0;
half_width_ = width_ / 2.0;
}
void AABox2d::MergeFrom(const Vec2d &other_point) {
const double x1 = std::min(min_x(), other_point.x());
const double x2 = std::max(max_x(), other_point.x());
const double y1 = std::min(min_y(), other_point.y());
const double y2 = std::max(max_y(), other_point.y());
center_ = Vec2d((x1 + x2) / 2.0, (y1 + y2) / 2.0);
length_ = x2 - x1;
width_ = y2 - y1;
half_length_ = length_ / 2.0;
half_width_ = width_ / 2.0;
}
std::string AABox2d::DebugString() const {
return absl::StrCat("aabox2d ( center = ", center_.DebugString(),
" length = ", length_, " width = ", width_, " )");
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/sin_table.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Exports the SIN_TABLE, used by the Angle class.
*/
#pragma once
/**
* @namespace apollo::common::math
* @brief apollo::common::math
*/
namespace apollo {
namespace common {
namespace math {
//! Used by Angle class to speed-up computation of trigonometric functions.
#define SIN_TABLE_SIZE 16385
extern const float SIN_TABLE[SIN_TABLE_SIZE];
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/box2d_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/box2d.h"
#include "gtest/gtest.h"
#include "modules/common/math/line_segment2d.h"
#include "modules/common/math/math_utils.h"
#include "modules/common/math/polygon2d.h"
namespace apollo {
namespace common {
namespace math {
namespace {
bool CheckBoxOverlapSlow(const Box2d &box1, const Box2d &box2,
bool *const ambiguous) {
double headings[4] = {box1.heading(), box1.heading() + M_PI_2, box2.heading(),
box2.heading() + M_PI_2};
*ambiguous = false;
for (int k = 0; k < 4; ++k) {
const double heading = headings[k];
const double cos_heading = cos(heading);
const double sin_heading = sin(heading);
std::vector<Vec2d> c1, c2;
box1.GetAllCorners(&c1);
box2.GetAllCorners(&c2);
double s1 = std::numeric_limits<double>::infinity();
double t1 = -std::numeric_limits<double>::infinity();
double s2 = std::numeric_limits<double>::infinity();
double t2 = -std::numeric_limits<double>::infinity();
for (const auto &p : c1) {
const double proj = p.x() * cos_heading + p.y() * sin_heading;
if (proj < s1) {
s1 = proj;
}
if (proj > t1) {
t1 = proj;
}
}
for (const auto &p : c2) {
const double proj = p.x() * cos_heading + p.y() * sin_heading;
if (proj < s2) {
s2 = proj;
}
if (proj > t2) {
t2 = proj;
}
}
if (std::abs(s1 - t2) <= 1e-5 || std::abs(s2 - t1) <= 1e-5) {
*ambiguous = true;
}
if (s1 > t2 || s2 > t1) {
return false;
}
}
return true;
}
Box2d box1({0, 0}, 0, 4, 2);
Box2d box2({5, 2}, 0, 4, 2);
Box2d box3(LineSegment2d({2, 3}, {6, 3}), 2);
Box2d box4({7, 8}, M_PI_4, 5.0, 3.0);
Box2d box5({-2, -3}, -M_PI, 0.0, 0.0);
Box2d box6(LineSegment2d({2, 3}, {6, 3}), 0.0);
Box2d box7(AABox2d({4, 5}, 0, 0));
} // namespace
TEST(Box2dTest, DebugString) {
Box2d box1({0, 0}, 0, 4, 2);
Box2d box2({5, 2}, 0, 4, 2);
EXPECT_EQ(box1.DebugString(),
"box2d ( center = vec2d ( x = 0 y = 0 ) heading = 0 length = 4 "
"width = 2 )");
EXPECT_EQ(box2.DebugString(),
"box2d ( center = vec2d ( x = 5 y = 2 ) heading = 0 length = 4 "
"width = 2 )");
}
TEST(Box2dTest, GetAllCorners) {
std::vector<Vec2d> corners1;
box1.GetAllCorners(&corners1);
EXPECT_NEAR(corners1[0].x(), 2.0, 1e-5);
EXPECT_NEAR(corners1[0].y(), -1.0, 1e-5);
EXPECT_NEAR(corners1[1].x(), 2.0, 1e-5);
EXPECT_NEAR(corners1[1].y(), 1.0, 1e-5);
EXPECT_NEAR(corners1[2].x(), -2.0, 1e-5);
EXPECT_NEAR(corners1[2].y(), 1.0, 1e-5);
EXPECT_NEAR(corners1[3].x(), -2.0, 1e-5);
EXPECT_NEAR(corners1[3].y(), -1.0, 1e-5);
std::vector<Vec2d> corners2;
box3.GetAllCorners(&corners2);
EXPECT_NEAR(corners2[0].x(), 6.0, 1e-5);
EXPECT_NEAR(corners2[0].y(), 2.0, 1e-5);
EXPECT_NEAR(corners2[1].x(), 6.0, 1e-5);
EXPECT_NEAR(corners2[1].y(), 4.0, 1e-5);
EXPECT_NEAR(corners2[2].x(), 2.0, 1e-5);
EXPECT_NEAR(corners2[2].y(), 4.0, 1e-5);
EXPECT_NEAR(corners2[3].x(), 2.0, 1e-5);
EXPECT_NEAR(corners2[3].y(), 2.0, 1e-5);
}
TEST(Box2dTest, CenterAndLength) {
EXPECT_NEAR(4, box3.center().x(), 1e-5);
EXPECT_NEAR(3, box3.center().y(), 1e-5);
EXPECT_NEAR(4, box3.length(), 1e-5);
EXPECT_NEAR(2, box3.width(), 1e-5);
EXPECT_NEAR(2, box3.half_length(), 1e-5);
EXPECT_NEAR(1, box3.half_width(), 1e-5);
EXPECT_NEAR(std::hypot(4.0, 2.0), box3.diagonal(), 1e-5);
}
TEST(Box2dTest, HasOverlap) {
EXPECT_FALSE(box1.HasOverlap(box2));
EXPECT_FALSE(box1.HasOverlap(box3));
EXPECT_FALSE(box1.HasOverlap(box4));
EXPECT_FALSE(box2.HasOverlap(box4));
EXPECT_FALSE(box3.HasOverlap(box4));
EXPECT_TRUE(box1.HasOverlap(LineSegment2d({0, 0}, {1, 1})));
EXPECT_TRUE(box1.HasOverlap(LineSegment2d({0, 0}, {3, 3})));
EXPECT_TRUE(box1.HasOverlap(LineSegment2d({0, -3}, {0, 3})));
EXPECT_TRUE(box1.HasOverlap(LineSegment2d({4, 0}, {-4, 0})));
EXPECT_TRUE(box1.HasOverlap(LineSegment2d({-4, -4}, {4, 4})));
EXPECT_TRUE(box1.HasOverlap(LineSegment2d({4, -4}, {-4, 4})));
EXPECT_FALSE(box1.HasOverlap(LineSegment2d({-4, -4}, {4, -4})));
EXPECT_FALSE(box1.HasOverlap(LineSegment2d({4, -4}, {4, 4})));
}
TEST(Box2dTest, GetAABox) {
AABox2d aabox1 = box1.GetAABox();
AABox2d aabox2 = box2.GetAABox();
AABox2d aabox3 = box3.GetAABox();
AABox2d aabox4 = box4.GetAABox();
EXPECT_NEAR(aabox1.center_x(), 0.0, 1e-5);
EXPECT_NEAR(aabox1.center_y(), 0.0, 1e-5);
EXPECT_NEAR(aabox1.length(), 4.0, 1e-5);
EXPECT_NEAR(aabox1.width(), 2.0, 1e-5);
EXPECT_NEAR(aabox2.center_x(), 5.0, 1e-5);
EXPECT_NEAR(aabox2.center_y(), 2.0, 1e-5);
EXPECT_NEAR(aabox2.length(), 4.0, 1e-5);
EXPECT_NEAR(aabox2.width(), 2.0, 1e-5);
EXPECT_NEAR(aabox3.center_x(), 4.0, 1e-5);
EXPECT_NEAR(aabox3.center_y(), 3.0, 1e-5);
EXPECT_NEAR(aabox3.length(), 4.0, 1e-5);
EXPECT_NEAR(aabox3.width(), 2.0, 1e-5);
EXPECT_NEAR(aabox4.center_x(), 7.0, 1e-5);
EXPECT_NEAR(aabox4.center_y(), 8.0, 1e-5);
EXPECT_NEAR(aabox4.length(), 4.0 * sqrt(2.0), 1e-5);
EXPECT_NEAR(aabox4.width(), 4.0 * sqrt(2.0), 1e-5);
}
TEST(Box2dTest, DistanceTo) {
EXPECT_NEAR(box1.DistanceTo({3, 0}), 1.0, 1e-5);
EXPECT_NEAR(box1.DistanceTo({-3, 0}), 1.0, 1e-5);
EXPECT_NEAR(box1.DistanceTo({0, 2}), 1.0, 1e-5);
EXPECT_NEAR(box1.DistanceTo({0, -2}), 1.0, 1e-5);
EXPECT_NEAR(box1.DistanceTo({0, 0}), 0.0, 1e-5);
EXPECT_NEAR(box1.DistanceTo({0, 1}), 0.0, 1e-5);
EXPECT_NEAR(box1.DistanceTo({1, 0}), 0.0, 1e-5);
EXPECT_NEAR(box1.DistanceTo({0, -1}), 0.0, 1e-5);
EXPECT_NEAR(box1.DistanceTo({-1, 0}), 0.0, 1e-5);
EXPECT_NEAR(box1.DistanceTo(LineSegment2d({-4, -4}, {4, 4})), 0.0, 1e-5);
EXPECT_NEAR(box1.DistanceTo(LineSegment2d({4, -4}, {-4, 4})), 0.0, 1e-5);
EXPECT_NEAR(box1.DistanceTo(LineSegment2d({0, 2}, {4, 4})), 1.0, 1e-5);
EXPECT_NEAR(box1.DistanceTo(LineSegment2d({2, 2}, {3, 1})),
std::sqrt(2.0) / 2.0, 1e-5);
}
TEST(Box2dTest, IsPointIn) {
EXPECT_TRUE(box1.IsPointIn({0, 0}));
EXPECT_TRUE(box1.IsPointIn({1, 0.5}));
EXPECT_TRUE(box1.IsPointIn({-0.5, -1}));
EXPECT_TRUE(box1.IsPointIn({2, 1}));
EXPECT_FALSE(box1.IsPointIn({-3, 0}));
EXPECT_FALSE(box1.IsPointIn({0, 2}));
EXPECT_FALSE(box1.IsPointIn({-4, -2}));
}
TEST(Box2dTest, IsPointOnBoundary) {
EXPECT_FALSE(box1.IsPointOnBoundary({0, 0}));
EXPECT_FALSE(box1.IsPointOnBoundary({1, 0.5}));
EXPECT_TRUE(box1.IsPointOnBoundary({-0.5, -1}));
EXPECT_TRUE(box1.IsPointOnBoundary({2, 0.5}));
EXPECT_TRUE(box1.IsPointOnBoundary({-2, 1}));
EXPECT_FALSE(box1.IsPointOnBoundary({-3, 0}));
EXPECT_FALSE(box1.IsPointOnBoundary({0, 2}));
EXPECT_FALSE(box1.IsPointOnBoundary({-4, -2}));
}
TEST(Box2dTest, RotateFromCenterAndShift) {
Box2d box({0, 0}, 0, 4, 2);
std::vector<Vec2d> corners;
EXPECT_NEAR(box.heading(), 0.0, 1e-5);
box.RotateFromCenter(M_PI_2);
EXPECT_NEAR(box.heading(), M_PI_2, 1e-5);
box.GetAllCorners(&corners);
EXPECT_NEAR(corners[0].x(), 1.0, 1e-5);
EXPECT_NEAR(corners[0].y(), 2.0, 1e-5);
EXPECT_NEAR(corners[1].x(), -1.0, 1e-5);
EXPECT_NEAR(corners[1].y(), 2.0, 1e-5);
EXPECT_NEAR(corners[2].x(), -1.0, 1e-5);
EXPECT_NEAR(corners[2].y(), -2.0, 1e-5);
EXPECT_NEAR(corners[3].x(), 1.0, 1e-5);
EXPECT_NEAR(corners[3].y(), -2.0, 1e-5);
box.Shift({30, 40});
box.GetAllCorners(&corners);
EXPECT_NEAR(corners[0].x(), 31.0, 1e-5);
EXPECT_NEAR(corners[0].y(), 42.0, 1e-5);
EXPECT_NEAR(corners[1].x(), 29.0, 1e-5);
EXPECT_NEAR(corners[1].y(), 42.0, 1e-5);
EXPECT_NEAR(corners[2].x(), 29.0, 1e-5);
EXPECT_NEAR(corners[2].y(), 38.0, 1e-5);
EXPECT_NEAR(corners[3].x(), 31.0, 1e-5);
EXPECT_NEAR(corners[3].y(), 38.0, 1e-5);
}
TEST(Box2dTest, TestByRandom) {
bool ambiguous = false;
for (int iter = 0; iter < 10000; ++iter) {
const double x1 = RandomDouble(-10, 10);
const double y1 = RandomDouble(-10, 10);
const double x2 = RandomDouble(-10, 10);
const double y2 = RandomDouble(-10, 10);
const double heading1 = RandomDouble(0, M_PI * 2.0);
const double heading2 = RandomDouble(0, M_PI * 2.0);
const double l1 = RandomDouble(1, 5);
const double l2 = RandomDouble(1, 5);
const double w1 = RandomDouble(1, 5);
const double w2 = RandomDouble(1, 5);
const Box2d box1({x1, y1}, heading1, l1, w1);
const Box2d box2({x2, y2}, heading2, l2, w2);
bool overlap = CheckBoxOverlapSlow(box1, box2, &ambiguous);
if (!ambiguous) {
EXPECT_EQ(overlap, box1.HasOverlap(box2));
}
}
for (int iter = 0; iter < 100; ++iter) {
const double x = RandomDouble(-10, 10);
const double y = RandomDouble(-10, 10);
const double heading = RandomDouble(0, M_PI * 2.0);
const double length = RandomDouble(1, 5);
const double width = RandomDouble(1, 5);
const Box2d box({x, y}, heading, length, width);
const Polygon2d poly(box);
for (int iter2 = 0; iter2 < 1000; ++iter2) {
const double x = RandomDouble(-20, 20);
const double y = RandomDouble(-20, 20);
EXPECT_EQ(box.IsPointIn({x, y}), poly.IsPointIn({x, y}));
EXPECT_EQ(box.IsPointOnBoundary({x, y}), poly.IsPointOnBoundary({x, y}));
EXPECT_NEAR(box.DistanceTo({x, y}), poly.DistanceTo({x, y}), 1e-3);
const double other_x = RandomDouble(-20, 20);
const double other_y = RandomDouble(-20, 20);
const LineSegment2d segment({x, y}, {other_x, other_y});
EXPECT_EQ(box.HasOverlap(segment), poly.HasOverlap(segment));
EXPECT_NEAR(box.DistanceTo(segment), poly.DistanceTo(segment), 1e-3);
}
}
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/linear_quadratic_regulator.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Solver for discrete-time linear quadratic problem.
*/
#pragma once
#include "Eigen/Core"
/**
* @namespace apollo::common::math
* @brief apollo::common::math
*/
namespace apollo {
namespace common {
namespace math {
/**
* @brief Solver for discrete-time linear quadratic problem.
* @param A The system dynamic matrix
* @param B The control matrix
* @param Q The cost matrix for system state
* @param R The cost matrix for control output
* @param M is the cross term between x and u, i.e. x'Qx + u'Ru + 2x'Mu
* @param tolerance The numerical tolerance for solving Discrete
* Algebraic Riccati equation (DARE)
* @param max_num_iteration The maximum iterations for solving ARE
* @param ptr_K The feedback control matrix (pointer)
*/
void SolveLQRProblem(const Eigen::MatrixXd &A, const Eigen::MatrixXd &B,
const Eigen::MatrixXd &Q, const Eigen::MatrixXd &R,
const Eigen::MatrixXd &M, const double tolerance,
const uint max_num_iteration, Eigen::MatrixXd *ptr_K);
/**
* @brief Solver for discrete-time linear quadratic problem.
* @param A The system dynamic matrix
* @param B The control matrix
* @param Q The cost matrix for system state
* @param R The cost matrix for control output
* @param tolerance The numerical tolerance for solving Discrete
* Algebraic Riccati equation (DARE)
* @param max_num_iteration The maximum iterations for solving ARE
* @param ptr_K The feedback control matrix (pointer)
*/
void SolveLQRProblem(const Eigen::MatrixXd &A, const Eigen::MatrixXd &B,
const Eigen::MatrixXd &Q, const Eigen::MatrixXd &R,
const double tolerance, const uint max_num_iteration,
Eigen::MatrixXd *ptr_K);
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/curve_fitting.h | /******************************************************************************
* Copyright 2018 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
*/
#pragma once
#include <array>
#include "Eigen/Dense"
#include "modules/common/math/matrix_operations.h"
namespace apollo {
namespace common {
namespace math {
// The coef is in ascending order,
// i.e., f(x) = coef[0] + coef[1] * x + coef[2] * x^2 ...
template <std::size_t N>
double EvaluatePolynomial(const std::array<double, N + 1>& coef,
const double p) {
double r = 0.0;
for (int i = N; i >= 0; --i) {
r = r * p + coef[i];
}
return r;
}
// Fit a Nth order polynomial using M 2d points.
template <std::size_t N, std::size_t M>
std::array<double, N + 1> FitPolynomial(
const std::array<Eigen::Vector2d, M>& points,
double* ptr_error_square = nullptr) {
Eigen::Matrix<double, M, N + 1> X;
Eigen::Matrix<double, M, 1> Y;
for (std::size_t i = 0; i < M; ++i) {
double x = points[i].x();
double y = points[i].y();
X(i, 0) = 1.0;
for (std::size_t j = 1; j < N + 1; ++j) {
X(i, j) = X(i, j - 1) * x;
}
Y(i, 0) = y;
}
Eigen::Matrix<double, N + 1, 1> t =
PseudoInverse<double, N + 1, N + 1>(X.transpose() * X) * X.transpose() *
Y;
std::array<double, N + 1> coefs;
for (std::size_t i = 0; i < N + 1; ++i) {
coefs[i] = t(i, 0);
}
if (ptr_error_square != nullptr) {
*ptr_error_square = 0.0;
for (const Eigen::Vector2d& point : points) {
double error = EvaluatePolynomial(coefs, point.x()) - point.y();
*ptr_error_square += error * error;
}
}
return coefs;
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/BUILD | load("@rules_cc//cc:defs.bzl", "cc_binary", "cc_library", "cc_test")
load("//tools:cpplint.bzl", "cpplint")
load("//tools/install:install.bzl", "install")
install(
name = "install",
library_dest = "common/lib",
data_dest = "common",
runtime_dest = "common/bin",
targets = [
":libmath.so",
],
visibility = ["//visibility:public"],
)
cc_binary(
name = "libmath.so",
linkshared = True,
linkstatic = True,
deps = [
":angle",
":cartesian_frenet_conversion",
":curve_fitting",
":euler_angles_zxy",
":factorial",
":geometry",
":integral",
":kalman_filter",
":linear_interpolation",
":lqr",
":matrix_operations",
":mpc_osqp",
":path_matcher",
":quaternion",
":search",
":sin_table",
"//modules/common/math/qp_solver",
],
)
cc_library(
name = "math",
srcs = ["libmath.so"],
hdrs = glob(["*.h"]),
deps = [
"//cyber",
"//modules/common_msgs/basic_msgs:geometry_cc_proto",
"//modules/common_msgs/basic_msgs:pnc_point_cc_proto",
"//modules/common/util:util_tool",
"@com_google_absl//:absl",
"@eigen",
"@osqp",
],
visibility = ["//visibility:public"],
)
cc_library(
name = "math_utils",
srcs = ["math_utils.cc"],
hdrs = ["math_utils.h"],
alwayslink = True,
linkopts = ["-lm"],
deps = [
":vec2d",
"@eigen",
],
)
cc_library(
name = "vec2d",
srcs = ["vec2d.cc"],
hdrs = ["vec2d.h"],
alwayslink = True,
linkopts = ["-lm"],
deps = [
"//cyber",
"@com_google_absl//:absl",
],
)
cc_library(
name = "geometry",
srcs = [
"aabox2d.cc",
"box2d.cc",
"line_segment2d.cc",
"polygon2d.cc",
],
hdrs = [
"aabox2d.h",
"aaboxkdtree2d.h",
"box2d.h",
"line_segment2d.h",
"polygon2d.h",
],
alwayslink = True,
linkopts = ["-lm"],
deps = [
":math_utils",
"//cyber",
"//modules/common/util:util_tool",
"@com_google_absl//:absl",
"@osqp",
],
)
cc_library(
name = "sin_table",
srcs = ["sin_table.cc"],
hdrs = ["sin_table.h"],
alwayslink = True,
)
cc_library(
name = "angle",
srcs = ["angle.cc"],
hdrs = ["angle.h"],
alwayslink = True,
deps = [
":sin_table",
],
)
cc_library(
name = "euler_angles_zxy",
hdrs = ["euler_angles_zxy.h"],
alwayslink = True,
deps = [
":geometry",
"@eigen",
],
)
cc_library(
name = "quaternion",
hdrs = ["quaternion.h"],
alwayslink = True,
deps = [
":euler_angles_zxy",
":geometry",
"//modules/common_msgs/basic_msgs:geometry_cc_proto",
"@eigen",
],
)
cc_library(
name = "curve_fitting",
hdrs = ["curve_fitting.h"],
alwayslink = True,
deps = [
":matrix_operations",
"@eigen",
],
)
cc_library(
name = "matrix_operations",
srcs = ["matrix_operations.cc"],
hdrs = ["matrix_operations.h"],
alwayslink = True,
deps = [
"//cyber",
"@eigen",
],
)
cc_test(
name = "matrix_operations_test",
size = "small",
srcs = ["matrix_operations_test.cc"],
linkopts = ["-lm"],
deps = [
":matrix_operations",
"@com_google_googletest//:gtest_main",
],
)
cc_library(
name = "kalman_filter",
hdrs = ["kalman_filter.h"],
alwayslink = True,
deps = [
"//cyber",
":matrix_operations",
"@eigen",
],
)
cc_library(
name = "factorial",
hdrs = ["factorial.h"],
alwayslink = True,
)
cc_library(
name = "path_matcher",
srcs = ["path_matcher.cc"],
hdrs = ["path_matcher.h"],
deps = [
":linear_interpolation",
"//modules/common_msgs/basic_msgs:pnc_point_cc_proto",
],
alwayslink = True,
)
cc_library(
name = "mpc_osqp",
srcs = ["mpc_osqp.cc"],
hdrs = ["mpc_osqp.h"],
alwayslink = True,
deps = [
"//cyber",
"@eigen",
"@osqp",
],
)
cc_test(
name = "angle_test",
size = "small",
srcs = ["angle_test.cc"],
linkopts = [
"-lm",
],
deps = [
":angle",
"@com_google_googletest//:gtest_main",
],
)
cc_library(
name = "search",
srcs = ["search.cc"],
hdrs = ["search.h"],
alwayslink = True,
)
cc_library(
name = "linear_interpolation",
srcs = ["linear_interpolation.cc"],
hdrs = ["linear_interpolation.h"],
alwayslink = True,
deps = [
":geometry",
"//modules/common_msgs/basic_msgs:pnc_point_cc_proto",
],
)
cc_library(
name = "integral",
srcs = ["integral.cc"],
hdrs = ["integral.h"],
alwayslink = True,
deps = [
"//cyber",
],
)
cc_library(
name = "lqr",
srcs = ["linear_quadratic_regulator.cc"],
hdrs = ["linear_quadratic_regulator.h"],
alwayslink = True,
deps = [
"//cyber",
"@eigen",
],
)
cc_library(
name = "cartesian_frenet_conversion",
srcs = ["cartesian_frenet_conversion.cc"],
hdrs = ["cartesian_frenet_conversion.h"],
alwayslink = True,
deps = [
":geometry",
"//cyber",
"@eigen",
],
)
cc_library(
name = "hermite_spline",
hdrs = ["hermite_spline.h"],
alwayslink = True,
deps = [
"//cyber",
],
)
cc_test(
name = "mpc_osqp_test",
size = "small",
srcs = ["mpc_osqp_test.cc"],
deps = [
":mpc_osqp",
"//cyber",
"@com_google_googletest//:gtest_main",
],
)
cc_test(
name = "math_utils_test",
size = "small",
srcs = ["math_utils_test.cc"],
deps = [
":geometry",
"@com_google_googletest//:gtest_main",
],
)
cc_test(
name = "linear_interpolation_test",
size = "small",
srcs = ["linear_interpolation_test.cc"],
deps = [
":linear_interpolation",
"//cyber",
"@com_google_googletest//:gtest_main",
"@eigen",
],
)
cc_test(
name = "search_test",
size = "small",
srcs = ["search_test.cc"],
linkopts = [
"-lm",
],
deps = [
":search",
"@com_google_googletest//:gtest_main",
],
)
cc_test(
name = "integral_test",
size = "small",
srcs = ["integral_test.cc"],
linkopts = [
"-lm",
],
deps = [
":integral",
"@com_google_googletest//:gtest_main",
],
linkstatic = True,
)
cc_test(
name = "vec2d_test",
size = "small",
srcs = ["vec2d_test.cc"],
deps = [
":geometry",
"@com_google_googletest//:gtest_main",
],
)
cc_test(
name = "quaternion_test",
size = "small",
srcs = ["quaternion_test.cc"],
deps = [
":quaternion",
"@com_google_googletest//:gtest_main",
],
)
cc_test(
name = "euler_angles_zxy_test",
size = "small",
srcs = ["euler_angles_zxy_test.cc"],
deps = [
":euler_angles_zxy",
"@com_google_googletest//:gtest_main",
],
linkstatic = True,
)
cc_test(
name = "aabox2d_test",
size = "small",
srcs = ["aabox2d_test.cc"],
deps = [
":geometry",
"@com_google_googletest//:gtest_main",
],
)
cc_test(
name = "aaboxkdtree2d_test",
size = "small",
srcs = ["aaboxkdtree2d_test.cc"],
deps = [
":geometry",
"@com_google_googletest//:gtest_main",
],
)
cc_test(
name = "box2d_test",
size = "small",
srcs = ["box2d_test.cc"],
deps = [
":geometry",
"@com_google_googletest//:gtest_main",
],
)
cc_test(
name = "polygon2d_test",
size = "small",
srcs = ["polygon2d_test.cc"],
deps = [
":geometry",
"@com_google_googletest//:gtest_main",
],
)
cc_test(
name = "line_segment2d_test",
size = "small",
srcs = ["line_segment2d_test.cc"],
deps = [
":geometry",
"@com_google_googletest//:gtest_main",
],
linkstatic = True,
)
cc_test(
name = "kalman_filter_test",
size = "small",
srcs = ["kalman_filter_test.cc"],
linkopts = ["-lm"],
deps = [
":kalman_filter",
"@com_google_googletest//:gtest_main",
],
linkstatic = True,
)
cc_test(
name = "cartesian_frenet_conversion_test",
size = "small",
srcs = ["cartesian_frenet_conversion_test.cc"],
deps = [
":cartesian_frenet_conversion",
"@com_google_googletest//:gtest_main",
],
)
cpplint()
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/integral.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Functions to compute integral.
*/
#pragma once
#include <array>
#include <functional>
#include <utility>
#include <vector>
/**
* @namespace apollo::common::math
* @brief apollo::common::math
*/
namespace apollo {
namespace common {
namespace math {
double IntegrateBySimpson(const std::vector<double>& funv_vec, const double dx,
const std::size_t nsteps);
double IntegrateByTrapezoidal(const std::vector<double>& funv_vec,
const double dx, const std::size_t nsteps);
/**
* @brief Get the points and weights for different ordered Gauss-Legendre
* integration. Currently support order 2 - 10. Other input order will
* trigger compiling error.
*/
template <std::size_t N>
std::pair<std::array<double, N>, std::array<double, N>>
GetGaussLegendrePoints();
template <>
inline std::pair<std::array<double, 2>, std::array<double, 2>>
GetGaussLegendrePoints<2>() {
std::array<double, 2> x;
x[0] = -5.77350269189625764507e-01;
x[1] = 5.77350269189625764507e-01;
std::array<double, 2> w;
w[0] = 1.0;
w[1] = 1.0;
return std::make_pair(x, w);
}
template <>
inline std::pair<std::array<double, 3>, std::array<double, 3>>
GetGaussLegendrePoints<3>() {
std::array<double, 3> x;
x[0] = 0.00000000000000000000e+00;
x[1] = 7.74596669241483377010e-01;
x[2] = -7.74596669241483377010e-01;
std::array<double, 3> w;
w[0] = 8.88888888888888888877e-01;
w[1] = 5.55555555555555555562e-01;
w[2] = 5.55555555555555555562e-01;
return std::make_pair(x, w);
}
template <>
inline std::pair<std::array<double, 4>, std::array<double, 4>>
GetGaussLegendrePoints<4>() {
std::array<double, 4> x;
x[0] = 3.39981043584856264792e-01;
x[1] = -3.39981043584856264792e-01;
x[2] = 8.61136311594052575248e-01;
x[3] = -8.61136311594052575248e-01;
std::array<double, 4> w;
w[0] = 6.52145154862546142644e-01;
w[1] = 6.52145154862546142644e-01;
w[2] = 3.47854845137453857383e-01;
w[3] = 3.47854845137453857383e-01;
return std::make_pair(x, w);
}
template <>
inline std::pair<std::array<double, 5>, std::array<double, 5>>
GetGaussLegendrePoints<5>() {
std::array<double, 5> x;
x[0] = 0.00000000000000000000e+00;
x[1] = 5.38469310105683091018e-01;
x[2] = -5.38469310105683091018e-01;
x[3] = 9.06179845938663992811e-01;
x[4] = -9.06179845938663992811e-01;
std::array<double, 5> w;
w[0] = 5.68888888888888888883e-01;
w[1] = 4.78628670499366468030e-01;
w[2] = 4.78628670499366468030e-01;
w[3] = 2.36926885056189087515e-01;
w[4] = 2.36926885056189087515e-01;
return std::make_pair(x, w);
}
template <>
inline std::pair<std::array<double, 6>, std::array<double, 6>>
GetGaussLegendrePoints<6>() {
std::array<double, 6> x;
x[0] = 6.61209386466264513688e-01;
x[1] = -6.61209386466264513688e-01;
x[2] = 2.38619186083196908630e-01;
x[3] = -2.38619186083196908630e-01;
x[4] = 9.32469514203152027832e-01;
x[5] = -9.32469514203152027832e-01;
std::array<double, 6> w;
w[0] = 3.60761573048138607569e-01;
w[1] = 3.60761573048138607569e-01;
w[2] = 4.67913934572691047389e-01;
w[3] = 4.67913934572691047389e-01;
w[4] = 1.71324492379170345043e-01;
w[5] = 1.71324492379170345043e-01;
return std::make_pair(x, w);
}
template <>
inline std::pair<std::array<double, 7>, std::array<double, 7>>
GetGaussLegendrePoints<7>() {
std::array<double, 7> x;
x[0] = 0.00000000000000000000e+00;
x[1] = 4.05845151377397166917e-01;
x[2] = -4.05845151377397166917e-01;
x[3] = 7.41531185599394439864e-01;
x[4] = -7.41531185599394439864e-01;
x[5] = 9.49107912342758524541e-01;
x[6] = -9.49107912342758524541e-01;
std::array<double, 7> w;
w[0] = 4.17959183673469387749e-01;
w[1] = 3.81830050505118944961e-01;
w[2] = 3.81830050505118944961e-01;
w[3] = 2.79705391489276667890e-01;
w[4] = 2.79705391489276667890e-01;
w[5] = 1.29484966168869693274e-01;
w[6] = 1.29484966168869693274e-01;
return std::make_pair(x, w);
}
template <>
inline std::pair<std::array<double, 8>, std::array<double, 8>>
GetGaussLegendrePoints<8>() {
std::array<double, 8> x;
x[0] = 1.83434642495649804936e-01;
x[1] = -1.83434642495649804936e-01;
x[2] = 5.25532409916328985830e-01;
x[3] = -5.25532409916328985830e-01;
x[4] = 7.96666477413626739567e-01;
x[5] = -7.96666477413626739567e-01;
x[6] = 9.60289856497536231661e-01;
x[7] = -9.60289856497536231661e-01;
std::array<double, 8> w;
w[0] = 3.62683783378361982976e-01;
w[1] = 3.62683783378361982976e-01;
w[2] = 3.13706645877887287338e-01;
w[3] = 3.13706645877887287338e-01;
w[4] = 2.22381034453374470546e-01;
w[5] = 2.22381034453374470546e-01;
w[6] = 1.01228536290376259154e-01;
w[7] = 1.01228536290376259154e-01;
return std::make_pair(x, w);
}
template <>
inline std::pair<std::array<double, 9>, std::array<double, 9>>
GetGaussLegendrePoints<9>() {
std::array<double, 9> x;
x[0] = 0.00000000000000000000e+00;
x[1] = 8.36031107326635794313e-01;
x[2] = -8.36031107326635794313e-01;
x[3] = 9.68160239507626089810e-01;
x[4] = -9.68160239507626089810e-01;
x[5] = 3.24253423403808929042e-01;
x[6] = -3.24253423403808929042e-01;
x[7] = 6.13371432700590397285e-01;
x[8] = -6.13371432700590397285e-01;
std::array<double, 9> w;
w[0] = 3.30239355001259763154e-01;
w[1] = 1.80648160694857404059e-01;
w[2] = 1.80648160694857404059e-01;
w[3] = 8.12743883615744119737e-02;
w[4] = 8.12743883615744119737e-02;
w[5] = 3.12347077040002840057e-01;
w[6] = 3.12347077040002840057e-01;
w[7] = 2.60610696402935462313e-01;
w[8] = 2.60610696402935462313e-01;
return std::make_pair(x, w);
}
template <>
inline std::pair<std::array<double, 10>, std::array<double, 10>>
GetGaussLegendrePoints<10>() {
std::array<double, 10> x;
x[0] = 1.48874338981631210881e-01;
x[1] = -1.48874338981631210881e-01;
x[2] = 4.33395394129247190794e-01;
x[3] = -4.33395394129247190794e-01;
x[4] = 6.79409568299024406207e-01;
x[5] = -6.79409568299024406207e-01;
x[6] = 8.65063366688984510759e-01;
x[7] = -8.65063366688984510759e-01;
x[8] = 9.73906528517171720066e-01;
x[9] = -9.73906528517171720066e-01;
std::array<double, 10> w;
w[0] = 2.95524224714752870187e-01;
w[1] = 2.95524224714752870187e-01;
w[2] = 2.69266719309996355105e-01;
w[3] = 2.69266719309996355105e-01;
w[4] = 2.19086362515982044000e-01;
w[5] = 2.19086362515982044000e-01;
w[6] = 1.49451349150580593150e-01;
w[7] = 1.49451349150580593150e-01;
w[8] = 6.66713443086881375920e-02;
w[9] = 6.66713443086881375920e-02;
return std::make_pair(x, w);
}
/**
* @brief Compute the integral of a target single-variable function
* from a lower bound to an upper bound, by 5-th Gauss-Legendre method
* Given a target function and integral lower and upper bound,
* compute the integral approximation using 5th order Gauss-Legendre
* integration.
* The target function must be a smooth function.
* Example:
* target function: auto func = [](const double x) {return x * x;};
* double integral = gauss_legendre(func, -2, 3);
* This gives you the approximated integral of function x^2 in bound [-2, 3]
*
* reference: https://en.wikipedia.org/wiki/Gaussian_quadrature
* http://www.mymathlib.com/quadrature/gauss_legendre.html
*
* @param func The target single-variable function
* @param lower_bound The lower bound of the integral
* @param upper_bound The upper bound of the integral
* @return The integral result
*/
template <std::size_t N>
double IntegrateByGaussLegendre(const std::function<double(double)>& func,
const double lower_bound,
const double upper_bound) {
auto p = GetGaussLegendrePoints<N>();
std::array<double, N> x = p.first;
std::array<double, N> w = p.second;
const double t = (upper_bound - lower_bound) * 0.5;
const double m = (upper_bound + lower_bound) * 0.5;
double integral = 0.0;
for (size_t i = 0; i < N; ++i) {
integral += w[i] * func(t * x[i] + m);
}
return integral * t;
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/vec2d_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/vec2d.h"
#include <cmath>
#include "gtest/gtest.h"
namespace apollo {
namespace common {
namespace math {
TEST(Vec2dTest, NomralCases) {
Vec2d pt(2, 3);
EXPECT_NEAR(pt.Length(), std::sqrt(13.0), 1e-5);
EXPECT_NEAR(pt.LengthSquare(), 13.0, 1e-5);
EXPECT_NEAR(pt.DistanceTo({0, 0}), std::sqrt(13.0), 1e-5);
EXPECT_NEAR(pt.DistanceSquareTo({0, 0}), 13.0, 1e-5);
EXPECT_NEAR(pt.DistanceTo({0, 2}), std::sqrt(5.0), 1e-5);
EXPECT_NEAR(pt.DistanceSquareTo({0, 2}), 5.0, 1e-5);
EXPECT_NEAR(pt.Angle(), std::atan2(3, 2), 1e-5);
EXPECT_NEAR(pt.CrossProd({4, 5}), -2, 1e-5);
EXPECT_NEAR(pt.InnerProd({4, 5}), 23, 1e-5);
EXPECT_EQ(pt.DebugString(), "vec2d ( x = 2 y = 3 )");
pt.set_x(4);
pt.set_y(5);
EXPECT_NEAR(pt.Length(), std::sqrt(41.0), 1e-5);
EXPECT_NEAR(pt.LengthSquare(), 41.0, 1e-5);
pt.Normalize();
EXPECT_NEAR(pt.x(), 4.0 / std::sqrt(41.0), 1e-5);
EXPECT_NEAR(pt.y(), 5.0 / std::sqrt(41.0), 1e-5);
EXPECT_NEAR(pt.Length(), 1.0, 1e-5);
const Vec2d d = Vec2d(0.5, 1.5) + Vec2d(2.5, 3.5);
EXPECT_NEAR(d.x(), 3.0, 1e-5);
EXPECT_NEAR(d.y(), 5.0, 1e-5);
const Vec2d e = Vec2d(0.5, 1.5) - Vec2d(2.5, 3.5);
EXPECT_NEAR(e.x(), -2.0, 1e-5);
EXPECT_NEAR(e.y(), -2.0, 1e-5);
const Vec2d f = d / 2.0;
EXPECT_NEAR(f.x(), 1.5, 1e-5);
EXPECT_NEAR(f.y(), 2.5, 1e-5);
const Vec2d g = e * (-3.0);
EXPECT_NEAR(g.x(), 6.0, 1e-5);
EXPECT_NEAR(g.y(), 6.0, 1e-5);
const Vec2d unit_pt = Vec2d::CreateUnitVec2d(M_PI_4);
EXPECT_NEAR(unit_pt.x(), std::sqrt(2.0) / 2.0, 1e-5);
EXPECT_NEAR(unit_pt.y(), std::sqrt(2.0) / 2.0, 1e-5);
EXPECT_NEAR(unit_pt.Angle(), M_PI_4, 1e-5);
}
TEST(Vec2dTest, rotate) {
Vec2d pt(4, 0);
auto p1 = pt.rotate(M_PI / 2.0);
EXPECT_NEAR(p1.x(), 0.0, 1e-5);
EXPECT_NEAR(p1.y(), 4.0, 1e-5);
auto p2 = pt.rotate(M_PI);
EXPECT_NEAR(p2.x(), -4.0, 1e-5);
EXPECT_NEAR(p2.y(), 0.0, 1e-5);
auto p3 = pt.rotate(-M_PI / 2.0);
EXPECT_NEAR(p3.x(), 0.0, 1e-5);
EXPECT_NEAR(p3.y(), -4.0, 1e-5);
auto p4 = pt.rotate(-M_PI);
EXPECT_NEAR(p4.x(), -4.0, 1e-5);
EXPECT_NEAR(p4.y(), 0.0, 1e-5);
}
TEST(Vec2dTest, selfrotate) {
Vec2d p1(4, 0);
p1.SelfRotate(M_PI / 2.0);
EXPECT_NEAR(p1.x(), 0.0, 1e-5);
EXPECT_NEAR(p1.y(), 4.0, 1e-5);
Vec2d p2(4, 0);
p2.SelfRotate(M_PI);
EXPECT_NEAR(p2.x(), -4.0, 1e-5);
EXPECT_NEAR(p2.y(), 0.0, 1e-5);
Vec2d p3(4, 0);
p3.SelfRotate(-M_PI / 2.0);
EXPECT_NEAR(p3.x(), 0.0, 1e-5);
EXPECT_NEAR(p3.y(), -4.0, 1e-5);
Vec2d p4(4, 0);
p4.SelfRotate(-M_PI);
EXPECT_NEAR(p4.x(), -4.0, 1e-5);
EXPECT_NEAR(p4.y(), 0.0, 1e-5);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/line_segment2d_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/line_segment2d.h"
#include <cmath>
#include "gtest/gtest.h"
namespace apollo {
namespace common {
namespace math {
TEST(LineSegment2dTest, Accessors) {
const LineSegment2d ls({1, 2}, {5, 4});
EXPECT_NEAR(ls.length(), std::sqrt(20.0), 1e-5);
EXPECT_NEAR(ls.length_sqr(), 20.0, 1e-5);
EXPECT_NEAR(ls.center().x(), 3, 1e-5);
EXPECT_NEAR(ls.center().y(), 3, 1e-5);
EXPECT_NEAR(ls.heading(), std::atan2(2, 4), 1e-5);
EXPECT_NEAR(ls.cos_heading(), 4.0 / std::sqrt(20.0), 1e-5);
EXPECT_NEAR(ls.sin_heading(), 2.0 / std::sqrt(20.0), 1e-5);
EXPECT_EQ(ls.DebugString(),
"segment2d ( start = vec2d ( x = 1 y = 2 ) end = vec2d ( x = 5 "
"y = 4 ) )");
}
TEST(LineSegment2dTest, DistanceTo) {
const LineSegment2d ls({1, 2}, {5, 4});
Vec2d nearest_pt;
EXPECT_NEAR(ls.DistanceTo({0, 0}, &nearest_pt), std::sqrt(5.0), 1e-5);
EXPECT_NEAR(nearest_pt.DistanceTo({0, 0}), std::sqrt(5.0), 1e-5);
EXPECT_NEAR(ls.DistanceTo({0, 0}), std::sqrt(5.0), 1e-5);
EXPECT_NEAR(ls.DistanceSquareTo({0, 0}), 5.0, 1e-5);
EXPECT_NEAR(ls.DistanceSquareTo({0, 0}, &nearest_pt), 5.0, 1e-5);
EXPECT_NEAR(ls.DistanceTo({10, 10}, &nearest_pt), std::sqrt(61.0), 1e-5);
EXPECT_NEAR(nearest_pt.DistanceTo({10, 10}), std::sqrt(61.0), 1e-5);
EXPECT_NEAR(ls.DistanceTo({1, 2}, &nearest_pt), 0, 1e-5);
EXPECT_NEAR(nearest_pt.DistanceTo({1, 2}), 0, 1e-5);
EXPECT_NEAR(ls.DistanceTo({5, 4}, &nearest_pt), 0, 1e-5);
EXPECT_NEAR(nearest_pt.DistanceTo({5, 4}), 0, 1e-5);
EXPECT_NEAR(ls.DistanceTo({3, 3}, &nearest_pt), 0, 1e-5);
EXPECT_NEAR(nearest_pt.DistanceTo({3, 3}), 0, 1e-5);
EXPECT_NEAR(ls.DistanceTo({4, 4}, &nearest_pt), 2.0 / std::sqrt(20.0), 1e-5);
EXPECT_NEAR(nearest_pt.DistanceTo({4, 4}), 2.0 / std::sqrt(20.0), 1e-5);
}
TEST(LineSegment2dTest, GetPerpendicularFoot) {
const LineSegment2d ls({1, 2}, {5, 4});
Vec2d foot_pt;
EXPECT_NEAR(ls.GetPerpendicularFoot({0, 0}, &foot_pt), 0.6 * std::sqrt(5.0),
1e-5);
EXPECT_NEAR(foot_pt.x(), -0.6, 1e-5);
EXPECT_NEAR(foot_pt.y(), 1.2, 1e-5);
EXPECT_NEAR(ls.GetPerpendicularFoot({3, 3}, &foot_pt), 0.0, 1e-5);
EXPECT_NEAR(foot_pt.x(), 3.0, 1e-5);
EXPECT_NEAR(foot_pt.y(), 3.0, 1e-5);
}
TEST(LineSegment2dTest, ProjectOntoUnit) {
const LineSegment2d ls({1, 2}, {5, 4});
EXPECT_NEAR(ls.ProjectOntoUnit({1, 2}), 0.0, 1e-5);
EXPECT_NEAR(ls.ProjectOntoUnit({5, 4}), std::sqrt(20.0), 1e-5);
EXPECT_NEAR(ls.ProjectOntoUnit({-2, -3}), -22.0 / std::sqrt(20.0), 1e-5);
EXPECT_NEAR(ls.ProjectOntoUnit({6, 7}), 30.0 / std::sqrt(20.0), 1e-5);
}
TEST(LineSegment2dTest, GetIntersect) {
const LineSegment2d ls({1, 2}, {5, 4});
Vec2d point;
EXPECT_FALSE(ls.GetIntersect({{1, 3}, {5, 5}}, &point));
EXPECT_FALSE(ls.GetIntersect({{2, 2}, {6, 4}}, &point));
EXPECT_TRUE(ls.GetIntersect({{1, 2}, {-3, 0}}, &point));
EXPECT_NEAR(point.x(), 1, 1e-5);
EXPECT_NEAR(point.y(), 2, 1e-5);
EXPECT_TRUE(ls.GetIntersect({{5, 4}, {9, 6}}, &point));
EXPECT_NEAR(point.x(), 5, 1e-5);
EXPECT_NEAR(point.y(), 4, 1e-5);
EXPECT_TRUE(ls.GetIntersect({{3, 0}, {3, 10}}, &point));
EXPECT_NEAR(point.x(), 3, 1e-5);
EXPECT_NEAR(point.y(), 3, 1e-5);
EXPECT_TRUE(ls.GetIntersect({{3, 10}, {3, 0}}, &point));
EXPECT_NEAR(point.x(), 3, 1e-5);
EXPECT_NEAR(point.y(), 3, 1e-5);
EXPECT_FALSE(ls.GetIntersect({{3, 5}, {3, 10}}, &point));
EXPECT_FALSE(ls.GetIntersect({{3, 2}, {3, 0}}, &point));
EXPECT_TRUE(ls.GetIntersect({{3, 3}, {3, 3}}, &point));
EXPECT_NEAR(point.x(), 3, 1e-5);
EXPECT_NEAR(point.y(), 3, 1e-5);
EXPECT_FALSE(ls.GetIntersect({{4, 4}, {4, 4}}, &point));
}
TEST(LineSegment2dTest, IsPointIn) {
const LineSegment2d ls({1, 2}, {5, 4});
EXPECT_TRUE(ls.IsPointIn({1, 2}));
EXPECT_TRUE(ls.IsPointIn({5, 4}));
EXPECT_TRUE(ls.IsPointIn({3, 3}));
EXPECT_FALSE(ls.IsPointIn({-1, 1}));
EXPECT_FALSE(ls.IsPointIn({7, 5}));
EXPECT_FALSE(ls.IsPointIn({0, 0}));
EXPECT_FALSE(ls.IsPointIn({6, 6}));
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/vec2d.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/vec2d.h"
#include <cmath>
#include "absl/strings/str_cat.h"
#include "cyber/common/log.h"
namespace apollo {
namespace common {
namespace math {
Vec2d Vec2d::CreateUnitVec2d(const double angle) {
return Vec2d(std::cos(angle), std::sin(angle));
}
double Vec2d::Length() const { return std::hypot(x_, y_); }
double Vec2d::LengthSquare() const { return x_ * x_ + y_ * y_; }
double Vec2d::Angle() const { return std::atan2(y_, x_); }
void Vec2d::Normalize() {
const double l = Length();
if (l > kMathEpsilon) {
x_ /= l;
y_ /= l;
}
}
double Vec2d::DistanceTo(const Vec2d &other) const {
return std::hypot(x_ - other.x_, y_ - other.y_);
}
double Vec2d::DistanceSquareTo(const Vec2d &other) const {
const double dx = x_ - other.x_;
const double dy = y_ - other.y_;
return dx * dx + dy * dy;
}
double Vec2d::CrossProd(const Vec2d &other) const {
return x_ * other.y() - y_ * other.x();
}
double Vec2d::InnerProd(const Vec2d &other) const {
return x_ * other.x() + y_ * other.y();
}
Vec2d Vec2d::rotate(const double angle) const {
return Vec2d(x_ * cos(angle) - y_ * sin(angle),
x_ * sin(angle) + y_ * cos(angle));
}
void Vec2d::SelfRotate(const double angle) {
double tmp_x = x_;
x_ = x_ * cos(angle) - y_ * sin(angle);
y_ = tmp_x * sin(angle) + y_ * cos(angle);
}
Vec2d Vec2d::operator+(const Vec2d &other) const {
return Vec2d(x_ + other.x(), y_ + other.y());
}
Vec2d Vec2d::operator-(const Vec2d &other) const {
return Vec2d(x_ - other.x(), y_ - other.y());
}
Vec2d Vec2d::operator*(const double ratio) const {
return Vec2d(x_ * ratio, y_ * ratio);
}
Vec2d Vec2d::operator/(const double ratio) const {
CHECK_GT(std::abs(ratio), kMathEpsilon);
return Vec2d(x_ / ratio, y_ / ratio);
}
Vec2d &Vec2d::operator+=(const Vec2d &other) {
x_ += other.x();
y_ += other.y();
return *this;
}
Vec2d &Vec2d::operator-=(const Vec2d &other) {
x_ -= other.x();
y_ -= other.y();
return *this;
}
Vec2d &Vec2d::operator*=(const double ratio) {
x_ *= ratio;
y_ *= ratio;
return *this;
}
Vec2d &Vec2d::operator/=(const double ratio) {
CHECK_GT(std::abs(ratio), kMathEpsilon);
x_ /= ratio;
y_ /= ratio;
return *this;
}
bool Vec2d::operator==(const Vec2d &other) const {
return (std::abs(x_ - other.x()) < kMathEpsilon &&
std::abs(y_ - other.y()) < kMathEpsilon);
}
Vec2d operator*(const double ratio, const Vec2d &vec) { return vec * ratio; }
std::string Vec2d::DebugString() const {
return absl::StrCat("vec2d ( x = ", x_, " y = ", y_, " )");
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/box2d.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/box2d.h"
#include <algorithm>
#include <cmath>
#include <utility>
#include "absl/strings/str_cat.h"
#include "cyber/common/log.h"
#include "modules/common/math/math_utils.h"
#include "modules/common/math/polygon2d.h"
namespace apollo {
namespace common {
namespace math {
namespace {
double PtSegDistance(double query_x, double query_y, double start_x,
double start_y, double end_x, double end_y,
double length) {
const double x0 = query_x - start_x;
const double y0 = query_y - start_y;
const double dx = end_x - start_x;
const double dy = end_y - start_y;
const double proj = x0 * dx + y0 * dy;
if (proj <= 0.0) {
return hypot(x0, y0);
}
if (proj >= length * length) {
return hypot(x0 - dx, y0 - dy);
}
return std::abs(x0 * dy - y0 * dx) / length;
}
} // namespace
Box2d::Box2d(const Vec2d ¢er, const double heading, const double length,
const double width)
: center_(center),
length_(length),
width_(width),
half_length_(length / 2.0),
half_width_(width / 2.0),
heading_(heading),
cos_heading_(cos(heading)),
sin_heading_(sin(heading)) {
CHECK_GT(length_, -kMathEpsilon);
CHECK_GT(width_, -kMathEpsilon);
InitCorners();
}
Box2d::Box2d(const LineSegment2d &axis, const double width)
: center_(axis.center()),
length_(axis.length()),
width_(width),
half_length_(axis.length() / 2.0),
half_width_(width / 2.0),
heading_(axis.heading()),
cos_heading_(axis.cos_heading()),
sin_heading_(axis.sin_heading()) {
CHECK_GT(length_, -kMathEpsilon);
CHECK_GT(width_, -kMathEpsilon);
InitCorners();
}
void Box2d::InitCorners() {
const double dx1 = cos_heading_ * half_length_;
const double dy1 = sin_heading_ * half_length_;
const double dx2 = sin_heading_ * half_width_;
const double dy2 = -cos_heading_ * half_width_;
corners_.clear();
corners_.emplace_back(center_.x() + dx1 + dx2, center_.y() + dy1 + dy2);
corners_.emplace_back(center_.x() + dx1 - dx2, center_.y() + dy1 - dy2);
corners_.emplace_back(center_.x() - dx1 - dx2, center_.y() - dy1 - dy2);
corners_.emplace_back(center_.x() - dx1 + dx2, center_.y() - dy1 + dy2);
for (auto &corner : corners_) {
max_x_ = std::fmax(corner.x(), max_x_);
min_x_ = std::fmin(corner.x(), min_x_);
max_y_ = std::fmax(corner.y(), max_y_);
min_y_ = std::fmin(corner.y(), min_y_);
}
}
Box2d::Box2d(const AABox2d &aabox)
: center_(aabox.center()),
length_(aabox.length()),
width_(aabox.width()),
half_length_(aabox.half_length()),
half_width_(aabox.half_width()),
heading_(0.0),
cos_heading_(1.0),
sin_heading_(0.0) {
CHECK_GT(length_, -kMathEpsilon);
CHECK_GT(width_, -kMathEpsilon);
}
Box2d Box2d::CreateAABox(const Vec2d &one_corner,
const Vec2d &opposite_corner) {
const double x1 = std::min(one_corner.x(), opposite_corner.x());
const double x2 = std::max(one_corner.x(), opposite_corner.x());
const double y1 = std::min(one_corner.y(), opposite_corner.y());
const double y2 = std::max(one_corner.y(), opposite_corner.y());
return Box2d({(x1 + x2) / 2.0, (y1 + y2) / 2.0}, 0.0, x2 - x1, y2 - y1);
}
void Box2d::GetAllCorners(std::vector<Vec2d> *const corners) const {
if (corners == nullptr) {
return;
}
*corners = corners_;
}
std::vector<Vec2d> Box2d::GetAllCorners() const { return corners_; }
bool Box2d::IsPointIn(const Vec2d &point) const {
const double x0 = point.x() - center_.x();
const double y0 = point.y() - center_.y();
const double dx = std::abs(x0 * cos_heading_ + y0 * sin_heading_);
const double dy = std::abs(-x0 * sin_heading_ + y0 * cos_heading_);
return dx <= half_length_ + kMathEpsilon && dy <= half_width_ + kMathEpsilon;
}
bool Box2d::IsPointOnBoundary(const Vec2d &point) const {
const double x0 = point.x() - center_.x();
const double y0 = point.y() - center_.y();
const double dx = std::abs(x0 * cos_heading_ + y0 * sin_heading_);
const double dy = std::abs(x0 * sin_heading_ - y0 * cos_heading_);
return (std::abs(dx - half_length_) <= kMathEpsilon &&
dy <= half_width_ + kMathEpsilon) ||
(std::abs(dy - half_width_) <= kMathEpsilon &&
dx <= half_length_ + kMathEpsilon);
}
double Box2d::DistanceTo(const Vec2d &point) const {
const double x0 = point.x() - center_.x();
const double y0 = point.y() - center_.y();
const double dx =
std::abs(x0 * cos_heading_ + y0 * sin_heading_) - half_length_;
const double dy =
std::abs(x0 * sin_heading_ - y0 * cos_heading_) - half_width_;
if (dx <= 0.0) {
return std::max(0.0, dy);
}
if (dy <= 0.0) {
return dx;
}
return hypot(dx, dy);
}
bool Box2d::HasOverlap(const LineSegment2d &line_segment) const {
if (line_segment.length() <= kMathEpsilon) {
return IsPointIn(line_segment.start());
}
if (std::fmax(line_segment.start().x(), line_segment.end().x()) < min_x() ||
std::fmin(line_segment.start().x(), line_segment.end().x()) > max_x() ||
std::fmax(line_segment.start().y(), line_segment.end().y()) < min_y() ||
std::fmin(line_segment.start().y(), line_segment.end().y()) > max_y()) {
return false;
}
return DistanceTo(line_segment) <= kMathEpsilon;
}
double Box2d::DistanceTo(const LineSegment2d &line_segment) const {
if (line_segment.length() <= kMathEpsilon) {
return DistanceTo(line_segment.start());
}
const double ref_x1 = line_segment.start().x() - center_.x();
const double ref_y1 = line_segment.start().y() - center_.y();
double x1 = ref_x1 * cos_heading_ + ref_y1 * sin_heading_;
double y1 = ref_x1 * sin_heading_ - ref_y1 * cos_heading_;
double box_x = half_length_;
double box_y = half_width_;
int gx1 = (x1 >= box_x ? 1 : (x1 <= -box_x ? -1 : 0));
int gy1 = (y1 >= box_y ? 1 : (y1 <= -box_y ? -1 : 0));
if (gx1 == 0 && gy1 == 0) {
return 0.0;
}
const double ref_x2 = line_segment.end().x() - center_.x();
const double ref_y2 = line_segment.end().y() - center_.y();
double x2 = ref_x2 * cos_heading_ + ref_y2 * sin_heading_;
double y2 = ref_x2 * sin_heading_ - ref_y2 * cos_heading_;
int gx2 = (x2 >= box_x ? 1 : (x2 <= -box_x ? -1 : 0));
int gy2 = (y2 >= box_y ? 1 : (y2 <= -box_y ? -1 : 0));
if (gx2 == 0 && gy2 == 0) {
return 0.0;
}
if (gx1 < 0 || (gx1 == 0 && gx2 < 0)) {
x1 = -x1;
gx1 = -gx1;
x2 = -x2;
gx2 = -gx2;
}
if (gy1 < 0 || (gy1 == 0 && gy2 < 0)) {
y1 = -y1;
gy1 = -gy1;
y2 = -y2;
gy2 = -gy2;
}
if (gx1 < gy1 || (gx1 == gy1 && gx2 < gy2)) {
std::swap(x1, y1);
std::swap(gx1, gy1);
std::swap(x2, y2);
std::swap(gx2, gy2);
std::swap(box_x, box_y);
}
if (gx1 == 1 && gy1 == 1) {
switch (gx2 * 3 + gy2) {
case 4:
return PtSegDistance(box_x, box_y, x1, y1, x2, y2,
line_segment.length());
case 3:
return (x1 > x2) ? (x2 - box_x)
: PtSegDistance(box_x, box_y, x1, y1, x2, y2,
line_segment.length());
case 2:
return (x1 > x2) ? PtSegDistance(box_x, -box_y, x1, y1, x2, y2,
line_segment.length())
: PtSegDistance(box_x, box_y, x1, y1, x2, y2,
line_segment.length());
case -1:
return CrossProd({x1, y1}, {x2, y2}, {box_x, -box_y}) >= 0.0
? 0.0
: PtSegDistance(box_x, -box_y, x1, y1, x2, y2,
line_segment.length());
case -4:
return CrossProd({x1, y1}, {x2, y2}, {box_x, -box_y}) <= 0.0
? PtSegDistance(box_x, -box_y, x1, y1, x2, y2,
line_segment.length())
: (CrossProd({x1, y1}, {x2, y2}, {-box_x, box_y}) <= 0.0
? 0.0
: PtSegDistance(-box_x, box_y, x1, y1, x2, y2,
line_segment.length()));
}
} else {
switch (gx2 * 3 + gy2) {
case 4:
return (x1 < x2) ? (x1 - box_x)
: PtSegDistance(box_x, box_y, x1, y1, x2, y2,
line_segment.length());
case 3:
return std::min(x1, x2) - box_x;
case 1:
case -2:
return CrossProd({x1, y1}, {x2, y2}, {box_x, box_y}) <= 0.0
? 0.0
: PtSegDistance(box_x, box_y, x1, y1, x2, y2,
line_segment.length());
case -3:
return 0.0;
}
}
ACHECK(0) << "unimplemented state: " << gx1 << " " << gy1 << " " << gx2 << " "
<< gy2;
return 0.0;
}
double Box2d::DistanceTo(const Box2d &box) const {
return Polygon2d(box).DistanceTo(*this);
}
bool Box2d::HasOverlap(const Box2d &box) const {
if (box.max_x() < min_x() || box.min_x() > max_x() || box.max_y() < min_y() ||
box.min_y() > max_y()) {
return false;
}
const double shift_x = box.center_x() - center_.x();
const double shift_y = box.center_y() - center_.y();
const double dx1 = cos_heading_ * half_length_;
const double dy1 = sin_heading_ * half_length_;
const double dx2 = sin_heading_ * half_width_;
const double dy2 = -cos_heading_ * half_width_;
const double dx3 = box.cos_heading() * box.half_length();
const double dy3 = box.sin_heading() * box.half_length();
const double dx4 = box.sin_heading() * box.half_width();
const double dy4 = -box.cos_heading() * box.half_width();
return std::abs(shift_x * cos_heading_ + shift_y * sin_heading_) <=
std::abs(dx3 * cos_heading_ + dy3 * sin_heading_) +
std::abs(dx4 * cos_heading_ + dy4 * sin_heading_) +
half_length_ &&
std::abs(shift_x * sin_heading_ - shift_y * cos_heading_) <=
std::abs(dx3 * sin_heading_ - dy3 * cos_heading_) +
std::abs(dx4 * sin_heading_ - dy4 * cos_heading_) +
half_width_ &&
std::abs(shift_x * box.cos_heading() + shift_y * box.sin_heading()) <=
std::abs(dx1 * box.cos_heading() + dy1 * box.sin_heading()) +
std::abs(dx2 * box.cos_heading() + dy2 * box.sin_heading()) +
box.half_length() &&
std::abs(shift_x * box.sin_heading() - shift_y * box.cos_heading()) <=
std::abs(dx1 * box.sin_heading() - dy1 * box.cos_heading()) +
std::abs(dx2 * box.sin_heading() - dy2 * box.cos_heading()) +
box.half_width();
}
AABox2d Box2d::GetAABox() const {
const double dx1 = std::abs(cos_heading_ * half_length_);
const double dy1 = std::abs(sin_heading_ * half_length_);
const double dx2 = std::abs(sin_heading_ * half_width_);
const double dy2 = std::abs(cos_heading_ * half_width_);
return AABox2d(center_, (dx1 + dx2) * 2.0, (dy1 + dy2) * 2.0);
}
void Box2d::RotateFromCenter(const double rotate_angle) {
heading_ = NormalizeAngle(heading_ + rotate_angle);
cos_heading_ = std::cos(heading_);
sin_heading_ = std::sin(heading_);
InitCorners();
}
void Box2d::Shift(const Vec2d &shift_vec) {
center_ += shift_vec;
InitCorners();
}
void Box2d::LongitudinalExtend(const double extension_length) {
length_ += extension_length;
half_length_ += extension_length / 2.0;
InitCorners();
}
void Box2d::LateralExtend(const double extension_length) {
width_ += extension_length;
half_width_ += extension_length / 2.0;
InitCorners();
}
std::string Box2d::DebugString() const {
return absl::StrCat("box2d ( center = ", center_.DebugString(),
" heading = ", heading_, " length = ", length_,
" width = ", width_, " )");
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/euler_angles_zxy_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/euler_angles_zxy.h"
#include <cmath>
#include "Eigen/Geometry"
#include "gtest/gtest.h"
namespace apollo {
namespace common {
namespace math {
namespace {
Eigen::Quaterniond GoldenEulerZXYToQuaternion(const double roll,
const double pitch,
const double yaw) {
return Eigen::AngleAxisd(yaw, Eigen::Vector3d::UnitZ()) *
Eigen::AngleAxisd(pitch, Eigen::Vector3d::UnitX()) *
Eigen::AngleAxisd(roll, Eigen::Vector3d::UnitY());
}
} // namespace
TEST(EulerAnglesZXYTest, SingleConstruct) {
EulerAnglesZXYd a(1.0);
EXPECT_DOUBLE_EQ(0.0, a.roll());
EXPECT_DOUBLE_EQ(0.0, a.pitch());
EXPECT_DOUBLE_EQ(1.0, a.yaw());
auto q = a.ToQuaternion();
EXPECT_DOUBLE_EQ(cos(0.5), q.w());
EXPECT_DOUBLE_EQ(0.0, q.x());
EXPECT_DOUBLE_EQ(0.0, q.y());
EXPECT_DOUBLE_EQ(sin(0.5), q.z());
}
TEST(EulerAnglesZXYTest, FullConstructDouble) {
EulerAnglesZXYd a(0.35, 0.24, -1.0);
auto q_golden = GoldenEulerZXYToQuaternion(0.35, 0.24, -1.0);
auto q = a.ToQuaternion();
EXPECT_DOUBLE_EQ(q_golden.w(), q.w());
EXPECT_DOUBLE_EQ(q_golden.x(), q.x());
EXPECT_DOUBLE_EQ(q_golden.y(), q.y());
EXPECT_DOUBLE_EQ(q_golden.z(), q.z());
EulerAnglesZXYd b(q);
EXPECT_DOUBLE_EQ(0.35, b.roll());
EXPECT_DOUBLE_EQ(0.24, b.pitch());
EXPECT_DOUBLE_EQ(-1.0, b.yaw());
}
TEST(EulerAnglesZXYTest, FullConstructFloat) {
Eigen::Quaternionf q(1.0f, 2.0f, -3.0f, 4.0f);
q.normalize();
EulerAnglesZXYf a(q);
auto q2 = a.ToQuaternion();
EXPECT_NEAR(q.w(), q2.w(), 5e-7);
EXPECT_NEAR(q.x(), q2.x(), 5e-7);
EXPECT_NEAR(q.y(), q2.y(), 5e-7);
EXPECT_NEAR(q.z(), q2.z(), 5e-7);
}
TEST(EulerAnglesZXYTest, IsValid) {
EulerAnglesZXYd a(0.35, 5.0, -1.0);
EXPECT_TRUE(a.IsValid());
EulerAnglesZXYd b(0.35, 2.0, -1.0);
EXPECT_FALSE(b.IsValid());
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/quaternion_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/quaternion.h"
#include <cmath>
#include "gtest/gtest.h"
namespace apollo {
namespace common {
namespace math {
TEST(QuaternionTest, QuaternionToHeading) {
const double v = sqrt(0.5); // = cos(pi / 4) = sin(pi / 4)
EXPECT_DOUBLE_EQ(0,
QuaternionToHeading(v, 0.0, 0.0, -v)); // Pointing to east.
EXPECT_DOUBLE_EQ(
M_PI_2, QuaternionToHeading(1.0, 0.0, 0.0, 0.0)); // Pointing to north.
EXPECT_DOUBLE_EQ(-M_PI_2, QuaternionToHeading(0.0, 0.0, 0.0,
1.0)); // Pointing to south.
EXPECT_DOUBLE_EQ(-M_PI,
QuaternionToHeading(v, 0.0, 0.0, v)); // Pointing to west.
Eigen::Quaternionf q(1.0, 0.0, 0.0, 0.0);
EXPECT_FLOAT_EQ(M_PI_2, QuaternionToHeading(q)); // Pointing to north.
const double headings[] = {-3.3, -2.2, -1.1, 1.2, 2.3, 3.4, 4.5, 5.6, 6.7};
for (double heading : headings) {
EXPECT_NEAR(NormalizeAngle(heading),
QuaternionToHeading(HeadingToQuaternion<double>(heading)),
1e-15);
}
}
TEST(QuaternionTest, QuaternionRotate) {
apollo::common::Quaternion q;
q.set_qx(0.016590540978116377);
q.set_qy(0.012968083311103572);
q.set_qz(-0.99256254167039326);
q.set_qw(-0.1199007240933047);
Eigen::Vector3d original(0.18112868882363914, 0.38614886414425986,
-0.15861744649897938);
auto rotated = QuaternionRotate(q, original);
EXPECT_NEAR(rotated[0], -0.26184808017295008, 1e-9);
EXPECT_NEAR(rotated[1], -0.32827419468368224, 1e-9);
EXPECT_NEAR(rotated[2], -0.17535585973456849, 1e-9);
}
TEST(QuaternionTest, InverseQuaternionRotate) {
apollo::common::Quaternion q;
q.set_qx(0.016590540978116377);
q.set_qy(0.012968083311103572);
q.set_qz(-0.99256254167039326);
q.set_qw(-0.1199007240933047);
Eigen::Vector3d rotated(-0.26184808017295008, -0.32827419468368224,
-0.17535585973456849);
auto original = InverseQuaternionRotate(q, rotated);
EXPECT_NEAR(original[0], 0.18112868882363914, 1e-9);
EXPECT_NEAR(original[1], 0.38614886414425986, 1e-9);
EXPECT_NEAR(original[2], -0.15861744649897938, 1e-9);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/polygon2d.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Define the Polygon2d class.
*/
#pragma once
#include <string>
#include <vector>
#include "modules/common/math/box2d.h"
#include "modules/common/math/line_segment2d.h"
#include "modules/common/math/vec2d.h"
/**
* @namespace apollo::common::math
* @brief apollo::common::math
*/
namespace apollo {
namespace common {
namespace math {
/**
* @class Polygon2d
* @brief The class of polygon in 2-D.
*/
class Polygon2d {
public:
/**
* @brief Empty constructor.
*/
Polygon2d() = default;
/**
* @brief Constructor which takes a box.
* @param box The box to construct the polygon.
*/
explicit Polygon2d(const Box2d &box);
/**
* @brief Constructor which takes a vector of points as its vertices.
* @param points The points to construct the polygon.
*/
explicit Polygon2d(std::vector<Vec2d> points);
/**
* @brief Get the vertices of the polygon.
* @return The vertices of the polygon.
*/
const std::vector<Vec2d> &points() const { return points_; }
/**
* @brief Get the edges of the polygon.
* @return The edges of the polygon.
*/
const std::vector<LineSegment2d> &line_segments() const {
return line_segments_;
}
/**
* @brief Get the number of vertices of the polygon.
* @return The number of vertices of the polygon.
*/
int num_points() const { return num_points_; }
/**
* @brief Check if the polygon is convex.
* @return Whether the polygon is convex or not.
*/
bool is_convex() const { return is_convex_; }
/**
* @brief Get the area of the polygon.
* @return The area of the polygon.
*/
double area() const { return area_; }
/**
* @brief Compute the distance from a point to the boundary of the polygon.
* This distance is equal to the minimal distance from the point
* to the edges of the polygon.
* @param point The point to compute whose distance to the polygon.
* @return The distance from the point to the polygon's boundary.
*/
double DistanceToBoundary(const Vec2d &point) const;
/**
* @brief Compute the distance from a point to the polygon. If the point is
* within the polygon, return 0. Otherwise, this distance is
* the minimal distance from the point to the edges of the polygon.
* @param point The point to compute whose distance to the polygon.
* @return The distance from the point to the polygon.
*/
double DistanceTo(const Vec2d &point) const;
/**
* @brief Compute the distance from a line segment to the polygon.
* If the line segment is within the polygon, or it has intersect with
* the polygon, return 0. Otherwise, this distance is
* the minimal distance between the distances from the two ends
* of the line segment to the polygon.
* @param line_segment The line segment to compute whose distance to
* the polygon.
* @return The distance from the line segment to the polygon.
*/
double DistanceTo(const LineSegment2d &line_segment) const;
/**
* @brief Compute the distance from a box to the polygon.
* If the box is within the polygon, or it has overlap with
* the polygon, return 0. Otherwise, this distance is
* the minimal distance among the distances from the edges
* of the box to the polygon.
* @param box The box to compute whose distance to the polygon.
* @return The distance from the box to the polygon.
*/
double DistanceTo(const Box2d &box) const;
/**
* @brief Compute the distance from another polygon to the polygon.
* If the other polygon is within this polygon, or it has overlap with
* this polygon, return 0. Otherwise, this distance is
* the minimal distance among the distances from the edges
* of the other polygon to this polygon.
* @param polygon The polygon to compute whose distance to this polygon.
* @return The distance from the other polygon to this polygon.
*/
double DistanceTo(const Polygon2d &polygon) const;
/**
* @brief Compute the square of distance from a point to the polygon.
* If the point is within the polygon, return 0. Otherwise,
* this square of distance is the minimal square of distance from
* the point to the edges of the polygon.
* @param point The point to compute whose square of distance to the polygon.
* @return The square of distance from the point to the polygon.
*/
double DistanceSquareTo(const Vec2d &point) const;
/**
* @brief Check if a point is within the polygon.
* @param point The target point. To check if it is within the polygon.
* @return Whether a point is within the polygon or not.
*/
bool IsPointIn(const Vec2d &point) const;
/**
* @brief Check if a point is on the boundary of the polygon.
* @param point The target point. To check if it is on the boundary
* of the polygon.
* @return Whether a point is on the boundary of the polygon or not.
*/
bool IsPointOnBoundary(const Vec2d &point) const;
/**
* @brief Check if the polygon contains a line segment.
* @param line_segment The target line segment. To check if the polygon
* contains it.
* @return Whether the polygon contains the line segment or not.
*/
bool Contains(const LineSegment2d &line_segment) const;
/**
* @brief Check if the polygon contains another polygon.
* @param polygon The target polygon. To check if this polygon contains it.
* @return Whether this polygon contains another polygon or not.
*/
bool Contains(const Polygon2d &polygon) const;
/**
* @brief Compute the convex hull of a group of points.
* @param points The target points. To compute the convex hull of them.
* @param polygon The convex hull of the points.
* @return If successfully compute the convex hull.
*/
static bool ComputeConvexHull(const std::vector<Vec2d> &points,
Polygon2d *const polygon);
/**
* @brief Check if a line segment has overlap with this polygon.
* @param line_segment The target line segment. To check if it has
* overlap with this polygon.
* @return Whether the target line segment has overlap with this
* polygon or not.
*/
bool HasOverlap(const LineSegment2d &line_segment) const;
/**
* @brief Get the overlap of a line segment and this polygon. If they have
* overlap, output the two ends of the overlapped line segment.
* @param line_segment The target line segment. To get its overlap with
* this polygon.
* @param first First end of the overlapped line segment.
* @param second Second end of the overlapped line segment.
* @return If the target line segment has overlap with this polygon.
*/
bool GetOverlap(const LineSegment2d &line_segment, Vec2d *const first,
Vec2d *const last) const;
/**
* @brief Get all vertices of the polygon
* @param All vertices of the polygon
*/
void GetAllVertices(std::vector<Vec2d> *const vertices) const;
/**
* @brief Get all vertices of the polygon
*/
std::vector<Vec2d> GetAllVertices() const;
/**
* @brief Get all overlapped line segments of a line segment and this polygon.
* There are possibly multiple overlapped line segments if this
* polygon is not convex.
* @param line_segment The target line segment. To get its all overlapped
* line segments with this polygon.
* @return A group of overlapped line segments.
*/
std::vector<LineSegment2d> GetAllOverlaps(
const LineSegment2d &line_segment) const;
/**
* @brief Check if this polygon has overlap with another polygon.
* @param polygon The target polygon. To check if it has overlap
* with this polygon.
* @return If this polygon has overlap with another polygon.
*/
bool HasOverlap(const Polygon2d &polygon) const;
// Only compute overlaps between two convex polygons.
/**
* @brief Compute the overlap of this polygon and the other polygon if any.
* Note: this function only works for computing overlap between
* two convex polygons.
* @param other_polygon The target polygon. To compute its overlap with
* this polygon.
* @param overlap_polygon The overlapped polygon.
* @param If there is an overlapped polygon.
*/
bool ComputeOverlap(const Polygon2d &other_polygon,
Polygon2d *const overlap_polygon) const;
// Only compute intersection over union ratio between two convex polygons.
/**
* @brief Compute intersection over union ratio of this polygon and the other
* polygon. Note: this function only works for computing overlap
* between two convex polygons.
* @param other_polygon The target polygon. To compute its overlap with
* this polygon.
* @return A value between 0.0 and 1.0, meaning no intersection to fully
* overlaping
*/
double ComputeIoU(const Polygon2d &other_polygon) const;
/**
* @brief Get the axis-aligned bound box of the polygon.
* @return The axis-aligned bound box of the polygon.
*/
AABox2d AABoundingBox() const;
/**
* @brief Get the bound box according to a heading.
* @param heading The specified heading of the bounding box.
* @return The bound box according to the specified heading.
*/
Box2d BoundingBoxWithHeading(const double heading) const;
/**
* @brief Get the bounding box with the minimal area.
* @return The bounding box with the minimal area.
*/
Box2d MinAreaBoundingBox() const;
/**
* @brief Get the extreme points along a heading direction.
* @param heading The specified heading.
* @param first The point on the boundary of this polygon with the minimal
* projection onto the heading direction.
* @param last The point on the boundary of this polygon with the maximal
* projection onto the heading direction.
*/
void ExtremePoints(const double heading, Vec2d *const first,
Vec2d *const last) const;
/**
* @brief Expand this polygon by a distance.
* @param distance The specified distance. To expand this polygon by it.
* @return The polygon after expansion.
*/
Polygon2d ExpandByDistance(const double distance) const;
/**
* @brief Get a string containing essential information about the polygon
* for debugging purpose.
* @return Essential information about the polygon for debugging purpose.
*/
std::string DebugString() const;
double min_x() const { return min_x_; }
double max_x() const { return max_x_; }
double min_y() const { return min_y_; }
double max_y() const { return max_y_; }
protected:
void BuildFromPoints();
int Next(int at) const;
int Prev(int at) const;
static bool ClipConvexHull(const LineSegment2d &line_segment,
std::vector<Vec2d> *const points);
std::vector<Vec2d> points_;
int num_points_ = 0;
std::vector<LineSegment2d> line_segments_;
bool is_convex_ = false;
double area_ = 0.0;
double min_x_ = 0.0;
double max_x_ = 0.0;
double min_y_ = 0.0;
double max_y_ = 0.0;
};
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/kalman_filter.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Defines the templated KalmanFilter class.
*/
#pragma once
#include <sstream>
#include <string>
#include "Eigen/Dense"
#include "cyber/common/log.h"
#include "modules/common/math/matrix_operations.h"
/**
* @namespace apollo::common::math
* @brief apollo::common::math
*/
namespace apollo {
namespace common {
namespace math {
/**
* @class KalmanFilter
*
* @brief Implements a discrete-time Kalman filter.
*
* @param XN dimension of state
* @param ZN dimension of observations
* @param UN dimension of controls
*/
template <typename T, unsigned int XN, unsigned int ZN, unsigned int UN>
class KalmanFilter {
public:
/**
* @brief Constructor which defers initialization until the initial state
* distribution parameters are set (with SetStateEstimate),
* typically on the first observation
*/
KalmanFilter() {
F_.setIdentity();
Q_.setZero();
H_.setIdentity();
R_.setZero();
B_.setZero();
x_.setZero();
P_.setZero();
y_.setZero();
S_.setZero();
K_.setZero();
}
/**
* @brief Sets the initial state belief distribution.
*
* @param x Mean of the state belief distribution
* @param P Covariance of the state belief distribution
*/
void SetStateEstimate(const Eigen::Matrix<T, XN, 1> &x,
const Eigen::Matrix<T, XN, XN> &P) {
x_ = x;
P_ = P;
is_initialized_ = true;
}
/**
* @brief Constructor which fully initializes the Kalman filter
* @param x Mean of the state belief distribution
* @param P Covariance of the state belief distribution
*/
KalmanFilter(const Eigen::Matrix<T, XN, 1> &x,
const Eigen::Matrix<T, XN, XN> &P)
: KalmanFilter() {
SetStateEstimate(x, P);
}
/**
* @brief Destructor
*/
virtual ~KalmanFilter() {}
/**
* @brief Changes the system transition function under zero control.
*
* @param F New transition matrix
*/
void SetTransitionMatrix(const Eigen::Matrix<T, XN, XN> &F) { F_ = F; }
/**
* @brief Changes the covariance matrix of the transition noise.
*
* @param Q New covariance matrix
*/
void SetTransitionNoise(const Eigen::Matrix<T, XN, XN> &Q) { Q_ = Q; }
/**
* @brief Changes the observation matrix, which maps states to observations.
*
* @param H New observation matrix
*/
void SetObservationMatrix(const Eigen::Matrix<T, ZN, XN> &H) { H_ = H; }
/**
* @brief Changes the covariance matrix of the observation noise.
*
* @param R New covariance matrix
*/
void SetObservationNoise(const Eigen::Matrix<T, ZN, ZN> &R) { R_ = R; }
/**
* @brief Changes the covariance matrix of current state belief distribution.
*
* @param P New state covariance matrix
*/
void SetStateCovariance(const Eigen::Matrix<T, XN, XN> &P) { P_ = P; }
/**
* @brief Changes the control matrix in the state transition rule.
*
* @param B New control matrix
*/
void SetControlMatrix(const Eigen::Matrix<T, XN, UN> &B) { B_ = B; }
/**
* @brief Get the system transition function under zero control.
*
* @return Transition matrix.
*/
const Eigen::Matrix<T, XN, XN> &GetTransitionMatrix() const { return F_; }
/**
* @brief Get the covariance matrix of the transition noise.
*
* @return Covariance matrix
*/
const Eigen::Matrix<T, XN, XN> &GetTransitionNoise() const { return Q_; }
/**
* @brief Get the observation matrix, which maps states to observations.
*
* @return Observation matrix
*/
const Eigen::Matrix<T, ZN, XN> &GetObservationMatrix() const { return H_; }
/**
* @brief Get the covariance matrix of the observation noise.
*
* @return Covariance matrix
*/
const Eigen::Matrix<T, ZN, ZN> &GetObservationNoise() const { return R_; }
/**
* @brief Get the control matrix in the state transition rule.
*
* @return Control matrix
*/
const Eigen::Matrix<T, XN, UN> &GetControlMatrix() const { return B_; }
/**
* @brief Updates the state belief distribution given the control input u.
*
* @param u Control input (by default, zero)
*/
void Predict(
const Eigen::Matrix<T, UN, 1> &u = Eigen::Matrix<T, UN, 1>::Zero());
/**
* @brief Updates the state belief distribution given an observation z.
*
* @param z Observation
*/
void Correct(const Eigen::Matrix<T, ZN, 1> &z);
/**
* @brief Gets mean of our current state belief distribution
*
* @return State vector
*/
Eigen::Matrix<T, XN, 1> GetStateEstimate() const { return x_; }
/**
* @brief Gets covariance of our current state belief distribution
*
* @return Covariance matrix
*/
Eigen::Matrix<T, XN, XN> GetStateCovariance() const { return P_; }
/**
* @brief Gets debug string containing detailed information about the filter.
*
* @return Debug string
*/
std::string DebugString() const;
/**
* @brief Get initialization state of the filter
* @return True if the filter is initialized
*/
bool IsInitialized() const { return is_initialized_; }
private:
// Mean of current state belief distribution
Eigen::Matrix<T, XN, 1> x_;
// Covariance of current state belief dist
Eigen::Matrix<T, XN, XN> P_;
// State transition matrix under zero control
Eigen::Matrix<T, XN, XN> F_;
// Covariance of the state transition noise
Eigen::Matrix<T, XN, XN> Q_;
// Observation matrix
Eigen::Matrix<T, ZN, XN> H_;
// Covariance of observation noise
Eigen::Matrix<T, ZN, ZN> R_;
// Control matrix in state transition rule
Eigen::Matrix<T, XN, UN> B_;
// Innovation; marked as member to prevent memory re-allocation.
Eigen::Matrix<T, ZN, 1> y_;
// Innovation covariance; marked as member to prevent memory re-allocation.
Eigen::Matrix<T, ZN, ZN> S_;
// Kalman gain; marked as member to prevent memory re-allocation.
Eigen::Matrix<T, XN, ZN> K_;
// true iff SetStateEstimate has been called.
bool is_initialized_ = false;
};
template <typename T, unsigned int XN, unsigned int ZN, unsigned int UN>
inline void KalmanFilter<T, XN, ZN, UN>::Predict(
const Eigen::Matrix<T, UN, 1> &u) {
ACHECK(is_initialized_);
x_ = F_ * x_ + B_ * u;
P_ = F_ * P_ * F_.transpose() + Q_;
}
template <typename T, unsigned int XN, unsigned int ZN, unsigned int UN>
inline void KalmanFilter<T, XN, ZN, UN>::Correct(
const Eigen::Matrix<T, ZN, 1> &z) {
ACHECK(is_initialized_);
y_ = z - H_ * x_;
S_ = static_cast<Eigen::Matrix<T, ZN, ZN>>(H_ * P_ * H_.transpose() + R_);
K_ = static_cast<Eigen::Matrix<T, XN, ZN>>(P_ * H_.transpose() *
PseudoInverse<T, ZN>(S_));
x_ = x_ + K_ * y_;
P_ = static_cast<Eigen::Matrix<T, XN, XN>>(
(Eigen::Matrix<T, XN, XN>::Identity() - K_ * H_) * P_);
}
template <typename T, unsigned int XN, unsigned int ZN, unsigned int UN>
inline std::string KalmanFilter<T, XN, ZN, UN>::DebugString() const {
Eigen::IOFormat clean_fmt(4, 0, ", ", " ", "[", "]");
std::stringstream ss;
ss << "F = " << F_.format(clean_fmt) << "\n"
<< "B = " << B_.format(clean_fmt) << "\n"
<< "H = " << H_.format(clean_fmt) << "\n"
<< "Q = " << Q_.format(clean_fmt) << "\n"
<< "R = " << R_.format(clean_fmt) << "\n"
<< "x = " << x_.format(clean_fmt) << "\n"
<< "P = " << P_.format(clean_fmt) << "\n";
return ss.str();
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/search.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Search-related functions.
*/
#pragma once
#include <functional>
/**
* @namespace apollo::common::math
* @brief apollo::common::math
*/
namespace apollo {
namespace common {
namespace math {
/**
* @brief Given a unimodal function defined on the interval,
* find a value on the interval to minimize the function.
* Reference: https://en.wikipedia.org/wiki/Golden-section_search
* @param func The target single-variable function to minimize.
* @param lower_bound The lower bound of the interval.
* @param upper_bound The upper bound of the interval.
* @param tol The tolerance of error.
* @return The value that minimize the function fun.
*/
double GoldenSectionSearch(const std::function<double(double)> &func,
const double lower_bound, const double upper_bound,
const double tol = 1e-6);
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/sin_table.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
// Do NOT modify this file. It was generated by gen_sin_table.py.
#include "modules/common/math/sin_table.h"
namespace apollo {
namespace common {
namespace math {
const float SIN_TABLE[16385] = {
0.000000000f, 0.000095874f, 0.000191748f, 0.000287621f, 0.000383495f,
0.000479369f, 0.000575243f, 0.000671117f, 0.000766990f, 0.000862864f,
0.000958738f, 0.001054612f, 0.001150485f, 0.001246359f, 0.001342233f,
0.001438106f, 0.001533980f, 0.001629854f, 0.001725728f, 0.001821601f,
0.001917475f, 0.002013348f, 0.002109222f, 0.002205096f, 0.002300969f,
0.002396843f, 0.002492716f, 0.002588590f, 0.002684463f, 0.002780337f,
0.002876210f, 0.002972083f, 0.003067957f, 0.003163830f, 0.003259703f,
0.003355577f, 0.003451450f, 0.003547323f, 0.003643196f, 0.003739069f,
0.003834943f, 0.003930816f, 0.004026689f, 0.004122562f, 0.004218435f,
0.004314308f, 0.004410180f, 0.004506053f, 0.004601926f, 0.004697799f,
0.004793672f, 0.004889544f, 0.004985417f, 0.005081289f, 0.005177162f,
0.005273035f, 0.005368907f, 0.005464779f, 0.005560652f, 0.005656524f,
0.005752396f, 0.005848268f, 0.005944141f, 0.006040013f, 0.006135885f,
0.006231757f, 0.006327629f, 0.006423500f, 0.006519372f, 0.006615244f,
0.006711116f, 0.006806987f, 0.006902859f, 0.006998730f, 0.007094602f,
0.007190473f, 0.007286344f, 0.007382215f, 0.007478087f, 0.007573958f,
0.007669829f, 0.007765700f, 0.007861571f, 0.007957441f, 0.008053312f,
0.008149183f, 0.008245053f, 0.008340924f, 0.008436794f, 0.008532665f,
0.008628535f, 0.008724405f, 0.008820275f, 0.008916145f, 0.009012015f,
0.009107885f, 0.009203755f, 0.009299624f, 0.009395494f, 0.009491364f,
0.009587233f, 0.009683102f, 0.009778972f, 0.009874841f, 0.009970710f,
0.010066579f, 0.010162448f, 0.010258317f, 0.010354185f, 0.010450054f,
0.010545922f, 0.010641791f, 0.010737659f, 0.010833527f, 0.010929396f,
0.011025264f, 0.011121131f, 0.011216999f, 0.011312867f, 0.011408735f,
0.011504602f, 0.011600470f, 0.011696337f, 0.011792204f, 0.011888071f,
0.011983938f, 0.012079805f, 0.012175672f, 0.012271538f, 0.012367405f,
0.012463271f, 0.012559138f, 0.012655004f, 0.012750870f, 0.012846736f,
0.012942602f, 0.013038467f, 0.013134333f, 0.013230198f, 0.013326064f,
0.013421929f, 0.013517794f, 0.013613659f, 0.013709524f, 0.013805389f,
0.013901253f, 0.013997118f, 0.014092982f, 0.014188846f, 0.014284710f,
0.014380574f, 0.014476438f, 0.014572302f, 0.014668165f, 0.014764029f,
0.014859892f, 0.014955755f, 0.015051618f, 0.015147481f, 0.015243344f,
0.015339206f, 0.015435069f, 0.015530931f, 0.015626793f, 0.015722655f,
0.015818517f, 0.015914379f, 0.016010240f, 0.016106102f, 0.016201963f,
0.016297824f, 0.016393685f, 0.016489546f, 0.016585407f, 0.016681267f,
0.016777128f, 0.016872988f, 0.016968848f, 0.017064708f, 0.017160568f,
0.017256427f, 0.017352287f, 0.017448146f, 0.017544005f, 0.017639864f,
0.017735723f, 0.017831582f, 0.017927440f, 0.018023298f, 0.018119156f,
0.018215014f, 0.018310872f, 0.018406730f, 0.018502587f, 0.018598445f,
0.018694302f, 0.018790159f, 0.018886016f, 0.018981872f, 0.019077729f,
0.019173585f, 0.019269441f, 0.019365297f, 0.019461153f, 0.019557008f,
0.019652864f, 0.019748719f, 0.019844574f, 0.019940429f, 0.020036283f,
0.020132138f, 0.020227992f, 0.020323846f, 0.020419700f, 0.020515554f,
0.020611407f, 0.020707261f, 0.020803114f, 0.020898967f, 0.020994819f,
0.021090672f, 0.021186524f, 0.021282376f, 0.021378228f, 0.021474080f,
0.021569932f, 0.021665783f, 0.021761634f, 0.021857485f, 0.021953336f,
0.022049187f, 0.022145037f, 0.022240887f, 0.022336737f, 0.022432587f,
0.022528437f, 0.022624286f, 0.022720135f, 0.022815984f, 0.022911833f,
0.023007681f, 0.023103530f, 0.023199378f, 0.023295226f, 0.023391073f,
0.023486921f, 0.023582768f, 0.023678615f, 0.023774462f, 0.023870309f,
0.023966155f, 0.024062001f, 0.024157847f, 0.024253693f, 0.024349538f,
0.024445383f, 0.024541229f, 0.024637073f, 0.024732918f, 0.024828762f,
0.024924606f, 0.025020450f, 0.025116294f, 0.025212137f, 0.025307981f,
0.025403824f, 0.025499666f, 0.025595509f, 0.025691351f, 0.025787193f,
0.025883035f, 0.025978877f, 0.026074718f, 0.026170559f, 0.026266400f,
0.026362240f, 0.026458081f, 0.026553921f, 0.026649761f, 0.026745600f,
0.026841440f, 0.026937279f, 0.027033118f, 0.027128956f, 0.027224795f,
0.027320633f, 0.027416471f, 0.027512308f, 0.027608146f, 0.027703983f,
0.027799820f, 0.027895656f, 0.027991493f, 0.028087329f, 0.028183165f,
0.028279000f, 0.028374836f, 0.028470671f, 0.028566505f, 0.028662340f,
0.028758174f, 0.028854008f, 0.028949842f, 0.029045676f, 0.029141509f,
0.029237342f, 0.029333174f, 0.029429007f, 0.029524839f, 0.029620671f,
0.029716502f, 0.029812334f, 0.029908165f, 0.030003996f, 0.030099826f,
0.030195656f, 0.030291486f, 0.030387316f, 0.030483145f, 0.030578974f,
0.030674803f, 0.030770632f, 0.030866460f, 0.030962288f, 0.031058116f,
0.031153943f, 0.031249770f, 0.031345597f, 0.031441424f, 0.031537250f,
0.031633076f, 0.031728901f, 0.031824727f, 0.031920552f, 0.032016377f,
0.032112201f, 0.032208025f, 0.032303849f, 0.032399673f, 0.032495496f,
0.032591319f, 0.032687142f, 0.032782964f, 0.032878787f, 0.032974608f,
0.033070430f, 0.033166251f, 0.033262072f, 0.033357893f, 0.033453713f,
0.033549533f, 0.033645352f, 0.033741172f, 0.033836991f, 0.033932810f,
0.034028628f, 0.034124446f, 0.034220264f, 0.034316081f, 0.034411899f,
0.034507716f, 0.034603532f, 0.034699348f, 0.034795164f, 0.034890980f,
0.034986795f, 0.035082610f, 0.035178425f, 0.035274239f, 0.035370053f,
0.035465867f, 0.035561680f, 0.035657493f, 0.035753305f, 0.035849118f,
0.035944930f, 0.036040742f, 0.036136553f, 0.036232364f, 0.036328175f,
0.036423985f, 0.036519795f, 0.036615605f, 0.036711414f, 0.036807223f,
0.036903032f, 0.036998840f, 0.037094648f, 0.037190456f, 0.037286263f,
0.037382070f, 0.037477876f, 0.037573683f, 0.037669489f, 0.037765294f,
0.037861099f, 0.037956904f, 0.038052709f, 0.038148513f, 0.038244317f,
0.038340120f, 0.038435924f, 0.038531726f, 0.038627529f, 0.038723331f,
0.038819132f, 0.038914934f, 0.039010735f, 0.039106535f, 0.039202336f,
0.039298136f, 0.039393935f, 0.039489734f, 0.039585533f, 0.039681332f,
0.039777130f, 0.039872928f, 0.039968725f, 0.040064522f, 0.040160319f,
0.040256115f, 0.040351911f, 0.040447706f, 0.040543501f, 0.040639296f,
0.040735091f, 0.040830885f, 0.040926678f, 0.041022472f, 0.041118265f,
0.041214057f, 0.041309849f, 0.041405641f, 0.041501432f, 0.041597223f,
0.041693014f, 0.041788804f, 0.041884594f, 0.041980384f, 0.042076173f,
0.042171961f, 0.042267750f, 0.042363538f, 0.042459325f, 0.042555112f,
0.042650899f, 0.042746685f, 0.042842471f, 0.042938257f, 0.043034042f,
0.043129827f, 0.043225611f, 0.043321395f, 0.043417179f, 0.043512962f,
0.043608745f, 0.043704527f, 0.043800309f, 0.043896091f, 0.043991872f,
0.044087653f, 0.044183433f, 0.044279213f, 0.044374993f, 0.044470772f,
0.044566551f, 0.044662329f, 0.044758107f, 0.044853884f, 0.044949661f,
0.045045438f, 0.045141214f, 0.045236990f, 0.045332766f, 0.045428541f,
0.045524315f, 0.045620090f, 0.045715863f, 0.045811637f, 0.045907410f,
0.046003182f, 0.046098954f, 0.046194726f, 0.046290497f, 0.046386268f,
0.046482038f, 0.046577808f, 0.046673578f, 0.046769347f, 0.046865116f,
0.046960884f, 0.047056652f, 0.047152419f, 0.047248186f, 0.047343952f,
0.047439719f, 0.047535484f, 0.047631249f, 0.047727014f, 0.047822778f,
0.047918542f, 0.048014306f, 0.048110069f, 0.048205831f, 0.048301593f,
0.048397355f, 0.048493116f, 0.048588877f, 0.048684637f, 0.048780397f,
0.048876157f, 0.048971916f, 0.049067674f, 0.049163432f, 0.049259190f,
0.049354947f, 0.049450704f, 0.049546460f, 0.049642216f, 0.049737971f,
0.049833726f, 0.049929481f, 0.050025235f, 0.050120988f, 0.050216741f,
0.050312494f, 0.050408246f, 0.050503998f, 0.050599749f, 0.050695500f,
0.050791250f, 0.050887000f, 0.050982749f, 0.051078498f, 0.051174247f,
0.051269994f, 0.051365742f, 0.051461489f, 0.051557235f, 0.051652982f,
0.051748727f, 0.051844472f, 0.051940217f, 0.052035961f, 0.052131705f,
0.052227448f, 0.052323191f, 0.052418933f, 0.052514675f, 0.052610416f,
0.052706157f, 0.052801897f, 0.052897637f, 0.052993376f, 0.053089115f,
0.053184853f, 0.053280591f, 0.053376328f, 0.053472065f, 0.053567802f,
0.053663538f, 0.053759273f, 0.053855008f, 0.053950742f, 0.054046476f,
0.054142210f, 0.054237943f, 0.054333675f, 0.054429407f, 0.054525138f,
0.054620869f, 0.054716600f, 0.054812330f, 0.054908059f, 0.055003788f,
0.055099516f, 0.055195244f, 0.055290972f, 0.055386699f, 0.055482425f,
0.055578151f, 0.055673876f, 0.055769601f, 0.055865325f, 0.055961049f,
0.056056773f, 0.056152495f, 0.056248218f, 0.056343939f, 0.056439661f,
0.056535381f, 0.056631101f, 0.056726821f, 0.056822540f, 0.056918259f,
0.057013977f, 0.057109695f, 0.057205412f, 0.057301128f, 0.057396844f,
0.057492560f, 0.057588275f, 0.057683989f, 0.057779703f, 0.057875416f,
0.057971129f, 0.058066842f, 0.058162553f, 0.058258265f, 0.058353975f,
0.058449685f, 0.058545395f, 0.058641104f, 0.058736813f, 0.058832521f,
0.058928228f, 0.059023935f, 0.059119641f, 0.059215347f, 0.059311052f,
0.059406757f, 0.059502461f, 0.059598165f, 0.059693868f, 0.059789571f,
0.059885273f, 0.059980974f, 0.060076675f, 0.060172375f, 0.060268075f,
0.060363775f, 0.060459473f, 0.060555171f, 0.060650869f, 0.060746566f,
0.060842262f, 0.060937958f, 0.061033654f, 0.061129348f, 0.061225043f,
0.061320736f, 0.061416429f, 0.061512122f, 0.061607814f, 0.061703505f,
0.061799196f, 0.061894886f, 0.061990576f, 0.062086265f, 0.062181954f,
0.062277642f, 0.062373329f, 0.062469016f, 0.062564702f, 0.062660388f,
0.062756073f, 0.062851758f, 0.062947442f, 0.063043125f, 0.063138808f,
0.063234490f, 0.063330172f, 0.063425853f, 0.063521533f, 0.063617213f,
0.063712892f, 0.063808571f, 0.063904249f, 0.063999927f, 0.064095604f,
0.064191280f, 0.064286956f, 0.064382631f, 0.064478306f, 0.064573980f,
0.064669653f, 0.064765326f, 0.064860998f, 0.064956670f, 0.065052341f,
0.065148011f, 0.065243681f, 0.065339350f, 0.065435019f, 0.065530687f,
0.065626354f, 0.065722021f, 0.065817687f, 0.065913353f, 0.066009018f,
0.066104682f, 0.066200346f, 0.066296009f, 0.066391672f, 0.066487334f,
0.066582995f, 0.066678656f, 0.066774316f, 0.066869975f, 0.066965634f,
0.067061293f, 0.067156950f, 0.067252607f, 0.067348264f, 0.067443920f,
0.067539575f, 0.067635229f, 0.067730883f, 0.067826537f, 0.067922189f,
0.068017841f, 0.068113493f, 0.068209144f, 0.068304794f, 0.068400443f,
0.068496092f, 0.068591741f, 0.068687388f, 0.068783035f, 0.068878682f,
0.068974328f, 0.069069973f, 0.069165617f, 0.069261261f, 0.069356904f,
0.069452547f, 0.069548189f, 0.069643830f, 0.069739471f, 0.069835111f,
0.069930750f, 0.070026389f, 0.070122027f, 0.070217665f, 0.070313302f,
0.070408938f, 0.070504573f, 0.070600208f, 0.070695843f, 0.070791476f,
0.070887109f, 0.070982741f, 0.071078373f, 0.071174004f, 0.071269634f,
0.071365264f, 0.071460893f, 0.071556521f, 0.071652149f, 0.071747776f,
0.071843402f, 0.071939028f, 0.072034653f, 0.072130278f, 0.072225901f,
0.072321524f, 0.072417147f, 0.072512769f, 0.072608390f, 0.072704010f,
0.072799630f, 0.072895249f, 0.072990867f, 0.073086485f, 0.073182102f,
0.073277718f, 0.073373334f, 0.073468949f, 0.073564564f, 0.073660177f,
0.073755790f, 0.073851403f, 0.073947014f, 0.074042625f, 0.074138236f,
0.074233845f, 0.074329454f, 0.074425062f, 0.074520670f, 0.074616277f,
0.074711883f, 0.074807488f, 0.074903093f, 0.074998697f, 0.075094301f,
0.075189904f, 0.075285506f, 0.075381107f, 0.075476708f, 0.075572308f,
0.075667907f, 0.075763506f, 0.075859103f, 0.075954701f, 0.076050297f,
0.076145893f, 0.076241488f, 0.076337082f, 0.076432676f, 0.076528269f,
0.076623861f, 0.076719453f, 0.076815044f, 0.076910634f, 0.077006223f,
0.077101812f, 0.077197400f, 0.077292988f, 0.077388574f, 0.077484160f,
0.077579745f, 0.077675330f, 0.077770914f, 0.077866497f, 0.077962079f,
0.078057661f, 0.078153242f, 0.078248822f, 0.078344401f, 0.078439980f,
0.078535558f, 0.078631135f, 0.078726712f, 0.078822288f, 0.078917863f,
0.079013437f, 0.079109011f, 0.079204584f, 0.079300156f, 0.079395728f,
0.079491299f, 0.079586869f, 0.079682438f, 0.079778007f, 0.079873574f,
0.079969142f, 0.080064708f, 0.080160274f, 0.080255838f, 0.080351403f,
0.080446966f, 0.080542529f, 0.080638091f, 0.080733652f, 0.080829212f,
0.080924772f, 0.081020331f, 0.081115889f, 0.081211447f, 0.081307004f,
0.081402560f, 0.081498115f, 0.081593669f, 0.081689223f, 0.081784776f,
0.081880328f, 0.081975880f, 0.082071431f, 0.082166981f, 0.082262530f,
0.082358078f, 0.082453626f, 0.082549173f, 0.082644719f, 0.082740265f,
0.082835809f, 0.082931353f, 0.083026896f, 0.083122439f, 0.083217980f,
0.083313521f, 0.083409061f, 0.083504601f, 0.083600139f, 0.083695677f,
0.083791214f, 0.083886750f, 0.083982286f, 0.084077820f, 0.084173354f,
0.084268888f, 0.084364420f, 0.084459952f, 0.084555482f, 0.084651013f,
0.084746542f, 0.084842070f, 0.084937598f, 0.085033125f, 0.085128651f,
0.085224177f, 0.085319701f, 0.085415225f, 0.085510748f, 0.085606270f,
0.085701792f, 0.085797312f, 0.085892832f, 0.085988351f, 0.086083870f,
0.086179387f, 0.086274904f, 0.086370420f, 0.086465935f, 0.086561449f,
0.086656963f, 0.086752476f, 0.086847987f, 0.086943499f, 0.087039009f,
0.087134519f, 0.087230027f, 0.087325535f, 0.087421042f, 0.087516549f,
0.087612054f, 0.087707559f, 0.087803063f, 0.087898566f, 0.087994068f,
0.088089570f, 0.088185070f, 0.088280570f, 0.088376069f, 0.088471568f,
0.088567065f, 0.088662562f, 0.088758058f, 0.088853553f, 0.088949047f,
0.089044540f, 0.089140033f, 0.089235524f, 0.089331015f, 0.089426505f,
0.089521995f, 0.089617483f, 0.089712971f, 0.089808457f, 0.089903943f,
0.089999429f, 0.090094913f, 0.090190396f, 0.090285879f, 0.090381361f,
0.090476842f, 0.090572322f, 0.090667801f, 0.090763280f, 0.090858758f,
0.090954234f, 0.091049710f, 0.091145185f, 0.091240660f, 0.091336133f,
0.091431606f, 0.091527078f, 0.091622549f, 0.091718019f, 0.091813488f,
0.091908956f, 0.092004424f, 0.092099891f, 0.092195357f, 0.092290822f,
0.092386286f, 0.092481749f, 0.092577212f, 0.092672673f, 0.092768134f,
0.092863594f, 0.092959053f, 0.093054511f, 0.093149969f, 0.093245425f,
0.093340881f, 0.093436336f, 0.093531790f, 0.093627243f, 0.093722695f,
0.093818146f, 0.093913597f, 0.094009047f, 0.094104495f, 0.094199943f,
0.094295390f, 0.094390837f, 0.094486282f, 0.094581726f, 0.094677170f,
0.094772613f, 0.094868054f, 0.094963495f, 0.095058935f, 0.095154375f,
0.095249813f, 0.095345250f, 0.095440687f, 0.095536123f, 0.095631558f,
0.095726991f, 0.095822425f, 0.095917857f, 0.096013288f, 0.096108718f,
0.096204148f, 0.096299577f, 0.096395004f, 0.096490431f, 0.096585857f,
0.096681282f, 0.096776707f, 0.096872130f, 0.096967552f, 0.097062974f,
0.097158395f, 0.097253814f, 0.097349233f, 0.097444651f, 0.097540068f,
0.097635485f, 0.097730900f, 0.097826314f, 0.097921728f, 0.098017140f,
0.098112552f, 0.098207963f, 0.098303373f, 0.098398782f, 0.098494190f,
0.098589597f, 0.098685003f, 0.098780409f, 0.098875813f, 0.098971217f,
0.099066619f, 0.099162021f, 0.099257422f, 0.099352822f, 0.099448221f,
0.099543619f, 0.099639016f, 0.099734412f, 0.099829807f, 0.099925202f,
0.100020595f, 0.100115988f, 0.100211379f, 0.100306770f, 0.100402160f,
0.100497549f, 0.100592937f, 0.100688324f, 0.100783710f, 0.100879095f,
0.100974479f, 0.101069863f, 0.101165245f, 0.101260627f, 0.101356007f,
0.101451387f, 0.101546765f, 0.101642143f, 0.101737520f, 0.101832896f,
0.101928271f, 0.102023645f, 0.102119018f, 0.102214390f, 0.102309761f,
0.102405131f, 0.102500501f, 0.102595869f, 0.102691236f, 0.102786603f,
0.102881968f, 0.102977333f, 0.103072697f, 0.103168059f, 0.103263421f,
0.103358782f, 0.103454142f, 0.103549501f, 0.103644859f, 0.103740215f,
0.103835572f, 0.103930927f, 0.104026281f, 0.104121634f, 0.104216986f,
0.104312337f, 0.104407688f, 0.104503037f, 0.104598385f, 0.104693733f,
0.104789079f, 0.104884425f, 0.104979769f, 0.105075113f, 0.105170455f,
0.105265797f, 0.105361138f, 0.105456477f, 0.105551816f, 0.105647154f,
0.105742490f, 0.105837826f, 0.105933161f, 0.106028495f, 0.106123828f,
0.106219160f, 0.106314491f, 0.106409821f, 0.106505150f, 0.106600478f,
0.106695805f, 0.106791131f, 0.106886456f, 0.106981780f, 0.107077103f,
0.107172425f, 0.107267746f, 0.107363066f, 0.107458385f, 0.107553704f,
0.107649021f, 0.107744337f, 0.107839652f, 0.107934966f, 0.108030279f,
0.108125592f, 0.108220903f, 0.108316213f, 0.108411522f, 0.108506831f,
0.108602138f, 0.108697444f, 0.108792749f, 0.108888053f, 0.108983357f,
0.109078659f, 0.109173960f, 0.109269260f, 0.109364560f, 0.109459858f,
0.109555155f, 0.109650451f, 0.109745746f, 0.109841041f, 0.109936334f,
0.110031626f, 0.110126917f, 0.110222207f, 0.110317496f, 0.110412785f,
0.110508072f, 0.110603358f, 0.110698643f, 0.110793927f, 0.110889210f,
0.110984492f, 0.111079773f, 0.111175053f, 0.111270332f, 0.111365610f,
0.111460887f, 0.111556163f, 0.111651437f, 0.111746711f, 0.111841984f,
0.111937256f, 0.112032527f, 0.112127796f, 0.112223065f, 0.112318333f,
0.112413599f, 0.112508865f, 0.112604129f, 0.112699393f, 0.112794655f,
0.112889917f, 0.112985177f, 0.113080437f, 0.113175695f, 0.113270952f,
0.113366208f, 0.113461464f, 0.113556718f, 0.113651971f, 0.113747223f,
0.113842474f, 0.113937724f, 0.114032973f, 0.114128221f, 0.114223468f,
0.114318713f, 0.114413958f, 0.114509202f, 0.114604445f, 0.114699686f,
0.114794927f, 0.114890166f, 0.114985404f, 0.115080642f, 0.115175878f,
0.115271113f, 0.115366348f, 0.115461581f, 0.115556813f, 0.115652044f,
0.115747274f, 0.115842503f, 0.115937730f, 0.116032957f, 0.116128183f,
0.116223407f, 0.116318631f, 0.116413853f, 0.116509075f, 0.116604295f,
0.116699514f, 0.116794733f, 0.116889950f, 0.116985166f, 0.117080381f,
0.117175595f, 0.117270807f, 0.117366019f, 0.117461230f, 0.117556439f,
0.117651648f, 0.117746855f, 0.117842062f, 0.117937267f, 0.118032471f,
0.118127674f, 0.118222876f, 0.118318077f, 0.118413277f, 0.118508475f,
0.118603673f, 0.118698870f, 0.118794065f, 0.118889259f, 0.118984453f,
0.119079645f, 0.119174836f, 0.119270026f, 0.119365215f, 0.119460403f,
0.119555589f, 0.119650775f, 0.119745959f, 0.119841143f, 0.119936325f,
0.120031506f, 0.120126686f, 0.120221865f, 0.120317043f, 0.120412220f,
0.120507396f, 0.120602570f, 0.120697744f, 0.120792916f, 0.120888087f,
0.120983257f, 0.121078426f, 0.121173594f, 0.121268761f, 0.121363927f,
0.121459091f, 0.121554255f, 0.121649417f, 0.121744578f, 0.121839738f,
0.121934897f, 0.122030055f, 0.122125212f, 0.122220367f, 0.122315522f,
0.122410675f, 0.122505827f, 0.122600979f, 0.122696128f, 0.122791277f,
0.122886425f, 0.122981572f, 0.123076717f, 0.123171861f, 0.123267005f,
0.123362147f, 0.123457288f, 0.123552427f, 0.123647566f, 0.123742704f,
0.123837840f, 0.123932975f, 0.124028109f, 0.124123242f, 0.124218374f,
0.124313505f, 0.124408634f, 0.124503763f, 0.124598890f, 0.124694016f,
0.124789141f, 0.124884265f, 0.124979387f, 0.125074509f, 0.125169629f,
0.125264748f, 0.125359867f, 0.125454983f, 0.125550099f, 0.125645214f,
0.125740327f, 0.125835439f, 0.125930551f, 0.126025661f, 0.126120769f,
0.126215877f, 0.126310984f, 0.126406089f, 0.126501193f, 0.126596296f,
0.126691398f, 0.126786499f, 0.126881598f, 0.126976696f, 0.127071794f,
0.127166890f, 0.127261985f, 0.127357078f, 0.127452171f, 0.127547262f,
0.127642352f, 0.127737441f, 0.127832529f, 0.127927616f, 0.128022701f,
0.128117785f, 0.128212869f, 0.128307950f, 0.128403031f, 0.128498111f,
0.128593189f, 0.128688266f, 0.128783342f, 0.128878417f, 0.128973491f,
0.129068563f, 0.129163635f, 0.129258705f, 0.129353774f, 0.129448841f,
0.129543908f, 0.129638973f, 0.129734037f, 0.129829100f, 0.129924162f,
0.130019223f, 0.130114282f, 0.130209340f, 0.130304397f, 0.130399453f,
0.130494508f, 0.130589561f, 0.130684613f, 0.130779664f, 0.130874714f,
0.130969763f, 0.131064810f, 0.131159856f, 0.131254901f, 0.131349945f,
0.131444987f, 0.131540029f, 0.131635069f, 0.131730108f, 0.131825145f,
0.131920182f, 0.132015217f, 0.132110251f, 0.132205284f, 0.132300316f,
0.132395346f, 0.132490375f, 0.132585403f, 0.132680430f, 0.132775456f,
0.132870480f, 0.132965503f, 0.133060525f, 0.133155546f, 0.133250565f,
0.133345583f, 0.133440600f, 0.133535616f, 0.133630631f, 0.133725644f,
0.133820656f, 0.133915667f, 0.134010677f, 0.134105685f, 0.134200692f,
0.134295698f, 0.134390703f, 0.134485706f, 0.134580709f, 0.134675709f,
0.134770709f, 0.134865708f, 0.134960705f, 0.135055701f, 0.135150696f,
0.135245689f, 0.135340682f, 0.135435673f, 0.135530663f, 0.135625651f,
0.135720638f, 0.135815624f, 0.135910609f, 0.136005593f, 0.136100575f,
0.136195556f, 0.136290536f, 0.136385515f, 0.136480492f, 0.136575468f,
0.136670443f, 0.136765416f, 0.136860389f, 0.136955360f, 0.137050329f,
0.137145298f, 0.137240265f, 0.137335231f, 0.137430196f, 0.137525159f,
0.137620122f, 0.137715083f, 0.137810042f, 0.137905001f, 0.137999958f,
0.138094914f, 0.138189868f, 0.138284822f, 0.138379774f, 0.138474724f,
0.138569674f, 0.138664622f, 0.138759569f, 0.138854515f, 0.138949459f,
0.139044402f, 0.139139344f, 0.139234285f, 0.139329224f, 0.139424162f,
0.139519099f, 0.139614034f, 0.139708968f, 0.139803901f, 0.139898833f,
0.139993763f, 0.140088692f, 0.140183620f, 0.140278546f, 0.140373472f,
0.140468395f, 0.140563318f, 0.140658239f, 0.140753159f, 0.140848078f,
0.140942995f, 0.141037912f, 0.141132826f, 0.141227740f, 0.141322652f,
0.141417563f, 0.141512473f, 0.141607381f, 0.141702288f, 0.141797194f,
0.141892098f, 0.141987001f, 0.142081903f, 0.142176804f, 0.142271703f,
0.142366601f, 0.142461497f, 0.142556392f, 0.142651286f, 0.142746179f,
0.142841070f, 0.142935960f, 0.143030849f, 0.143125736f, 0.143220623f,
0.143315507f, 0.143410391f, 0.143505273f, 0.143600154f, 0.143695033f,
0.143789911f, 0.143884788f, 0.143979664f, 0.144074538f, 0.144169411f,
0.144264282f, 0.144359152f, 0.144454021f, 0.144548889f, 0.144643755f,
0.144738620f, 0.144833484f, 0.144928346f, 0.145023207f, 0.145118066f,
0.145212925f, 0.145307782f, 0.145402637f, 0.145497491f, 0.145592344f,
0.145687196f, 0.145782046f, 0.145876895f, 0.145971742f, 0.146066589f,
0.146161434f, 0.146256277f, 0.146351119f, 0.146445960f, 0.146540800f,
0.146635638f, 0.146730474f, 0.146825310f, 0.146920144f, 0.147014977f,
0.147109808f, 0.147204638f, 0.147299467f, 0.147394294f, 0.147489120f,
0.147583945f, 0.147678768f, 0.147773590f, 0.147868410f, 0.147963230f,
0.148058047f, 0.148152864f, 0.148247679f, 0.148342493f, 0.148437305f,
0.148532116f, 0.148626926f, 0.148721734f, 0.148816541f, 0.148911346f,
0.149006151f, 0.149100953f, 0.149195755f, 0.149290555f, 0.149385354f,
0.149480151f, 0.149574947f, 0.149669741f, 0.149764535f, 0.149859326f,
0.149954117f, 0.150048906f, 0.150143694f, 0.150238480f, 0.150333265f,
0.150428048f, 0.150522831f, 0.150617611f, 0.150712391f, 0.150807169f,
0.150901945f, 0.150996721f, 0.151091494f, 0.151186267f, 0.151281038f,
0.151375808f, 0.151470576f, 0.151565343f, 0.151660108f, 0.151754872f,
0.151849635f, 0.151944396f, 0.152039156f, 0.152133915f, 0.152228672f,
0.152323428f, 0.152418182f, 0.152512935f, 0.152607686f, 0.152702437f,
0.152797185f, 0.152891933f, 0.152986678f, 0.153081423f, 0.153176166f,
0.153270908f, 0.153365648f, 0.153460387f, 0.153555124f, 0.153649860f,
0.153744595f, 0.153839328f, 0.153934060f, 0.154028790f, 0.154123519f,
0.154218247f, 0.154312973f, 0.154407698f, 0.154502421f, 0.154597143f,
0.154691863f, 0.154786582f, 0.154881300f, 0.154976016f, 0.155070731f,
0.155165444f, 0.155260156f, 0.155354867f, 0.155449576f, 0.155544283f,
0.155638990f, 0.155733694f, 0.155828398f, 0.155923100f, 0.156017800f,
0.156112499f, 0.156207197f, 0.156301893f, 0.156396588f, 0.156491281f,
0.156585973f, 0.156680663f, 0.156775352f, 0.156870040f, 0.156964726f,
0.157059410f, 0.157154094f, 0.157248775f, 0.157343456f, 0.157438134f,
0.157532812f, 0.157627488f, 0.157722162f, 0.157816835f, 0.157911507f,
0.158006177f, 0.158100846f, 0.158195513f, 0.158290179f, 0.158384843f,
0.158479506f, 0.158574168f, 0.158668828f, 0.158763486f, 0.158858143f,
0.158952799f, 0.159047453f, 0.159142106f, 0.159236757f, 0.159331407f,
0.159426055f, 0.159520702f, 0.159615347f, 0.159709991f, 0.159804634f,
0.159899275f, 0.159993914f, 0.160088552f, 0.160183189f, 0.160277824f,
0.160372457f, 0.160467089f, 0.160561720f, 0.160656349f, 0.160750977f,
0.160845603f, 0.160940228f, 0.161034851f, 0.161129473f, 0.161224093f,
0.161318712f, 0.161413329f, 0.161507945f, 0.161602560f, 0.161697172f,
0.161791784f, 0.161886394f, 0.161981002f, 0.162075609f, 0.162170215f,
0.162264819f, 0.162359421f, 0.162454022f, 0.162548621f, 0.162643219f,
0.162737816f, 0.162832411f, 0.162927004f, 0.163021596f, 0.163116187f,
0.163210776f, 0.163305363f, 0.163399949f, 0.163494534f, 0.163589117f,
0.163683698f, 0.163778278f, 0.163872857f, 0.163967434f, 0.164062009f,
0.164156583f, 0.164251156f, 0.164345727f, 0.164440296f, 0.164534864f,
0.164629430f, 0.164723995f, 0.164818559f, 0.164913120f, 0.165007681f,
0.165102240f, 0.165196797f, 0.165291353f, 0.165385907f, 0.165480460f,
0.165575011f, 0.165669561f, 0.165764109f, 0.165858656f, 0.165953201f,
0.166047744f, 0.166142286f, 0.166236827f, 0.166331366f, 0.166425904f,
0.166520440f, 0.166614974f, 0.166709507f, 0.166804038f, 0.166898568f,
0.166993096f, 0.167087623f, 0.167182148f, 0.167276672f, 0.167371194f,
0.167465715f, 0.167560234f, 0.167654752f, 0.167749268f, 0.167843782f,
0.167938295f, 0.168032806f, 0.168127316f, 0.168221824f, 0.168316331f,
0.168410836f, 0.168505340f, 0.168599842f, 0.168694343f, 0.168788842f,
0.168883339f, 0.168977835f, 0.169072329f, 0.169166822f, 0.169261313f,
0.169355803f, 0.169450291f, 0.169544778f, 0.169639263f, 0.169733746f,
0.169828228f, 0.169922708f, 0.170017187f, 0.170111664f, 0.170206140f,
0.170300614f, 0.170395087f, 0.170489558f, 0.170584027f, 0.170678495f,
0.170772961f, 0.170867426f, 0.170961889f, 0.171056350f, 0.171150810f,
0.171245269f, 0.171339725f, 0.171434181f, 0.171528634f, 0.171623086f,
0.171717537f, 0.171811986f, 0.171906433f, 0.172000879f, 0.172095323f,
0.172189766f, 0.172284207f, 0.172378646f, 0.172473084f, 0.172567520f,
0.172661955f, 0.172756388f, 0.172850820f, 0.172945249f, 0.173039678f,
0.173134105f, 0.173228530f, 0.173322953f, 0.173417375f, 0.173511796f,
0.173606214f, 0.173700631f, 0.173795047f, 0.173889461f, 0.173983873f,
0.174078284f, 0.174172693f, 0.174267101f, 0.174361507f, 0.174455911f,
0.174550314f, 0.174644715f, 0.174739115f, 0.174833513f, 0.174927909f,
0.175022304f, 0.175116697f, 0.175211088f, 0.175305478f, 0.175399867f,
0.175494253f, 0.175588638f, 0.175683022f, 0.175777404f, 0.175871784f,
0.175966163f, 0.176060540f, 0.176154915f, 0.176249289f, 0.176343661f,
0.176438031f, 0.176532400f, 0.176626768f, 0.176721133f, 0.176815497f,
0.176909860f, 0.177004220f, 0.177098580f, 0.177192937f, 0.177287293f,
0.177381647f, 0.177476000f, 0.177570351f, 0.177664700f, 0.177759048f,
0.177853394f, 0.177947739f, 0.178042081f, 0.178136423f, 0.178230762f,
0.178325100f, 0.178419436f, 0.178513771f, 0.178608104f, 0.178702435f,
0.178796765f, 0.178891093f, 0.178985420f, 0.179079744f, 0.179174067f,
0.179268389f, 0.179362709f, 0.179457027f, 0.179551343f, 0.179645658f,
0.179739972f, 0.179834283f, 0.179928593f, 0.180022901f, 0.180117208f,
0.180211513f, 0.180305816f, 0.180400118f, 0.180494418f, 0.180588716f,
0.180683013f, 0.180777308f, 0.180871601f, 0.180965893f, 0.181060183f,
0.181154471f, 0.181248758f, 0.181343043f, 0.181437327f, 0.181531608f,
0.181625888f, 0.181720167f, 0.181814443f, 0.181908718f, 0.182002992f,
0.182097263f, 0.182191533f, 0.182285802f, 0.182380068f, 0.182474333f,
0.182568597f, 0.182662858f, 0.182757118f, 0.182851376f, 0.182945633f,
0.183039888f, 0.183134141f, 0.183228393f, 0.183322643f, 0.183416891f,
0.183511137f, 0.183605382f, 0.183699625f, 0.183793867f, 0.183888106f,
0.183982344f, 0.184076581f, 0.184170815f, 0.184265048f, 0.184359279f,
0.184453509f, 0.184547737f, 0.184641963f, 0.184736188f, 0.184830410f,
0.184924631f, 0.185018851f, 0.185113069f, 0.185207285f, 0.185301499f,
0.185395711f, 0.185489922f, 0.185584131f, 0.185678339f, 0.185772545f,
0.185866749f, 0.185960951f, 0.186055152f, 0.186149351f, 0.186243548f,
0.186337743f, 0.186431937f, 0.186526129f, 0.186620320f, 0.186714508f,
0.186808695f, 0.186902880f, 0.186997064f, 0.187091246f, 0.187185426f,
0.187279604f, 0.187373781f, 0.187467955f, 0.187562129f, 0.187656300f,
0.187750470f, 0.187844638f, 0.187938804f, 0.188032969f, 0.188127131f,
0.188221292f, 0.188315452f, 0.188409609f, 0.188503765f, 0.188597919f,
0.188692072f, 0.188786223f, 0.188880371f, 0.188974519f, 0.189068664f,
0.189162808f, 0.189256950f, 0.189351090f, 0.189445229f, 0.189539365f,
0.189633500f, 0.189727634f, 0.189821765f, 0.189915895f, 0.190010023f,
0.190104149f, 0.190198274f, 0.190292397f, 0.190386518f, 0.190480637f,
0.190574755f, 0.190668871f, 0.190762985f, 0.190857097f, 0.190951208f,
0.191045316f, 0.191139423f, 0.191233529f, 0.191327632f, 0.191421734f,
0.191515834f, 0.191609932f, 0.191704029f, 0.191798123f, 0.191892216f,
0.191986308f, 0.192080397f, 0.192174485f, 0.192268571f, 0.192362655f,
0.192456737f, 0.192550818f, 0.192644897f, 0.192738974f, 0.192833049f,
0.192927122f, 0.193021194f, 0.193115264f, 0.193209332f, 0.193303399f,
0.193397463f, 0.193491526f, 0.193585587f, 0.193679647f, 0.193773704f,
0.193867760f, 0.193961814f, 0.194055866f, 0.194149916f, 0.194243965f,
0.194338012f, 0.194432057f, 0.194526100f, 0.194620142f, 0.194714181f,
0.194808219f, 0.194902255f, 0.194996290f, 0.195090322f, 0.195184353f,
0.195278382f, 0.195372409f, 0.195466434f, 0.195560458f, 0.195654479f,
0.195748499f, 0.195842517f, 0.195936534f, 0.196030548f, 0.196124561f,
0.196218572f, 0.196312581f, 0.196406588f, 0.196500594f, 0.196594598f,
0.196688600f, 0.196782600f, 0.196876598f, 0.196970594f, 0.197064589f,
0.197158582f, 0.197252573f, 0.197346562f, 0.197440550f, 0.197534535f,
0.197628519f, 0.197722501f, 0.197816481f, 0.197910460f, 0.198004436f,
0.198098411f, 0.198192384f, 0.198286355f, 0.198380324f, 0.198474291f,
0.198568257f, 0.198662221f, 0.198756183f, 0.198850143f, 0.198944101f,
0.199038057f, 0.199132012f, 0.199225965f, 0.199319916f, 0.199413865f,
0.199507812f, 0.199601758f, 0.199695701f, 0.199789643f, 0.199883583f,
0.199977521f, 0.200071457f, 0.200165392f, 0.200259324f, 0.200353255f,
0.200447184f, 0.200541111f, 0.200635036f, 0.200728960f, 0.200822881f,
0.200916801f, 0.201010719f, 0.201104635f, 0.201198549f, 0.201292461f,
0.201386372f, 0.201480280f, 0.201574187f, 0.201668092f, 0.201761995f,
0.201855896f, 0.201949796f, 0.202043693f, 0.202137589f, 0.202231482f,
0.202325374f, 0.202419264f, 0.202513153f, 0.202607039f, 0.202700923f,
0.202794806f, 0.202888687f, 0.202982565f, 0.203076442f, 0.203170318f,
0.203264191f, 0.203358062f, 0.203451932f, 0.203545799f, 0.203639665f,
0.203733529f, 0.203827391f, 0.203921251f, 0.204015110f, 0.204108966f,
0.204202821f, 0.204296673f, 0.204390524f, 0.204484373f, 0.204578220f,
0.204672065f, 0.204765908f, 0.204859750f, 0.204953589f, 0.205047427f,
0.205141263f, 0.205235097f, 0.205328928f, 0.205422759f, 0.205516587f,
0.205610413f, 0.205704237f, 0.205798060f, 0.205891881f, 0.205985699f,
0.206079516f, 0.206173331f, 0.206267144f, 0.206360955f, 0.206454765f,
0.206548572f, 0.206642377f, 0.206736181f, 0.206829983f, 0.206923782f,
0.207017580f, 0.207111376f, 0.207205170f, 0.207298962f, 0.207392753f,
0.207486541f, 0.207580327f, 0.207674112f, 0.207767895f, 0.207861675f,
0.207955454f, 0.208049231f, 0.208143006f, 0.208236779f, 0.208330550f,
0.208424319f, 0.208518087f, 0.208611852f, 0.208705615f, 0.208799377f,
0.208893137f, 0.208986894f, 0.209080650f, 0.209174404f, 0.209268156f,
0.209361906f, 0.209455654f, 0.209549400f, 0.209643145f, 0.209736887f,
0.209830627f, 0.209924366f, 0.210018102f, 0.210111837f, 0.210205570f,
0.210299300f, 0.210393029f, 0.210486756f, 0.210580481f, 0.210674204f,
0.210767925f, 0.210861644f, 0.210955361f, 0.211049077f, 0.211142790f,
0.211236501f, 0.211330211f, 0.211423918f, 0.211517624f, 0.211611327f,
0.211705029f, 0.211798729f, 0.211892427f, 0.211986122f, 0.212079816f,
0.212173508f, 0.212267198f, 0.212360886f, 0.212454572f, 0.212548256f,
0.212641938f, 0.212735619f, 0.212829297f, 0.212922973f, 0.213016648f,
0.213110320f, 0.213203990f, 0.213297659f, 0.213391325f, 0.213484990f,
0.213578652f, 0.213672313f, 0.213765972f, 0.213859628f, 0.213953283f,
0.214046936f, 0.214140587f, 0.214234235f, 0.214327882f, 0.214421527f,
0.214515170f, 0.214608811f, 0.214702450f, 0.214796087f, 0.214889722f,
0.214983355f, 0.215076986f, 0.215170615f, 0.215264242f, 0.215357867f,
0.215451491f, 0.215545112f, 0.215638731f, 0.215732348f, 0.215825963f,
0.215919577f, 0.216013188f, 0.216106797f, 0.216200404f, 0.216294010f,
0.216387613f, 0.216481214f, 0.216574814f, 0.216668411f, 0.216762006f,
0.216855600f, 0.216949191f, 0.217042780f, 0.217136368f, 0.217229953f,
0.217323536f, 0.217417118f, 0.217510697f, 0.217604275f, 0.217697850f,
0.217791423f, 0.217884995f, 0.217978564f, 0.218072132f, 0.218165697f,
0.218259260f, 0.218352822f, 0.218446381f, 0.218539938f, 0.218633494f,
0.218727047f, 0.218820598f, 0.218914148f, 0.219007695f, 0.219101240f,
0.219194783f, 0.219288325f, 0.219381864f, 0.219475401f, 0.219568936f,
0.219662469f, 0.219756001f, 0.219849530f, 0.219943057f, 0.220036582f,
0.220130105f, 0.220223626f, 0.220317145f, 0.220410662f, 0.220504177f,
0.220597690f, 0.220691201f, 0.220784710f, 0.220878217f, 0.220971722f,
0.221065224f, 0.221158725f, 0.221252224f, 0.221345721f, 0.221439215f,
0.221532708f, 0.221626199f, 0.221719687f, 0.221813174f, 0.221906658f,
0.222000141f, 0.222093621f, 0.222187099f, 0.222280576f, 0.222374050f,
0.222467522f, 0.222560992f, 0.222654461f, 0.222747927f, 0.222841391f,
0.222934853f, 0.223028313f, 0.223121771f, 0.223215226f, 0.223308680f,
0.223402132f, 0.223495582f, 0.223589029f, 0.223682475f, 0.223775918f,
0.223869360f, 0.223962799f, 0.224056237f, 0.224149672f, 0.224243105f,
0.224336536f, 0.224429965f, 0.224523392f, 0.224616817f, 0.224710240f,
0.224803661f, 0.224897080f, 0.224990497f, 0.225083911f, 0.225177324f,
0.225270734f, 0.225364143f, 0.225457549f, 0.225550954f, 0.225644356f,
0.225737756f, 0.225831154f, 0.225924550f, 0.226017944f, 0.226111336f,
0.226204726f, 0.226298113f, 0.226391499f, 0.226484882f, 0.226578264f,
0.226671643f, 0.226765020f, 0.226858396f, 0.226951769f, 0.227045140f,
0.227138509f, 0.227231876f, 0.227325240f, 0.227418603f, 0.227511964f,
0.227605322f, 0.227698679f, 0.227792033f, 0.227885385f, 0.227978735f,
0.228072083f, 0.228165429f, 0.228258773f, 0.228352115f, 0.228445454f,
0.228538792f, 0.228632127f, 0.228725461f, 0.228818792f, 0.228912121f,
0.229005448f, 0.229098773f, 0.229192096f, 0.229285416f, 0.229378735f,
0.229472051f, 0.229565366f, 0.229658678f, 0.229751988f, 0.229845296f,
0.229938602f, 0.230031906f, 0.230125208f, 0.230218507f, 0.230311805f,
0.230405100f, 0.230498393f, 0.230591685f, 0.230684974f, 0.230778260f,
0.230871545f, 0.230964828f, 0.231058108f, 0.231151387f, 0.231244663f,
0.231337937f, 0.231431209f, 0.231524479f, 0.231617747f, 0.231711012f,
0.231804276f, 0.231897537f, 0.231990796f, 0.232084054f, 0.232177309f,
0.232270561f, 0.232363812f, 0.232457061f, 0.232550307f, 0.232643551f,
0.232736793f, 0.232830033f, 0.232923271f, 0.233016507f, 0.233109741f,
0.233202972f, 0.233296201f, 0.233389429f, 0.233482654f, 0.233575876f,
0.233669097f, 0.233762316f, 0.233855532f, 0.233948746f, 0.234041959f,
0.234135169f, 0.234228376f, 0.234321582f, 0.234414786f, 0.234507987f,
0.234601186f, 0.234694383f, 0.234787578f, 0.234880771f, 0.234973961f,
0.235067150f, 0.235160336f, 0.235253520f, 0.235346702f, 0.235439882f,
0.235533059f, 0.235626235f, 0.235719408f, 0.235812579f, 0.235905748f,
0.235998915f, 0.236092080f, 0.236185242f, 0.236278402f, 0.236371560f,
0.236464716f, 0.236557870f, 0.236651021f, 0.236744171f, 0.236837318f,
0.236930463f, 0.237023606f, 0.237116747f, 0.237209885f, 0.237303021f,
0.237396156f, 0.237489288f, 0.237582417f, 0.237675545f, 0.237768670f,
0.237861794f, 0.237954915f, 0.238048033f, 0.238141150f, 0.238234265f,
0.238327377f, 0.238420487f, 0.238513595f, 0.238606701f, 0.238699804f,
0.238792905f, 0.238886004f, 0.238979101f, 0.239072196f, 0.239165289f,
0.239258379f, 0.239351467f, 0.239444553f, 0.239537637f, 0.239630718f,
0.239723798f, 0.239816875f, 0.239909950f, 0.240003022f, 0.240096093f,
0.240189161f, 0.240282227f, 0.240375291f, 0.240468353f, 0.240561412f,
0.240654470f, 0.240747525f, 0.240840578f, 0.240933628f, 0.241026677f,
0.241119723f, 0.241212767f, 0.241305808f, 0.241398848f, 0.241491885f,
0.241584920f, 0.241677953f, 0.241770984f, 0.241864012f, 0.241957039f,
0.242050063f, 0.242143084f, 0.242236104f, 0.242329121f, 0.242422136f,
0.242515149f, 0.242608160f, 0.242701168f, 0.242794174f, 0.242887178f,
0.242980180f, 0.243073179f, 0.243166177f, 0.243259172f, 0.243352164f,
0.243445155f, 0.243538143f, 0.243631129f, 0.243724113f, 0.243817095f,
0.243910074f, 0.244003051f, 0.244096026f, 0.244188998f, 0.244281969f,
0.244374937f, 0.244467903f, 0.244560866f, 0.244653828f, 0.244746787f,
0.244839744f, 0.244932698f, 0.245025651f, 0.245118601f, 0.245211549f,
0.245304494f, 0.245397438f, 0.245490379f, 0.245583318f, 0.245676254f,
0.245769188f, 0.245862121f, 0.245955050f, 0.246047978f, 0.246140903f,
0.246233826f, 0.246326747f, 0.246419665f, 0.246512582f, 0.246605496f,
0.246698407f, 0.246791317f, 0.246884224f, 0.246977129f, 0.247070031f,
0.247162932f, 0.247255830f, 0.247348726f, 0.247441619f, 0.247534510f,
0.247627399f, 0.247720286f, 0.247813171f, 0.247906053f, 0.247998933f,
0.248091810f, 0.248184685f, 0.248277558f, 0.248370429f, 0.248463298f,
0.248556164f, 0.248649028f, 0.248741889f, 0.248834749f, 0.248927606f,
0.249020460f, 0.249113313f, 0.249206163f, 0.249299011f, 0.249391857f,
0.249484700f, 0.249577541f, 0.249670380f, 0.249763216f, 0.249856050f,
0.249948882f, 0.250041711f, 0.250134539f, 0.250227364f, 0.250320186f,
0.250413007f, 0.250505825f, 0.250598640f, 0.250691454f, 0.250784265f,
0.250877074f, 0.250969880f, 0.251062684f, 0.251155486f, 0.251248286f,
0.251341083f, 0.251433878f, 0.251526671f, 0.251619461f, 0.251712249f,
0.251805035f, 0.251897818f, 0.251990599f, 0.252083378f, 0.252176154f,
0.252268929f, 0.252361700f, 0.252454470f, 0.252547237f, 0.252640002f,
0.252732764f, 0.252825525f, 0.252918282f, 0.253011038f, 0.253103791f,
0.253196542f, 0.253289291f, 0.253382037f, 0.253474781f, 0.253567522f,
0.253660262f, 0.253752999f, 0.253845733f, 0.253938466f, 0.254031195f,
0.254123923f, 0.254216648f, 0.254309371f, 0.254402092f, 0.254494810f,
0.254587526f, 0.254680240f, 0.254772951f, 0.254865660f, 0.254958366f,
0.255051070f, 0.255143772f, 0.255236472f, 0.255329169f, 0.255421864f,
0.255514556f, 0.255607246f, 0.255699934f, 0.255792619f, 0.255885302f,
0.255977983f, 0.256070662f, 0.256163338f, 0.256256011f, 0.256348682f,
0.256441351f, 0.256534018f, 0.256626682f, 0.256719344f, 0.256812004f,
0.256904661f, 0.256997316f, 0.257089968f, 0.257182618f, 0.257275266f,
0.257367911f, 0.257460554f, 0.257553195f, 0.257645833f, 0.257738469f,
0.257831102f, 0.257923733f, 0.258016362f, 0.258108988f, 0.258201612f,
0.258294234f, 0.258386853f, 0.258479470f, 0.258572085f, 0.258664697f,
0.258757307f, 0.258849914f, 0.258942519f, 0.259035122f, 0.259127722f,
0.259220320f, 0.259312915f, 0.259405508f, 0.259498099f, 0.259590687f,
0.259683273f, 0.259775857f, 0.259868438f, 0.259961017f, 0.260053593f,
0.260146167f, 0.260238739f, 0.260331308f, 0.260423875f, 0.260516439f,
0.260609001f, 0.260701561f, 0.260794118f, 0.260886673f, 0.260979225f,
0.261071775f, 0.261164323f, 0.261256868f, 0.261349411f, 0.261441951f,
0.261534489f, 0.261627025f, 0.261719558f, 0.261812089f, 0.261904617f,
0.261997143f, 0.262089667f, 0.262182188f, 0.262274707f, 0.262367223f,
0.262459737f, 0.262552249f, 0.262644758f, 0.262737265f, 0.262829769f,
0.262922271f, 0.263014770f, 0.263107267f, 0.263199762f, 0.263292254f,
0.263384744f, 0.263477231f, 0.263569716f, 0.263662199f, 0.263754679f,
0.263847157f, 0.263939632f, 0.264032105f, 0.264124575f, 0.264217043f,
0.264309509f, 0.264401972f, 0.264494432f, 0.264586891f, 0.264679346f,
0.264771800f, 0.264864251f, 0.264956699f, 0.265049145f, 0.265141589f,
0.265234030f, 0.265326469f, 0.265418905f, 0.265511339f, 0.265603771f,
0.265696200f, 0.265788626f, 0.265881050f, 0.265973472f, 0.266065891f,
0.266158308f, 0.266250722f, 0.266343134f, 0.266435544f, 0.266527951f,
0.266620355f, 0.266712757f, 0.266805157f, 0.266897554f, 0.266989949f,
0.267082341f, 0.267174731f, 0.267267119f, 0.267359503f, 0.267451886f,
0.267544266f, 0.267636643f, 0.267729019f, 0.267821391f, 0.267913761f,
0.268006129f, 0.268098494f, 0.268190857f, 0.268283217f, 0.268375575f,
0.268467931f, 0.268560283f, 0.268652634f, 0.268744982f, 0.268837327f,
0.268929670f, 0.269022011f, 0.269114349f, 0.269206685f, 0.269299018f,
0.269391348f, 0.269483677f, 0.269576002f, 0.269668326f, 0.269760646f,
0.269852965f, 0.269945280f, 0.270037594f, 0.270129905f, 0.270222213f,
0.270314519f, 0.270406822f, 0.270499123f, 0.270591421f, 0.270683717f,
0.270776011f, 0.270868302f, 0.270960590f, 0.271052876f, 0.271145160f,
0.271237441f, 0.271329719f, 0.271421995f, 0.271514268f, 0.271606539f,
0.271698808f, 0.271791074f, 0.271883337f, 0.271975598f, 0.272067857f,
0.272160113f, 0.272252366f, 0.272344617f, 0.272436866f, 0.272529112f,
0.272621355f, 0.272713596f, 0.272805835f, 0.272898071f, 0.272990304f,
0.273082535f, 0.273174764f, 0.273266990f, 0.273359213f, 0.273451434f,
0.273543652f, 0.273635868f, 0.273728082f, 0.273820292f, 0.273912501f,
0.274004707f, 0.274096910f, 0.274189111f, 0.274281309f, 0.274373505f,
0.274465698f, 0.274557889f, 0.274650077f, 0.274742262f, 0.274834445f,
0.274926626f, 0.275018804f, 0.275110980f, 0.275203153f, 0.275295323f,
0.275387491f, 0.275479656f, 0.275571819f, 0.275663980f, 0.275756137f,
0.275848293f, 0.275940445f, 0.276032596f, 0.276124743f, 0.276216888f,
0.276309031f, 0.276401171f, 0.276493309f, 0.276585444f, 0.276677576f,
0.276769706f, 0.276861833f, 0.276953958f, 0.277046080f, 0.277138200f,
0.277230317f, 0.277322432f, 0.277414544f, 0.277506653f, 0.277598760f,
0.277690865f, 0.277782967f, 0.277875066f, 0.277967163f, 0.278059257f,
0.278151348f, 0.278243438f, 0.278335524f, 0.278427608f, 0.278519689f,
0.278611768f, 0.278703845f, 0.278795918f, 0.278887989f, 0.278980058f,
0.279072124f, 0.279164187f, 0.279256248f, 0.279348307f, 0.279440362f,
0.279532416f, 0.279624466f, 0.279716514f, 0.279808560f, 0.279900603f,
0.279992643f, 0.280084681f, 0.280176716f, 0.280268749f, 0.280360779f,
0.280452806f, 0.280544831f, 0.280636853f, 0.280728873f, 0.280820890f,
0.280912905f, 0.281004917f, 0.281096926f, 0.281188933f, 0.281280937f,
0.281372939f, 0.281464938f, 0.281556934f, 0.281648928f, 0.281740920f,
0.281832908f, 0.281924894f, 0.282016878f, 0.282108859f, 0.282200837f,
0.282292813f, 0.282384786f, 0.282476757f, 0.282568725f, 0.282660690f,
0.282752653f, 0.282844613f, 0.282936570f, 0.283028525f, 0.283120478f,
0.283212428f, 0.283304375f, 0.283396319f, 0.283488261f, 0.283580201f,
0.283672137f, 0.283764071f, 0.283856003f, 0.283947932f, 0.284039858f,
0.284131782f, 0.284223703f, 0.284315621f, 0.284407537f, 0.284499450f,
0.284591361f, 0.284683269f, 0.284775174f, 0.284867077f, 0.284958977f,
0.285050875f, 0.285142770f, 0.285234662f, 0.285326552f, 0.285418439f,
0.285510323f, 0.285602205f, 0.285694084f, 0.285785961f, 0.285877835f,
0.285969706f, 0.286061575f, 0.286153441f, 0.286245304f, 0.286337165f,
0.286429023f, 0.286520879f, 0.286612731f, 0.286704582f, 0.286796429f,
0.286888274f, 0.286980117f, 0.287071956f, 0.287163793f, 0.287255628f,
0.287347460f, 0.287439289f, 0.287531115f, 0.287622939f, 0.287714760f,
0.287806579f, 0.287898395f, 0.287990208f, 0.288082019f, 0.288173827f,
0.288265632f, 0.288357435f, 0.288449235f, 0.288541032f, 0.288632827f,
0.288724619f, 0.288816408f, 0.288908195f, 0.288999979f, 0.289091761f,
0.289183539f, 0.289275315f, 0.289367089f, 0.289458860f, 0.289550628f,
0.289642393f, 0.289734156f, 0.289825916f, 0.289917674f, 0.290009429f,
0.290101181f, 0.290192930f, 0.290284677f, 0.290376421f, 0.290468163f,
0.290559902f, 0.290651638f, 0.290743371f, 0.290835102f, 0.290926830f,
0.291018556f, 0.291110279f, 0.291201999f, 0.291293716f, 0.291385431f,
0.291477143f, 0.291568852f, 0.291660559f, 0.291752263f, 0.291843965f,
0.291935663f, 0.292027359f, 0.292119053f, 0.292210743f, 0.292302431f,
0.292394116f, 0.292485799f, 0.292577479f, 0.292669156f, 0.292760831f,
0.292852502f, 0.292944171f, 0.293035838f, 0.293127502f, 0.293219163f,
0.293310821f, 0.293402477f, 0.293494130f, 0.293585780f, 0.293677427f,
0.293769072f, 0.293860714f, 0.293952354f, 0.294043991f, 0.294135625f,
0.294227256f, 0.294318885f, 0.294410511f, 0.294502134f, 0.294593754f,
0.294685372f, 0.294776987f, 0.294868600f, 0.294960209f, 0.295051816f,
0.295143421f, 0.295235022f, 0.295326621f, 0.295418217f, 0.295509811f,
0.295601401f, 0.295692989f, 0.295784574f, 0.295876157f, 0.295967737f,
0.296059314f, 0.296150888f, 0.296242460f, 0.296334029f, 0.296425595f,
0.296517159f, 0.296608719f, 0.296700277f, 0.296791833f, 0.296883385f,
0.296974935f, 0.297066482f, 0.297158027f, 0.297249568f, 0.297341107f,
0.297432643f, 0.297524177f, 0.297615707f, 0.297707235f, 0.297798761f,
0.297890283f, 0.297981803f, 0.298073320f, 0.298164834f, 0.298256346f,
0.298347855f, 0.298439361f, 0.298530864f, 0.298622365f, 0.298713862f,
0.298805358f, 0.298896850f, 0.298988339f, 0.299079826f, 0.299171310f,
0.299262792f, 0.299354270f, 0.299445746f, 0.299537219f, 0.299628690f,
0.299720157f, 0.299811622f, 0.299903084f, 0.299994543f, 0.300086000f,
0.300177454f, 0.300268905f, 0.300360353f, 0.300451799f, 0.300543241f,
0.300634681f, 0.300726119f, 0.300817553f, 0.300908985f, 0.301000414f,
0.301091840f, 0.301183263f, 0.301274684f, 0.301366102f, 0.301457517f,
0.301548929f, 0.301640339f, 0.301731746f, 0.301823150f, 0.301914551f,
0.302005949f, 0.302097345f, 0.302188738f, 0.302280128f, 0.302371515f,
0.302462900f, 0.302554282f, 0.302645661f, 0.302737037f, 0.302828410f,
0.302919781f, 0.303011149f, 0.303102514f, 0.303193876f, 0.303285236f,
0.303376593f, 0.303467947f, 0.303559298f, 0.303650646f, 0.303741992f,
0.303833334f, 0.303924674f, 0.304016012f, 0.304107346f, 0.304198678f,
0.304290006f, 0.304381332f, 0.304472656f, 0.304563976f, 0.304655294f,
0.304746609f, 0.304837921f, 0.304929230f, 0.305020536f, 0.305111840f,
0.305203141f, 0.305294439f, 0.305385734f, 0.305477026f, 0.305568316f,
0.305659602f, 0.305750886f, 0.305842168f, 0.305933446f, 0.306024721f,
0.306115994f, 0.306207264f, 0.306298531f, 0.306389795f, 0.306481057f,
0.306572315f, 0.306663571f, 0.306754824f, 0.306846074f, 0.306937322f,
0.307028566f, 0.307119808f, 0.307211047f, 0.307302283f, 0.307393516f,
0.307484747f, 0.307575974f, 0.307667199f, 0.307758421f, 0.307849640f,
0.307940856f, 0.308032070f, 0.308123280f, 0.308214488f, 0.308305693f,
0.308396895f, 0.308488094f, 0.308579291f, 0.308670485f, 0.308761675f,
0.308852863f, 0.308944048f, 0.309035231f, 0.309126410f, 0.309217587f,
0.309308760f, 0.309399931f, 0.309491099f, 0.309582264f, 0.309673427f,
0.309764586f, 0.309855743f, 0.309946897f, 0.310038048f, 0.310129196f,
0.310220341f, 0.310311484f, 0.310402623f, 0.310493760f, 0.310584894f,
0.310676025f, 0.310767153f, 0.310858278f, 0.310949400f, 0.311040520f,
0.311131637f, 0.311222751f, 0.311313862f, 0.311404970f, 0.311496075f,
0.311587177f, 0.311678277f, 0.311769374f, 0.311860467f, 0.311951558f,
0.312042646f, 0.312133732f, 0.312224814f, 0.312315893f, 0.312406970f,
0.312498044f, 0.312589115f, 0.312680183f, 0.312771248f, 0.312862310f,
0.312953369f, 0.313044426f, 0.313135479f, 0.313226530f, 0.313317578f,
0.313408623f, 0.313499665f, 0.313590704f, 0.313681740f, 0.313772774f,
0.313863804f, 0.313954832f, 0.314045857f, 0.314136879f, 0.314227898f,
0.314318914f, 0.314409927f, 0.314500937f, 0.314591945f, 0.314682949f,
0.314773951f, 0.314864950f, 0.314955946f, 0.315046939f, 0.315137929f,
0.315228916f, 0.315319900f, 0.315410882f, 0.315501860f, 0.315592836f,
0.315683808f, 0.315774778f, 0.315865745f, 0.315956709f, 0.316047670f,
0.316138628f, 0.316229584f, 0.316320536f, 0.316411485f, 0.316502432f,
0.316593376f, 0.316684316f, 0.316775254f, 0.316866189f, 0.316957121f,
0.317048050f, 0.317138976f, 0.317229899f, 0.317320820f, 0.317411737f,
0.317502652f, 0.317593563f, 0.317684472f, 0.317775378f, 0.317866281f,
0.317957180f, 0.318048077f, 0.318138971f, 0.318229863f, 0.318320751f,
0.318411636f, 0.318502518f, 0.318593398f, 0.318684274f, 0.318775148f,
0.318866018f, 0.318956886f, 0.319047751f, 0.319138613f, 0.319229472f,
0.319320328f, 0.319411181f, 0.319502031f, 0.319592878f, 0.319683722f,
0.319774563f, 0.319865402f, 0.319956237f, 0.320047070f, 0.320137899f,
0.320228726f, 0.320319549f, 0.320410370f, 0.320501188f, 0.320592003f,
0.320682815f, 0.320773623f, 0.320864429f, 0.320955232f, 0.321046032f,
0.321136830f, 0.321227624f, 0.321318415f, 0.321409203f, 0.321499989f,
0.321590771f, 0.321681550f, 0.321772327f, 0.321863100f, 0.321953871f,
0.322044638f, 0.322135403f, 0.322226164f, 0.322316923f, 0.322407679f,
0.322498432f, 0.322589181f, 0.322679928f, 0.322770672f, 0.322861413f,
0.322952151f, 0.323042886f, 0.323133618f, 0.323224347f, 0.323315073f,
0.323405796f, 0.323496516f, 0.323587233f, 0.323677947f, 0.323768658f,
0.323859367f, 0.323950072f, 0.324040774f, 0.324131473f, 0.324222170f,
0.324312863f, 0.324403553f, 0.324494240f, 0.324584925f, 0.324675606f,
0.324766285f, 0.324856960f, 0.324947632f, 0.325038302f, 0.325128968f,
0.325219632f, 0.325310292f, 0.325400950f, 0.325491604f, 0.325582256f,
0.325672904f, 0.325763550f, 0.325854192f, 0.325944832f, 0.326035468f,
0.326126102f, 0.326216732f, 0.326307360f, 0.326397984f, 0.326488606f,
0.326579224f, 0.326669840f, 0.326760452f, 0.326851062f, 0.326941668f,
0.327032272f, 0.327122872f, 0.327213470f, 0.327304064f, 0.327394656f,
0.327485244f, 0.327575830f, 0.327666412f, 0.327756992f, 0.327847568f,
0.327938141f, 0.328028712f, 0.328119279f, 0.328209844f, 0.328300405f,
0.328390963f, 0.328481519f, 0.328572071f, 0.328662620f, 0.328753166f,
0.328843710f, 0.328934250f, 0.329024787f, 0.329115321f, 0.329205852f,
0.329296380f, 0.329386905f, 0.329477428f, 0.329567947f, 0.329658463f,
0.329748975f, 0.329839485f, 0.329929992f, 0.330020496f, 0.330110997f,
0.330201495f, 0.330291990f, 0.330382481f, 0.330472970f, 0.330563456f,
0.330653938f, 0.330744418f, 0.330834894f, 0.330925368f, 0.331015838f,
0.331106306f, 0.331196770f, 0.331287231f, 0.331377690f, 0.331468145f,
0.331558597f, 0.331649046f, 0.331739492f, 0.331829935f, 0.331920375f,
0.332010812f, 0.332101246f, 0.332191677f, 0.332282105f, 0.332372530f,
0.332462951f, 0.332553370f, 0.332643785f, 0.332734198f, 0.332824607f,
0.332915014f, 0.333005417f, 0.333095817f, 0.333186215f, 0.333276609f,
0.333367000f, 0.333457388f, 0.333547773f, 0.333638155f, 0.333728533f,
0.333818909f, 0.333909282f, 0.333999651f, 0.334090018f, 0.334180381f,
0.334270742f, 0.334361099f, 0.334451453f, 0.334541805f, 0.334632153f,
0.334722498f, 0.334812840f, 0.334903179f, 0.334993514f, 0.335083847f,
0.335174177f, 0.335264503f, 0.335354827f, 0.335445147f, 0.335535464f,
0.335625779f, 0.335716090f, 0.335806398f, 0.335896703f, 0.335987005f,
0.336077303f, 0.336167599f, 0.336257892f, 0.336348181f, 0.336438468f,
0.336528751f, 0.336619031f, 0.336709308f, 0.336799582f, 0.336889853f,
0.336980121f, 0.337070386f, 0.337160648f, 0.337250906f, 0.337341162f,
0.337431414f, 0.337521663f, 0.337611909f, 0.337702153f, 0.337792392f,
0.337882629f, 0.337972863f, 0.338063094f, 0.338153321f, 0.338243546f,
0.338333767f, 0.338423985f, 0.338514200f, 0.338604412f, 0.338694621f,
0.338784827f, 0.338875029f, 0.338965229f, 0.339055425f, 0.339145619f,
0.339235809f, 0.339325996f, 0.339416180f, 0.339506361f, 0.339596538f,
0.339686713f, 0.339776884f, 0.339867053f, 0.339957218f, 0.340047380f,
0.340137539f, 0.340227695f, 0.340317848f, 0.340407997f, 0.340498144f,
0.340588287f, 0.340678427f, 0.340768564f, 0.340858698f, 0.340948829f,
0.341038956f, 0.341129081f, 0.341219202f, 0.341309321f, 0.341399436f,
0.341489548f, 0.341579656f, 0.341669762f, 0.341759865f, 0.341849964f,
0.341940060f, 0.342030154f, 0.342120243f, 0.342210330f, 0.342300414f,
0.342390495f, 0.342480572f, 0.342570646f, 0.342660717f, 0.342750785f,
0.342840850f, 0.342930912f, 0.343020970f, 0.343111026f, 0.343201078f,
0.343291127f, 0.343381173f, 0.343471215f, 0.343561255f, 0.343651291f,
0.343741325f, 0.343831355f, 0.343921382f, 0.344011405f, 0.344101426f,
0.344191443f, 0.344281458f, 0.344371469f, 0.344461477f, 0.344551482f,
0.344641483f, 0.344731482f, 0.344821477f, 0.344911469f, 0.345001458f,
0.345091444f, 0.345181426f, 0.345271406f, 0.345361382f, 0.345451355f,
0.345541325f, 0.345631292f, 0.345721255f, 0.345811216f, 0.345901173f,
0.345991127f, 0.346081078f, 0.346171025f, 0.346260970f, 0.346350911f,
0.346440849f, 0.346530784f, 0.346620716f, 0.346710644f, 0.346800570f,
0.346890492f, 0.346980411f, 0.347070327f, 0.347160239f, 0.347250149f,
0.347340055f, 0.347429958f, 0.347519858f, 0.347609754f, 0.347699648f,
0.347789538f, 0.347879425f, 0.347969309f, 0.348059190f, 0.348149067f,
0.348238941f, 0.348328812f, 0.348418680f, 0.348508545f, 0.348598406f,
0.348688265f, 0.348778120f, 0.348867971f, 0.348957820f, 0.349047666f,
0.349137508f, 0.349227347f, 0.349317183f, 0.349407015f, 0.349496844f,
0.349586671f, 0.349676494f, 0.349766313f, 0.349856130f, 0.349945943f,
0.350035753f, 0.350125560f, 0.350215364f, 0.350305164f, 0.350394961f,
0.350484755f, 0.350574546f, 0.350664334f, 0.350754118f, 0.350843899f,
0.350933677f, 0.351023452f, 0.351113223f, 0.351202991f, 0.351292756f,
0.351382518f, 0.351472276f, 0.351562032f, 0.351651784f, 0.351741532f,
0.351831278f, 0.351921020f, 0.352010759f, 0.352100495f, 0.352190228f,
0.352279957f, 0.352369684f, 0.352459406f, 0.352549126f, 0.352638843f,
0.352728556f, 0.352818266f, 0.352907972f, 0.352997676f, 0.353087376f,
0.353177073f, 0.353266767f, 0.353356457f, 0.353446145f, 0.353535829f,
0.353625509f, 0.353715187f, 0.353804861f, 0.353894532f, 0.353984200f,
0.354073864f, 0.354163525f, 0.354253183f, 0.354342838f, 0.354432490f,
0.354522138f, 0.354611783f, 0.354701424f, 0.354791063f, 0.354880698f,
0.354970330f, 0.355059958f, 0.355149584f, 0.355239206f, 0.355328825f,
0.355418440f, 0.355508053f, 0.355597662f, 0.355687267f, 0.355776870f,
0.355866469f, 0.355956065f, 0.356045658f, 0.356135247f, 0.356224833f,
0.356314416f, 0.356403996f, 0.356493572f, 0.356583145f, 0.356672715f,
0.356762281f, 0.356851845f, 0.356941405f, 0.357030961f, 0.357120515f,
0.357210065f, 0.357299611f, 0.357389155f, 0.357478695f, 0.357568232f,
0.357657766f, 0.357747296f, 0.357836823f, 0.357926347f, 0.358015868f,
0.358105385f, 0.358194899f, 0.358284409f, 0.358373917f, 0.358463421f,
0.358552921f, 0.358642419f, 0.358731913f, 0.358821404f, 0.358910891f,
0.359000376f, 0.359089857f, 0.359179334f, 0.359268809f, 0.359358280f,
0.359447747f, 0.359537212f, 0.359626673f, 0.359716131f, 0.359805585f,
0.359895037f, 0.359984484f, 0.360073929f, 0.360163370f, 0.360252808f,
0.360342243f, 0.360431674f, 0.360521102f, 0.360610527f, 0.360699949f,
0.360789367f, 0.360878781f, 0.360968193f, 0.361057601f, 0.361147006f,
0.361236407f, 0.361325806f, 0.361415200f, 0.361504592f, 0.361593980f,
0.361683365f, 0.361772747f, 0.361862125f, 0.361951500f, 0.362040871f,
0.362130240f, 0.362219605f, 0.362308966f, 0.362398325f, 0.362487680f,
0.362577031f, 0.362666379f, 0.362755724f, 0.362845066f, 0.362934404f,
0.363023739f, 0.363113071f, 0.363202399f, 0.363291724f, 0.363381046f,
0.363470364f, 0.363559679f, 0.363648990f, 0.363738299f, 0.363827603f,
0.363916905f, 0.364006203f, 0.364095498f, 0.364184790f, 0.364274078f,
0.364363363f, 0.364452644f, 0.364541922f, 0.364631197f, 0.364720468f,
0.364809736f, 0.364899001f, 0.364988262f, 0.365077520f, 0.365166775f,
0.365256026f, 0.365345274f, 0.365434519f, 0.365523760f, 0.365612998f,
0.365702232f, 0.365791463f, 0.365880691f, 0.365969916f, 0.366059137f,
0.366148354f, 0.366237569f, 0.366326780f, 0.366415987f, 0.366505191f,
0.366594392f, 0.366683590f, 0.366772784f, 0.366861974f, 0.366951162f,
0.367040346f, 0.367129526f, 0.367218704f, 0.367307877f, 0.367397048f,
0.367486215f, 0.367575379f, 0.367664539f, 0.367753696f, 0.367842850f,
0.367932000f, 0.368021147f, 0.368110290f, 0.368199430f, 0.368288567f,
0.368377700f, 0.368466830f, 0.368555956f, 0.368645080f, 0.368734199f,
0.368823316f, 0.368912429f, 0.369001538f, 0.369090644f, 0.369179747f,
0.369268847f, 0.369357943f, 0.369447035f, 0.369536124f, 0.369625210f,
0.369714293f, 0.369803372f, 0.369892447f, 0.369981519f, 0.370070588f,
0.370159654f, 0.370248716f, 0.370337774f, 0.370426829f, 0.370515881f,
0.370604930f, 0.370693975f, 0.370783016f, 0.370872054f, 0.370961089f,
0.371050120f, 0.371139148f, 0.371228173f, 0.371317194f, 0.371406212f,
0.371495226f, 0.371584237f, 0.371673244f, 0.371762248f, 0.371851249f,
0.371940246f, 0.372029240f, 0.372118230f, 0.372207217f, 0.372296201f,
0.372385181f, 0.372474158f, 0.372563131f, 0.372652101f, 0.372741067f,
0.372830030f, 0.372918990f, 0.373007946f, 0.373096898f, 0.373185848f,
0.373274793f, 0.373363736f, 0.373452675f, 0.373541610f, 0.373630542f,
0.373719471f, 0.373808396f, 0.373897318f, 0.373986237f, 0.374075151f,
0.374164063f, 0.374252971f, 0.374341876f, 0.374430777f, 0.374519675f,
0.374608569f, 0.374697460f, 0.374786347f, 0.374875231f, 0.374964112f,
0.375052989f, 0.375141862f, 0.375230732f, 0.375319599f, 0.375408462f,
0.375497322f, 0.375586178f, 0.375675031f, 0.375763881f, 0.375852727f,
0.375941569f, 0.376030408f, 0.376119244f, 0.376208076f, 0.376296905f,
0.376385730f, 0.376474552f, 0.376563370f, 0.376652185f, 0.376740997f,
0.376829805f, 0.376918609f, 0.377007410f, 0.377096208f, 0.377185002f,
0.377273793f, 0.377362580f, 0.377451363f, 0.377540144f, 0.377628920f,
0.377717694f, 0.377806463f, 0.377895230f, 0.377983993f, 0.378072752f,
0.378161508f, 0.378250260f, 0.378339009f, 0.378427755f, 0.378516497f,
0.378605235f, 0.378693970f, 0.378782702f, 0.378871430f, 0.378960155f,
0.379048876f, 0.379137593f, 0.379226308f, 0.379315018f, 0.379403725f,
0.379492429f, 0.379581129f, 0.379669826f, 0.379758519f, 0.379847209f,
0.379935895f, 0.380024578f, 0.380113257f, 0.380201933f, 0.380290605f,
0.380379274f, 0.380467939f, 0.380556601f, 0.380645259f, 0.380733914f,
0.380822565f, 0.380911213f, 0.380999857f, 0.381088498f, 0.381177135f,
0.381265769f, 0.381354399f, 0.381443026f, 0.381531650f, 0.381620269f,
0.381708885f, 0.381797498f, 0.381886107f, 0.381974713f, 0.382063315f,
0.382151914f, 0.382240509f, 0.382329101f, 0.382417689f, 0.382506274f,
0.382594855f, 0.382683432f, 0.382772006f, 0.382860577f, 0.382949144f,
0.383037708f, 0.383126268f, 0.383214824f, 0.383303377f, 0.383391926f,
0.383480472f, 0.383569015f, 0.383657554f, 0.383746089f, 0.383834621f,
0.383923149f, 0.384011674f, 0.384100195f, 0.384188713f, 0.384277227f,
0.384365737f, 0.384454245f, 0.384542748f, 0.384631248f, 0.384719745f,
0.384808238f, 0.384896727f, 0.384985213f, 0.385073695f, 0.385162174f,
0.385250649f, 0.385339121f, 0.385427589f, 0.385516054f, 0.385604515f,
0.385692972f, 0.385781426f, 0.385869877f, 0.385958324f, 0.386046767f,
0.386135207f, 0.386223643f, 0.386312076f, 0.386400505f, 0.386488931f,
0.386577353f, 0.386665771f, 0.386754186f, 0.386842598f, 0.386931006f,
0.387019410f, 0.387107811f, 0.387196208f, 0.387284601f, 0.387372991f,
0.387461378f, 0.387549761f, 0.387638140f, 0.387726516f, 0.387814888f,
0.387903257f, 0.387991622f, 0.388079983f, 0.388168341f, 0.388256696f,
0.388345047f, 0.388433394f, 0.388521738f, 0.388610078f, 0.388698414f,
0.388786747f, 0.388875077f, 0.388963403f, 0.389051725f, 0.389140044f,
0.389228359f, 0.389316670f, 0.389404978f, 0.389493282f, 0.389581583f,
0.389669880f, 0.389758174f, 0.389846464f, 0.389934751f, 0.390023033f,
0.390111313f, 0.390199588f, 0.390287861f, 0.390376129f, 0.390464394f,
0.390552655f, 0.390640913f, 0.390729167f, 0.390817418f, 0.390905665f,
0.390993908f, 0.391082148f, 0.391170384f, 0.391258617f, 0.391346846f,
0.391435071f, 0.391523293f, 0.391611511f, 0.391699726f, 0.391787937f,
0.391876144f, 0.391964348f, 0.392052548f, 0.392140745f, 0.392228938f,
0.392317128f, 0.392405313f, 0.392493495f, 0.392581674f, 0.392669849f,
0.392758020f, 0.392846188f, 0.392934352f, 0.393022513f, 0.393110670f,
0.393198823f, 0.393286973f, 0.393375119f, 0.393463261f, 0.393551400f,
0.393639535f, 0.393727667f, 0.393815795f, 0.393903919f, 0.393992040f,
0.394080157f, 0.394168271f, 0.394256381f, 0.394344487f, 0.394432589f,
0.394520688f, 0.394608784f, 0.394696876f, 0.394784964f, 0.394873048f,
0.394961129f, 0.395049206f, 0.395137280f, 0.395225350f, 0.395313416f,
0.395401479f, 0.395489538f, 0.395577593f, 0.395665645f, 0.395753693f,
0.395841738f, 0.395929779f, 0.396017816f, 0.396105850f, 0.396193880f,
0.396281906f, 0.396369929f, 0.396457948f, 0.396545963f, 0.396633975f,
0.396721983f, 0.396809987f, 0.396897988f, 0.396985985f, 0.397073979f,
0.397161969f, 0.397249955f, 0.397337938f, 0.397425916f, 0.397513892f,
0.397601863f, 0.397689831f, 0.397777796f, 0.397865756f, 0.397953713f,
0.398041666f, 0.398129616f, 0.398217562f, 0.398305504f, 0.398393443f,
0.398481378f, 0.398569310f, 0.398657237f, 0.398745161f, 0.398833082f,
0.398920998f, 0.399008911f, 0.399096821f, 0.399184726f, 0.399272628f,
0.399360527f, 0.399448421f, 0.399536313f, 0.399624200f, 0.399712084f,
0.399799964f, 0.399887840f, 0.399975712f, 0.400063581f, 0.400151447f,
0.400239308f, 0.400327166f, 0.400415021f, 0.400502871f, 0.400590718f,
0.400678561f, 0.400766401f, 0.400854237f, 0.400942069f, 0.401029897f,
0.401117722f, 0.401205543f, 0.401293360f, 0.401381174f, 0.401468984f,
0.401556791f, 0.401644593f, 0.401732392f, 0.401820187f, 0.401907979f,
0.401995767f, 0.402083551f, 0.402171332f, 0.402259108f, 0.402346881f,
0.402434651f, 0.402522417f, 0.402610179f, 0.402697937f, 0.402785691f,
0.402873442f, 0.402961190f, 0.403048933f, 0.403136673f, 0.403224409f,
0.403312141f, 0.403399870f, 0.403487595f, 0.403575316f, 0.403663034f,
0.403750747f, 0.403838458f, 0.403926164f, 0.404013867f, 0.404101566f,
0.404189261f, 0.404276952f, 0.404364640f, 0.404452324f, 0.404540005f,
0.404627681f, 0.404715354f, 0.404803024f, 0.404890689f, 0.404978351f,
0.405066009f, 0.405153663f, 0.405241314f, 0.405328961f, 0.405416604f,
0.405504244f, 0.405591879f, 0.405679511f, 0.405767140f, 0.405854764f,
0.405942385f, 0.406030002f, 0.406117615f, 0.406205225f, 0.406292831f,
0.406380433f, 0.406468031f, 0.406555626f, 0.406643217f, 0.406730804f,
0.406818388f, 0.406905967f, 0.406993543f, 0.407081115f, 0.407168684f,
0.407256249f, 0.407343810f, 0.407431367f, 0.407518920f, 0.407606470f,
0.407694016f, 0.407781559f, 0.407869097f, 0.407956632f, 0.408044163f,
0.408131690f, 0.408219214f, 0.408306733f, 0.408394249f, 0.408481762f,
0.408569270f, 0.408656775f, 0.408744276f, 0.408831773f, 0.408919267f,
0.409006756f, 0.409094242f, 0.409181725f, 0.409269203f, 0.409356678f,
0.409444149f, 0.409531616f, 0.409619079f, 0.409706539f, 0.409793995f,
0.409881447f, 0.409968895f, 0.410056340f, 0.410143781f, 0.410231218f,
0.410318651f, 0.410406080f, 0.410493506f, 0.410580928f, 0.410668346f,
0.410755760f, 0.410843171f, 0.410930578f, 0.411017981f, 0.411105380f,
0.411192776f, 0.411280167f, 0.411367555f, 0.411454940f, 0.411542320f,
0.411629697f, 0.411717069f, 0.411804438f, 0.411891804f, 0.411979165f,
0.412066523f, 0.412153877f, 0.412241227f, 0.412328573f, 0.412415915f,
0.412503254f, 0.412590589f, 0.412677920f, 0.412765248f, 0.412852571f,
0.412939891f, 0.413027207f, 0.413114519f, 0.413201827f, 0.413289132f,
0.413376433f, 0.413463730f, 0.413551023f, 0.413638312f, 0.413725598f,
0.413812880f, 0.413900158f, 0.413987432f, 0.414074702f, 0.414161969f,
0.414249231f, 0.414336490f, 0.414423745f, 0.414510997f, 0.414598244f,
0.414685488f, 0.414772728f, 0.414859964f, 0.414947196f, 0.415034424f,
0.415121649f, 0.415208870f, 0.415296087f, 0.415383300f, 0.415470509f,
0.415557715f, 0.415644917f, 0.415732115f, 0.415819309f, 0.415906499f,
0.415993685f, 0.416080868f, 0.416168047f, 0.416255222f, 0.416342393f,
0.416429560f, 0.416516724f, 0.416603883f, 0.416691039f, 0.416778191f,
0.416865339f, 0.416952484f, 0.417039624f, 0.417126761f, 0.417213893f,
0.417301022f, 0.417388148f, 0.417475269f, 0.417562386f, 0.417649500f,
0.417736610f, 0.417823716f, 0.417910818f, 0.417997916f, 0.418085011f,
0.418172101f, 0.418259188f, 0.418346271f, 0.418433350f, 0.418520425f,
0.418607497f, 0.418694564f, 0.418781628f, 0.418868688f, 0.418955744f,
0.419042796f, 0.419129844f, 0.419216888f, 0.419303929f, 0.419390966f,
0.419477998f, 0.419565027f, 0.419652053f, 0.419739074f, 0.419826091f,
0.419913105f, 0.420000115f, 0.420087120f, 0.420174122f, 0.420261121f,
0.420348115f, 0.420435105f, 0.420522092f, 0.420609074f, 0.420696053f,
0.420783028f, 0.420869999f, 0.420956966f, 0.421043930f, 0.421130889f,
0.421217845f, 0.421304797f, 0.421391744f, 0.421478688f, 0.421565628f,
0.421652565f, 0.421739497f, 0.421826425f, 0.421913350f, 0.422000271f,
0.422087188f, 0.422174101f, 0.422261010f, 0.422347915f, 0.422434816f,
0.422521714f, 0.422608607f, 0.422695497f, 0.422782383f, 0.422869264f,
0.422956142f, 0.423043017f, 0.423129887f, 0.423216753f, 0.423303616f,
0.423390474f, 0.423477329f, 0.423564180f, 0.423651026f, 0.423737869f,
0.423824709f, 0.423911544f, 0.423998375f, 0.424085202f, 0.424172026f,
0.424258846f, 0.424345661f, 0.424432473f, 0.424519281f, 0.424606085f,
0.424692885f, 0.424779681f, 0.424866473f, 0.424953262f, 0.425040046f,
0.425126827f, 0.425213604f, 0.425300376f, 0.425387145f, 0.425473910f,
0.425560671f, 0.425647428f, 0.425734181f, 0.425820931f, 0.425907676f,
0.425994418f, 0.426081155f, 0.426167889f, 0.426254618f, 0.426341344f,
0.426428066f, 0.426514784f, 0.426601498f, 0.426688208f, 0.426774914f,
0.426861617f, 0.426948315f, 0.427035009f, 0.427121700f, 0.427208386f,
0.427295069f, 0.427381748f, 0.427468423f, 0.427555093f, 0.427641760f,
0.427728423f, 0.427815082f, 0.427901738f, 0.427988389f, 0.428075036f,
0.428161679f, 0.428248319f, 0.428334954f, 0.428421586f, 0.428508213f,
0.428594837f, 0.428681457f, 0.428768072f, 0.428854684f, 0.428941292f,
0.429027896f, 0.429114496f, 0.429201092f, 0.429287684f, 0.429374272f,
0.429460856f, 0.429547437f, 0.429634013f, 0.429720585f, 0.429807154f,
0.429893718f, 0.429980279f, 0.430066835f, 0.430153388f, 0.430239937f,
0.430326481f, 0.430413022f, 0.430499559f, 0.430586092f, 0.430672621f,
0.430759145f, 0.430845666f, 0.430932183f, 0.431018696f, 0.431105206f,
0.431191711f, 0.431278212f, 0.431364709f, 0.431451202f, 0.431537691f,
0.431624177f, 0.431710658f, 0.431797135f, 0.431883609f, 0.431970078f,
0.432056544f, 0.432143005f, 0.432229463f, 0.432315916f, 0.432402366f,
0.432488811f, 0.432575253f, 0.432661690f, 0.432748124f, 0.432834554f,
0.432920979f, 0.433007401f, 0.433093819f, 0.433180233f, 0.433266642f,
0.433353048f, 0.433439450f, 0.433525848f, 0.433612242f, 0.433698631f,
0.433785017f, 0.433871399f, 0.433957777f, 0.434044151f, 0.434130521f,
0.434216887f, 0.434303249f, 0.434389607f, 0.434475961f, 0.434562311f,
0.434648656f, 0.434734998f, 0.434821336f, 0.434907670f, 0.434994000f,
0.435080326f, 0.435166648f, 0.435252966f, 0.435339280f, 0.435425590f,
0.435511896f, 0.435598198f, 0.435684496f, 0.435770790f, 0.435857080f,
0.435943366f, 0.436029648f, 0.436115926f, 0.436202200f, 0.436288470f,
0.436374735f, 0.436460997f, 0.436547255f, 0.436633509f, 0.436719759f,
0.436806005f, 0.436892247f, 0.436978484f, 0.437064718f, 0.437150948f,
0.437237174f, 0.437323395f, 0.437409613f, 0.437495827f, 0.437582036f,
0.437668242f, 0.437754444f, 0.437840641f, 0.437926835f, 0.438013024f,
0.438099210f, 0.438185391f, 0.438271569f, 0.438357742f, 0.438443912f,
0.438530077f, 0.438616239f, 0.438702396f, 0.438788549f, 0.438874698f,
0.438960844f, 0.439046985f, 0.439133122f, 0.439219255f, 0.439305384f,
0.439391509f, 0.439477630f, 0.439563747f, 0.439649860f, 0.439735969f,
0.439822074f, 0.439908175f, 0.439994271f, 0.440080364f, 0.440166453f,
0.440252537f, 0.440338618f, 0.440424694f, 0.440510767f, 0.440596835f,
0.440682900f, 0.440768960f, 0.440855016f, 0.440941068f, 0.441027117f,
0.441113161f, 0.441199201f, 0.441285237f, 0.441371269f, 0.441457297f,
0.441543320f, 0.441629340f, 0.441715356f, 0.441801368f, 0.441887375f,
0.441973379f, 0.442059378f, 0.442145374f, 0.442231365f, 0.442317352f,
0.442403335f, 0.442489315f, 0.442575290f, 0.442661261f, 0.442747228f,
0.442833190f, 0.442919149f, 0.443005104f, 0.443091055f, 0.443177001f,
0.443262944f, 0.443348882f, 0.443434816f, 0.443520747f, 0.443606673f,
0.443692595f, 0.443778513f, 0.443864427f, 0.443950337f, 0.444036243f,
0.444122145f, 0.444208042f, 0.444293936f, 0.444379825f, 0.444465711f,
0.444551592f, 0.444637469f, 0.444723342f, 0.444809211f, 0.444895076f,
0.444980937f, 0.445066794f, 0.445152647f, 0.445238495f, 0.445324340f,
0.445410180f, 0.445496017f, 0.445581849f, 0.445667677f, 0.445753501f,
0.445839321f, 0.445925137f, 0.446010948f, 0.446096756f, 0.446182560f,
0.446268359f, 0.446354154f, 0.446439946f, 0.446525733f, 0.446611516f,
0.446697295f, 0.446783069f, 0.446868840f, 0.446954607f, 0.447040369f,
0.447126128f, 0.447211882f, 0.447297632f, 0.447383378f, 0.447469120f,
0.447554858f, 0.447640592f, 0.447726321f, 0.447812047f, 0.447897768f,
0.447983485f, 0.448069198f, 0.448154907f, 0.448240612f, 0.448326313f,
0.448412010f, 0.448497702f, 0.448583391f, 0.448669075f, 0.448754755f,
0.448840431f, 0.448926103f, 0.449011771f, 0.449097434f, 0.449183094f,
0.449268749f, 0.449354401f, 0.449440048f, 0.449525691f, 0.449611330f,
0.449696964f, 0.449782595f, 0.449868221f, 0.449953844f, 0.450039462f,
0.450125076f, 0.450210686f, 0.450296292f, 0.450381893f, 0.450467491f,
0.450553084f, 0.450638674f, 0.450724259f, 0.450809840f, 0.450895416f,
0.450980989f, 0.451066558f, 0.451152122f, 0.451237682f, 0.451323238f,
0.451408790f, 0.451494338f, 0.451579882f, 0.451665421f, 0.451750956f,
0.451836487f, 0.451922014f, 0.452007537f, 0.452093056f, 0.452178571f,
0.452264081f, 0.452349587f, 0.452435089f, 0.452520587f, 0.452606081f,
0.452691571f, 0.452777056f, 0.452862537f, 0.452948014f, 0.453033487f,
0.453118956f, 0.453204421f, 0.453289881f, 0.453375338f, 0.453460790f,
0.453546238f, 0.453631681f, 0.453717121f, 0.453802556f, 0.453887988f,
0.453973415f, 0.454058838f, 0.454144257f, 0.454229671f, 0.454315081f,
0.454400488f, 0.454485890f, 0.454571288f, 0.454656681f, 0.454742071f,
0.454827456f, 0.454912837f, 0.454998214f, 0.455083587f, 0.455168956f,
0.455254320f, 0.455339680f, 0.455425036f, 0.455510388f, 0.455595736f,
0.455681080f, 0.455766419f, 0.455851754f, 0.455937085f, 0.456022412f,
0.456107734f, 0.456193053f, 0.456278367f, 0.456363677f, 0.456448982f,
0.456534284f, 0.456619581f, 0.456704875f, 0.456790164f, 0.456875448f,
0.456960729f, 0.457046005f, 0.457131277f, 0.457216545f, 0.457301809f,
0.457387069f, 0.457472324f, 0.457557575f, 0.457642822f, 0.457728065f,
0.457813304f, 0.457898538f, 0.457983768f, 0.458068994f, 0.458154216f,
0.458239433f, 0.458324646f, 0.458409856f, 0.458495060f, 0.458580261f,
0.458665457f, 0.458750650f, 0.458835838f, 0.458921021f, 0.459006201f,
0.459091376f, 0.459176548f, 0.459261714f, 0.459346877f, 0.459432036f,
0.459517190f, 0.459602340f, 0.459687486f, 0.459772627f, 0.459857765f,
0.459942898f, 0.460028026f, 0.460113151f, 0.460198272f, 0.460283388f,
0.460368500f, 0.460453607f, 0.460538711f, 0.460623810f, 0.460708905f,
0.460793996f, 0.460879083f, 0.460964165f, 0.461049243f, 0.461134317f,
0.461219386f, 0.461304452f, 0.461389513f, 0.461474570f, 0.461559623f,
0.461644671f, 0.461729715f, 0.461814755f, 0.461899791f, 0.461984822f,
0.462069849f, 0.462154872f, 0.462239891f, 0.462324905f, 0.462409916f,
0.462494922f, 0.462579923f, 0.462664921f, 0.462749914f, 0.462834903f,
0.462919887f, 0.463004868f, 0.463089844f, 0.463174816f, 0.463259784f,
0.463344747f, 0.463429706f, 0.463514661f, 0.463599612f, 0.463684558f,
0.463769500f, 0.463854438f, 0.463939371f, 0.464024301f, 0.464109226f,
0.464194146f, 0.464279063f, 0.464363975f, 0.464448883f, 0.464533787f,
0.464618686f, 0.464703581f, 0.464788472f, 0.464873359f, 0.464958241f,
0.465043119f, 0.465127993f, 0.465212863f, 0.465297728f, 0.465382589f,
0.465467446f, 0.465552298f, 0.465637146f, 0.465721990f, 0.465806829f,
0.465891665f, 0.465976496f, 0.466061322f, 0.466146145f, 0.466230963f,
0.466315777f, 0.466400587f, 0.466485392f, 0.466570193f, 0.466654990f,
0.466739782f, 0.466824570f, 0.466909354f, 0.466994133f, 0.467078909f,
0.467163680f, 0.467248446f, 0.467333209f, 0.467417967f, 0.467502721f,
0.467587470f, 0.467672215f, 0.467756956f, 0.467841693f, 0.467926425f,
0.468011153f, 0.468095877f, 0.468180596f, 0.468265311f, 0.468350022f,
0.468434728f, 0.468519431f, 0.468604128f, 0.468688822f, 0.468773511f,
0.468858196f, 0.468942877f, 0.469027553f, 0.469112225f, 0.469196893f,
0.469281556f, 0.469366215f, 0.469450870f, 0.469535520f, 0.469620167f,
0.469704808f, 0.469789446f, 0.469874079f, 0.469958708f, 0.470043332f,
0.470127953f, 0.470212569f, 0.470297180f, 0.470381787f, 0.470466390f,
0.470550989f, 0.470635583f, 0.470720173f, 0.470804759f, 0.470889340f,
0.470973917f, 0.471058490f, 0.471143058f, 0.471227622f, 0.471312182f,
0.471396737f, 0.471481288f, 0.471565834f, 0.471650377f, 0.471734915f,
0.471819448f, 0.471903978f, 0.471988503f, 0.472073023f, 0.472157540f,
0.472242051f, 0.472326559f, 0.472411062f, 0.472495561f, 0.472580056f,
0.472664546f, 0.472749032f, 0.472833513f, 0.472917991f, 0.473002464f,
0.473086932f, 0.473171396f, 0.473255856f, 0.473340311f, 0.473424763f,
0.473509209f, 0.473593652f, 0.473678090f, 0.473762523f, 0.473846953f,
0.473931378f, 0.474015798f, 0.474100215f, 0.474184627f, 0.474269034f,
0.474353437f, 0.474437836f, 0.474522231f, 0.474606621f, 0.474691006f,
0.474775388f, 0.474859765f, 0.474944138f, 0.475028506f, 0.475112870f,
0.475197229f, 0.475281584f, 0.475365935f, 0.475450282f, 0.475534624f,
0.475618962f, 0.475703295f, 0.475787624f, 0.475871948f, 0.475956269f,
0.476040584f, 0.476124896f, 0.476209203f, 0.476293506f, 0.476377804f,
0.476462098f, 0.476546388f, 0.476630673f, 0.476714954f, 0.476799230f,
0.476883502f, 0.476967770f, 0.477052033f, 0.477136292f, 0.477220546f,
0.477304797f, 0.477389042f, 0.477473284f, 0.477557521f, 0.477641753f,
0.477725981f, 0.477810205f, 0.477894425f, 0.477978640f, 0.478062850f,
0.478147056f, 0.478231258f, 0.478315456f, 0.478399649f, 0.478483837f,
0.478568022f, 0.478652201f, 0.478736377f, 0.478820548f, 0.478904715f,
0.478988877f, 0.479073035f, 0.479157188f, 0.479241337f, 0.479325482f,
0.479409622f, 0.479493758f, 0.479577889f, 0.479662016f, 0.479746139f,
0.479830257f, 0.479914371f, 0.479998480f, 0.480082585f, 0.480166685f,
0.480250781f, 0.480334873f, 0.480418960f, 0.480503043f, 0.480587122f,
0.480671196f, 0.480755265f, 0.480839331f, 0.480923391f, 0.481007448f,
0.481091500f, 0.481175547f, 0.481259590f, 0.481343629f, 0.481427663f,
0.481511693f, 0.481595718f, 0.481679739f, 0.481763756f, 0.481847768f,
0.481931776f, 0.482015779f, 0.482099778f, 0.482183772f, 0.482267762f,
0.482351748f, 0.482435729f, 0.482519705f, 0.482603678f, 0.482687645f,
0.482771609f, 0.482855568f, 0.482939522f, 0.483023472f, 0.483107418f,
0.483191359f, 0.483275295f, 0.483359228f, 0.483443156f, 0.483527079f,
0.483610998f, 0.483694912f, 0.483778822f, 0.483862728f, 0.483946629f,
0.484030526f, 0.484114418f, 0.484198306f, 0.484282189f, 0.484366068f,
0.484449943f, 0.484533813f, 0.484617678f, 0.484701539f, 0.484785396f,
0.484869248f, 0.484953096f, 0.485036939f, 0.485120778f, 0.485204612f,
0.485288442f, 0.485372267f, 0.485456088f, 0.485539905f, 0.485623717f,
0.485707524f, 0.485791328f, 0.485875126f, 0.485958920f, 0.486042710f,
0.486126495f, 0.486210276f, 0.486294052f, 0.486377824f, 0.486461592f,
0.486545355f, 0.486629113f, 0.486712867f, 0.486796616f, 0.486880361f,
0.486964102f, 0.487047838f, 0.487131569f, 0.487215297f, 0.487299019f,
0.487382737f, 0.487466451f, 0.487550160f, 0.487633865f, 0.487717565f,
0.487801261f, 0.487884952f, 0.487968639f, 0.488052321f, 0.488135999f,
0.488219672f, 0.488303341f, 0.488387005f, 0.488470665f, 0.488554320f,
0.488637971f, 0.488721618f, 0.488805260f, 0.488888897f, 0.488972530f,
0.489056158f, 0.489139782f, 0.489223401f, 0.489307016f, 0.489390627f,
0.489474233f, 0.489557834f, 0.489641431f, 0.489725023f, 0.489808611f,
0.489892195f, 0.489975774f, 0.490059348f, 0.490142918f, 0.490226483f,
0.490310044f, 0.490393601f, 0.490477152f, 0.490560700f, 0.490644243f,
0.490727781f, 0.490811315f, 0.490894844f, 0.490978369f, 0.491061889f,
0.491145405f, 0.491228916f, 0.491312423f, 0.491395925f, 0.491479423f,
0.491562916f, 0.491646405f, 0.491729889f, 0.491813369f, 0.491896844f,
0.491980314f, 0.492063780f, 0.492147242f, 0.492230699f, 0.492314151f,
0.492397599f, 0.492481043f, 0.492564482f, 0.492647916f, 0.492731346f,
0.492814771f, 0.492898192f, 0.492981609f, 0.493065020f, 0.493148427f,
0.493231830f, 0.493315228f, 0.493398622f, 0.493482011f, 0.493565396f,
0.493648776f, 0.493732151f, 0.493815522f, 0.493898888f, 0.493982250f,
0.494065608f, 0.494148960f, 0.494232309f, 0.494315652f, 0.494398991f,
0.494482326f, 0.494565656f, 0.494648982f, 0.494732302f, 0.494815619f,
0.494898931f, 0.494982238f, 0.495065541f, 0.495148839f, 0.495232133f,
0.495315422f, 0.495398706f, 0.495481986f, 0.495565262f, 0.495648533f,
0.495731799f, 0.495815061f, 0.495898318f, 0.495981571f, 0.496064819f,
0.496148062f, 0.496231301f, 0.496314536f, 0.496397766f, 0.496480991f,
0.496564212f, 0.496647428f, 0.496730640f, 0.496813847f, 0.496897049f,
0.496980247f, 0.497063440f, 0.497146629f, 0.497229813f, 0.497312993f,
0.497396168f, 0.497479338f, 0.497562504f, 0.497645666f, 0.497728822f,
0.497811975f, 0.497895122f, 0.497978265f, 0.498061404f, 0.498144538f,
0.498227667f, 0.498310792f, 0.498393912f, 0.498477027f, 0.498560138f,
0.498643245f, 0.498726347f, 0.498809444f, 0.498892537f, 0.498975625f,
0.499058708f, 0.499141787f, 0.499224861f, 0.499307931f, 0.499390996f,
0.499474057f, 0.499557113f, 0.499640164f, 0.499723211f, 0.499806253f,
0.499889290f, 0.499972323f, 0.500055352f, 0.500138376f, 0.500221395f,
0.500304409f, 0.500387419f, 0.500470425f, 0.500553425f, 0.500636422f,
0.500719413f, 0.500802400f, 0.500885383f, 0.500968360f, 0.501051334f,
0.501134302f, 0.501217266f, 0.501300225f, 0.501383180f, 0.501466130f,
0.501549076f, 0.501632017f, 0.501714953f, 0.501797885f, 0.501880812f,
0.501963734f, 0.502046652f, 0.502129565f, 0.502212474f, 0.502295378f,
0.502378277f, 0.502461172f, 0.502544062f, 0.502626948f, 0.502709829f,
0.502792705f, 0.502875577f, 0.502958444f, 0.503041306f, 0.503124164f,
0.503207017f, 0.503289866f, 0.503372710f, 0.503455549f, 0.503538384f,
0.503621214f, 0.503704039f, 0.503786860f, 0.503869676f, 0.503952488f,
0.504035295f, 0.504118097f, 0.504200894f, 0.504283687f, 0.504366476f,
0.504449259f, 0.504532039f, 0.504614813f, 0.504697583f, 0.504780348f,
0.504863109f, 0.504945864f, 0.505028616f, 0.505111362f, 0.505194104f,
0.505276842f, 0.505359574f, 0.505442302f, 0.505525026f, 0.505607744f,
0.505690458f, 0.505773168f, 0.505855873f, 0.505938573f, 0.506021268f,
0.506103959f, 0.506186645f, 0.506269327f, 0.506352004f, 0.506434676f,
0.506517344f, 0.506600006f, 0.506682665f, 0.506765318f, 0.506847967f,
0.506930612f, 0.507013251f, 0.507095886f, 0.507178516f, 0.507261142f,
0.507343763f, 0.507426379f, 0.507508991f, 0.507591598f, 0.507674200f,
0.507756798f, 0.507839391f, 0.507921979f, 0.508004563f, 0.508087142f,
0.508169716f, 0.508252286f, 0.508334851f, 0.508417411f, 0.508499967f,
0.508582518f, 0.508665064f, 0.508747606f, 0.508830143f, 0.508912675f,
0.508995202f, 0.509077725f, 0.509160243f, 0.509242757f, 0.509325266f,
0.509407770f, 0.509490269f, 0.509572764f, 0.509655254f, 0.509737740f,
0.509820221f, 0.509902697f, 0.509985168f, 0.510067635f, 0.510150097f,
0.510232554f, 0.510315007f, 0.510397455f, 0.510479898f, 0.510562336f,
0.510644770f, 0.510727199f, 0.510809624f, 0.510892044f, 0.510974459f,
0.511056869f, 0.511139275f, 0.511221676f, 0.511304072f, 0.511386464f,
0.511468850f, 0.511551233f, 0.511633610f, 0.511715983f, 0.511798351f,
0.511880714f, 0.511963073f, 0.512045427f, 0.512127776f, 0.512210121f,
0.512292461f, 0.512374796f, 0.512457126f, 0.512539452f, 0.512621773f,
0.512704089f, 0.512786401f, 0.512868707f, 0.512951010f, 0.513033307f,
0.513115600f, 0.513197888f, 0.513280171f, 0.513362450f, 0.513444723f,
0.513526993f, 0.513609257f, 0.513691517f, 0.513773772f, 0.513856022f,
0.513938267f, 0.514020508f, 0.514102744f, 0.514184976f, 0.514267202f,
0.514349424f, 0.514431641f, 0.514513854f, 0.514596061f, 0.514678264f,
0.514760463f, 0.514842656f, 0.514924845f, 0.515007029f, 0.515089208f,
0.515171383f, 0.515253553f, 0.515335718f, 0.515417878f, 0.515500034f,
0.515582185f, 0.515664331f, 0.515746472f, 0.515828609f, 0.515910741f,
0.515992868f, 0.516074990f, 0.516157108f, 0.516239221f, 0.516321329f,
0.516403433f, 0.516485531f, 0.516567625f, 0.516649715f, 0.516731799f,
0.516813879f, 0.516895954f, 0.516978024f, 0.517060089f, 0.517142150f,
0.517224206f, 0.517306257f, 0.517388304f, 0.517470345f, 0.517552382f,
0.517634415f, 0.517716442f, 0.517798465f, 0.517880483f, 0.517962496f,
0.518044504f, 0.518126508f, 0.518208507f, 0.518290501f, 0.518372490f,
0.518454475f, 0.518536454f, 0.518618429f, 0.518700400f, 0.518782365f,
0.518864326f, 0.518946282f, 0.519028233f, 0.519110180f, 0.519192121f,
0.519274058f, 0.519355990f, 0.519437917f, 0.519519840f, 0.519601758f,
0.519683671f, 0.519765579f, 0.519847483f, 0.519929381f, 0.520011275f,
0.520093164f, 0.520175049f, 0.520256928f, 0.520338803f, 0.520420673f,
0.520502538f, 0.520584399f, 0.520666254f, 0.520748105f, 0.520829951f,
0.520911792f, 0.520993629f, 0.521075461f, 0.521157287f, 0.521239110f,
0.521320927f, 0.521402739f, 0.521484547f, 0.521566350f, 0.521648148f,
0.521729942f, 0.521811730f, 0.521893514f, 0.521975293f, 0.522057067f,
0.522138836f, 0.522220601f, 0.522302361f, 0.522384116f, 0.522465866f,
0.522547611f, 0.522629352f, 0.522711088f, 0.522792819f, 0.522874545f,
0.522956266f, 0.523037983f, 0.523119694f, 0.523201401f, 0.523283103f,
0.523364801f, 0.523446493f, 0.523528181f, 0.523609864f, 0.523691542f,
0.523773215f, 0.523854884f, 0.523936547f, 0.524018206f, 0.524099860f,
0.524181509f, 0.524263153f, 0.524344793f, 0.524426428f, 0.524508058f,
0.524589683f, 0.524671303f, 0.524752918f, 0.524834529f, 0.524916135f,
0.524997736f, 0.525079332f, 0.525160923f, 0.525242510f, 0.525324091f,
0.525405668f, 0.525487240f, 0.525568807f, 0.525650369f, 0.525731927f,
0.525813480f, 0.525895027f, 0.525976570f, 0.526058109f, 0.526139642f,
0.526221170f, 0.526302694f, 0.526384213f, 0.526465727f, 0.526547236f,
0.526628740f, 0.526710240f, 0.526791734f, 0.526873224f, 0.526954709f,
0.527036189f, 0.527117664f, 0.527199135f, 0.527280600f, 0.527362061f,
0.527443517f, 0.527524968f, 0.527606414f, 0.527687855f, 0.527769292f,
0.527850723f, 0.527932150f, 0.528013572f, 0.528094989f, 0.528176401f,
0.528257809f, 0.528339211f, 0.528420609f, 0.528502002f, 0.528583389f,
0.528664773f, 0.528746151f, 0.528827524f, 0.528908893f, 0.528990256f,
0.529071615f, 0.529152969f, 0.529234318f, 0.529315662f, 0.529397001f,
0.529478336f, 0.529559665f, 0.529640990f, 0.529722310f, 0.529803625f,
0.529884935f, 0.529966240f, 0.530047540f, 0.530128836f, 0.530210126f,
0.530291412f, 0.530372693f, 0.530453969f, 0.530535240f, 0.530616506f,
0.530697768f, 0.530779024f, 0.530860276f, 0.530941522f, 0.531022764f,
0.531104001f, 0.531185233f, 0.531266460f, 0.531347683f, 0.531428900f,
0.531510113f, 0.531591320f, 0.531672523f, 0.531753721f, 0.531834914f,
0.531916102f, 0.531997285f, 0.532078464f, 0.532159637f, 0.532240805f,
0.532321969f, 0.532403128f, 0.532484282f, 0.532565431f, 0.532646575f,
0.532727714f, 0.532808848f, 0.532889978f, 0.532971102f, 0.533052222f,
0.533133336f, 0.533214446f, 0.533295551f, 0.533376651f, 0.533457746f,
0.533538836f, 0.533619921f, 0.533701002f, 0.533782077f, 0.533863148f,
0.533944213f, 0.534025274f, 0.534106330f, 0.534187381f, 0.534268427f,
0.534349468f, 0.534430504f, 0.534511535f, 0.534592562f, 0.534673583f,
0.534754600f, 0.534835611f, 0.534916618f, 0.534997620f, 0.535078617f,
0.535159609f, 0.535240596f, 0.535321578f, 0.535402555f, 0.535483527f,
0.535564495f, 0.535645457f, 0.535726415f, 0.535807367f, 0.535888315f,
0.535969257f, 0.536050195f, 0.536131128f, 0.536212056f, 0.536292979f,
0.536373897f, 0.536454810f, 0.536535719f, 0.536616622f, 0.536697520f,
0.536778414f, 0.536859302f, 0.536940186f, 0.537021064f, 0.537101938f,
0.537182807f, 0.537263670f, 0.537344529f, 0.537425383f, 0.537506232f,
0.537587076f, 0.537667915f, 0.537748750f, 0.537829579f, 0.537910403f,
0.537991222f, 0.538072037f, 0.538152846f, 0.538233651f, 0.538314450f,
0.538395245f, 0.538476035f, 0.538556819f, 0.538637599f, 0.538718374f,
0.538799144f, 0.538879909f, 0.538960668f, 0.539041423f, 0.539122173f,
0.539202919f, 0.539283659f, 0.539364394f, 0.539445124f, 0.539525849f,
0.539606570f, 0.539687285f, 0.539767995f, 0.539848701f, 0.539929401f,
0.540010097f, 0.540090787f, 0.540171473f, 0.540252153f, 0.540332829f,
0.540413500f, 0.540494165f, 0.540574826f, 0.540655482f, 0.540736133f,
0.540816778f, 0.540897419f, 0.540978055f, 0.541058686f, 0.541139312f,
0.541219933f, 0.541300549f, 0.541381160f, 0.541461766f, 0.541542367f,
0.541622963f, 0.541703554f, 0.541784140f, 0.541864721f, 0.541945297f,
0.542025869f, 0.542106435f, 0.542186996f, 0.542267552f, 0.542348103f,
0.542428650f, 0.542509191f, 0.542589727f, 0.542670259f, 0.542750785f,
0.542831306f, 0.542911823f, 0.542992334f, 0.543072840f, 0.543153342f,
0.543233838f, 0.543314329f, 0.543394816f, 0.543475297f, 0.543555773f,
0.543636245f, 0.543716711f, 0.543797173f, 0.543877629f, 0.543958080f,
0.544038527f, 0.544118968f, 0.544199405f, 0.544279836f, 0.544360262f,
0.544440684f, 0.544521100f, 0.544601511f, 0.544681918f, 0.544762319f,
0.544842716f, 0.544923107f, 0.545003493f, 0.545083875f, 0.545164251f,
0.545244622f, 0.545324988f, 0.545405350f, 0.545485706f, 0.545566057f,
0.545646403f, 0.545726745f, 0.545807081f, 0.545887412f, 0.545967738f,
0.546048059f, 0.546128376f, 0.546208687f, 0.546288993f, 0.546369294f,
0.546449590f, 0.546529881f, 0.546610167f, 0.546690448f, 0.546770724f,
0.546850995f, 0.546931261f, 0.547011522f, 0.547091777f, 0.547172028f,
0.547252274f, 0.547332515f, 0.547412750f, 0.547492981f, 0.547573207f,
0.547653427f, 0.547733643f, 0.547813854f, 0.547894059f, 0.547974260f,
0.548054455f, 0.548134646f, 0.548214831f, 0.548295011f, 0.548375187f,
0.548455357f, 0.548535522f, 0.548615682f, 0.548695837f, 0.548775987f,
0.548856132f, 0.548936272f, 0.549016407f, 0.549096537f, 0.549176662f,
0.549256782f, 0.549336897f, 0.549417006f, 0.549497111f, 0.549577211f,
0.549657305f, 0.549737395f, 0.549817479f, 0.549897559f, 0.549977633f,
0.550057702f, 0.550137767f, 0.550217826f, 0.550297880f, 0.550377929f,
0.550457973f, 0.550538012f, 0.550618046f, 0.550698075f, 0.550778098f,
0.550858117f, 0.550938131f, 0.551018139f, 0.551098143f, 0.551178141f,
0.551258135f, 0.551338123f, 0.551418106f, 0.551498084f, 0.551578057f,
0.551658025f, 0.551737988f, 0.551817946f, 0.551897899f, 0.551977847f,
0.552057790f, 0.552137727f, 0.552217660f, 0.552297587f, 0.552377509f,
0.552457427f, 0.552537339f, 0.552617246f, 0.552697148f, 0.552777045f,
0.552856937f, 0.552936824f, 0.553016706f, 0.553096582f, 0.553176454f,
0.553256320f, 0.553336182f, 0.553416038f, 0.553495889f, 0.553575735f,
0.553655576f, 0.553735412f, 0.553815243f, 0.553895069f, 0.553974890f,
0.554054705f, 0.554134516f, 0.554214321f, 0.554294121f, 0.554373917f,
0.554453707f, 0.554533492f, 0.554613272f, 0.554693047f, 0.554772816f,
0.554852581f, 0.554932340f, 0.555012095f, 0.555091844f, 0.555171588f,
0.555251328f, 0.555331062f, 0.555410791f, 0.555490514f, 0.555570233f,
0.555649947f, 0.555729655f, 0.555809358f, 0.555889057f, 0.555968750f,
0.556048438f, 0.556128121f, 0.556207799f, 0.556287471f, 0.556367139f,
0.556446802f, 0.556526459f, 0.556606111f, 0.556685758f, 0.556765400f,
0.556845037f, 0.556924669f, 0.557004296f, 0.557083917f, 0.557163534f,
0.557243145f, 0.557322751f, 0.557402352f, 0.557481948f, 0.557561539f,
0.557641125f, 0.557720705f, 0.557800281f, 0.557879851f, 0.557959416f,
0.558038976f, 0.558118531f, 0.558198081f, 0.558277626f, 0.558357165f,
0.558436700f, 0.558516229f, 0.558595753f, 0.558675272f, 0.558754786f,
0.558834295f, 0.558913798f, 0.558993297f, 0.559072790f, 0.559152278f,
0.559231761f, 0.559311239f, 0.559390712f, 0.559470179f, 0.559549642f,
0.559629099f, 0.559708551f, 0.559787999f, 0.559867440f, 0.559946877f,
0.560026309f, 0.560105735f, 0.560185157f, 0.560264573f, 0.560343984f,
0.560423390f, 0.560502790f, 0.560582186f, 0.560661576f, 0.560740961f,
0.560820342f, 0.560899716f, 0.560979086f, 0.561058451f, 0.561137810f,
0.561217165f, 0.561296514f, 0.561375858f, 0.561455197f, 0.561534530f,
0.561613859f, 0.561693182f, 0.561772500f, 0.561851813f, 0.561931121f,
0.562010424f, 0.562089721f, 0.562169014f, 0.562248301f, 0.562327583f,
0.562406860f, 0.562486132f, 0.562565398f, 0.562644659f, 0.562723916f,
0.562803167f, 0.562882412f, 0.562961653f, 0.563040889f, 0.563120119f,
0.563199344f, 0.563278564f, 0.563357779f, 0.563436988f, 0.563516193f,
0.563595392f, 0.563674586f, 0.563753775f, 0.563832959f, 0.563912137f,
0.563991310f, 0.564070479f, 0.564149642f, 0.564228799f, 0.564307952f,
0.564387099f, 0.564466242f, 0.564545379f, 0.564624510f, 0.564703637f,
0.564782758f, 0.564861875f, 0.564940986f, 0.565020092f, 0.565099192f,
0.565178288f, 0.565257378f, 0.565336463f, 0.565415543f, 0.565494618f,
0.565573687f, 0.565652752f, 0.565731811f, 0.565810865f, 0.565889913f,
0.565968957f, 0.566047995f, 0.566127028f, 0.566206056f, 0.566285079f,
0.566364096f, 0.566443109f, 0.566522116f, 0.566601118f, 0.566680114f,
0.566759106f, 0.566838092f, 0.566917073f, 0.566996049f, 0.567075019f,
0.567153985f, 0.567232945f, 0.567311900f, 0.567390850f, 0.567469794f,
0.567548734f, 0.567627668f, 0.567706597f, 0.567785520f, 0.567864439f,
0.567943352f, 0.568022260f, 0.568101163f, 0.568180060f, 0.568258953f,
0.568337840f, 0.568416722f, 0.568495598f, 0.568574470f, 0.568653336f,
0.568732197f, 0.568811053f, 0.568889903f, 0.568968749f, 0.569047589f,
0.569126424f, 0.569205253f, 0.569284078f, 0.569362897f, 0.569441711f,
0.569520519f, 0.569599323f, 0.569678121f, 0.569756914f, 0.569835702f,
0.569914484f, 0.569993262f, 0.570072034f, 0.570150800f, 0.570229562f,
0.570308318f, 0.570387069f, 0.570465815f, 0.570544556f, 0.570623291f,
0.570702021f, 0.570780746f, 0.570859465f, 0.570938180f, 0.571016889f,
0.571095593f, 0.571174291f, 0.571252985f, 0.571331673f, 0.571410356f,
0.571489033f, 0.571567706f, 0.571646373f, 0.571725035f, 0.571803691f,
0.571882342f, 0.571960989f, 0.572039629f, 0.572118265f, 0.572196895f,
0.572275520f, 0.572354140f, 0.572432754f, 0.572511364f, 0.572589968f,
0.572668566f, 0.572747160f, 0.572825748f, 0.572904331f, 0.572982909f,
0.573061481f, 0.573140048f, 0.573218610f, 0.573297167f, 0.573375718f,
0.573454264f, 0.573532805f, 0.573611340f, 0.573689871f, 0.573768396f,
0.573846915f, 0.573925430f, 0.574003939f, 0.574082443f, 0.574160941f,
0.574239435f, 0.574317923f, 0.574396405f, 0.574474883f, 0.574553355f,
0.574631822f, 0.574710284f, 0.574788740f, 0.574867191f, 0.574945637f,
0.575024077f, 0.575102512f, 0.575180942f, 0.575259367f, 0.575337786f,
0.575416200f, 0.575494609f, 0.575573013f, 0.575651411f, 0.575729804f,
0.575808191f, 0.575886574f, 0.575964951f, 0.576043322f, 0.576121689f,
0.576200050f, 0.576278406f, 0.576356756f, 0.576435102f, 0.576513442f,
0.576591776f, 0.576670106f, 0.576748430f, 0.576826748f, 0.576905062f,
0.576983370f, 0.577061673f, 0.577139970f, 0.577218263f, 0.577296550f,
0.577374831f, 0.577453107f, 0.577531378f, 0.577609644f, 0.577687905f,
0.577766160f, 0.577844409f, 0.577922654f, 0.578000893f, 0.578079127f,
0.578157355f, 0.578235579f, 0.578313796f, 0.578392009f, 0.578470216f,
0.578548418f, 0.578626615f, 0.578704806f, 0.578782992f, 0.578861173f,
0.578939348f, 0.579017518f, 0.579095683f, 0.579173842f, 0.579251996f,
0.579330145f, 0.579408288f, 0.579486426f, 0.579564559f, 0.579642687f,
0.579720809f, 0.579798925f, 0.579877037f, 0.579955143f, 0.580033244f,
0.580111339f, 0.580189429f, 0.580267514f, 0.580345593f, 0.580423668f,
0.580501736f, 0.580579800f, 0.580657858f, 0.580735911f, 0.580813958f,
0.580892000f, 0.580970037f, 0.581048068f, 0.581126094f, 0.581204115f,
0.581282131f, 0.581360141f, 0.581438145f, 0.581516145f, 0.581594139f,
0.581672127f, 0.581750111f, 0.581828089f, 0.581906061f, 0.581984028f,
0.582061990f, 0.582139947f, 0.582217898f, 0.582295844f, 0.582373785f,
0.582451720f, 0.582529649f, 0.582607574f, 0.582685493f, 0.582763407f,
0.582841315f, 0.582919218f, 0.582997116f, 0.583075008f, 0.583152895f,
0.583230777f, 0.583308653f, 0.583386524f, 0.583464389f, 0.583542249f,
0.583620104f, 0.583697954f, 0.583775798f, 0.583853636f, 0.583931470f,
0.584009298f, 0.584087120f, 0.584164937f, 0.584242749f, 0.584320556f,
0.584398357f, 0.584476153f, 0.584553943f, 0.584631728f, 0.584709508f,
0.584787282f, 0.584865051f, 0.584942814f, 0.585020572f, 0.585098325f,
0.585176072f, 0.585253814f, 0.585331551f, 0.585409282f, 0.585487008f,
0.585564728f, 0.585642443f, 0.585720153f, 0.585797857f, 0.585875556f,
0.585953250f, 0.586030938f, 0.586108621f, 0.586186298f, 0.586263970f,
0.586341637f, 0.586419298f, 0.586496954f, 0.586574604f, 0.586652249f,
0.586729889f, 0.586807523f, 0.586885152f, 0.586962775f, 0.587040394f,
0.587118006f, 0.587195613f, 0.587273215f, 0.587350812f, 0.587428403f,
0.587505989f, 0.587583569f, 0.587661144f, 0.587738713f, 0.587816277f,
0.587893836f, 0.587971389f, 0.588048937f, 0.588126480f, 0.588204017f,
0.588281548f, 0.588359074f, 0.588436595f, 0.588514111f, 0.588591621f,
0.588669125f, 0.588746625f, 0.588824118f, 0.588901607f, 0.588979090f,
0.589056567f, 0.589134039f, 0.589211506f, 0.589288967f, 0.589366423f,
0.589443874f, 0.589521319f, 0.589598758f, 0.589676192f, 0.589753621f,
0.589831045f, 0.589908463f, 0.589985875f, 0.590063282f, 0.590140684f,
0.590218080f, 0.590295471f, 0.590372856f, 0.590450236f, 0.590527611f,
0.590604980f, 0.590682344f, 0.590759702f, 0.590837055f, 0.590914402f,
0.590991744f, 0.591069081f, 0.591146412f, 0.591223737f, 0.591301058f,
0.591378372f, 0.591455682f, 0.591532986f, 0.591610284f, 0.591687577f,
0.591764865f, 0.591842147f, 0.591919424f, 0.591996695f, 0.592073961f,
0.592151221f, 0.592228476f, 0.592305726f, 0.592382970f, 0.592460208f,
0.592537442f, 0.592614669f, 0.592691892f, 0.592769108f, 0.592846320f,
0.592923526f, 0.593000726f, 0.593077921f, 0.593155111f, 0.593232295f,
0.593309474f, 0.593386647f, 0.593463815f, 0.593540977f, 0.593618134f,
0.593695285f, 0.593772431f, 0.593849572f, 0.593926707f, 0.594003836f,
0.594080961f, 0.594158079f, 0.594235192f, 0.594312300f, 0.594389402f,
0.594466499f, 0.594543591f, 0.594620676f, 0.594697757f, 0.594774832f,
0.594851901f, 0.594928965f, 0.595006024f, 0.595083077f, 0.595160124f,
0.595237167f, 0.595314203f, 0.595391234f, 0.595468260f, 0.595545280f,
0.595622295f, 0.595699304f, 0.595776308f, 0.595853307f, 0.595930300f,
0.596007287f, 0.596084269f, 0.596161245f, 0.596238216f, 0.596315182f,
0.596392142f, 0.596469096f, 0.596546045f, 0.596622989f, 0.596699927f,
0.596776859f, 0.596853786f, 0.596930708f, 0.597007624f, 0.597084535f,
0.597161440f, 0.597238340f, 0.597315234f, 0.597392122f, 0.597469006f,
0.597545883f, 0.597622755f, 0.597699622f, 0.597776483f, 0.597853339f,
0.597930189f, 0.598007034f, 0.598083873f, 0.598160707f, 0.598237535f,
0.598314358f, 0.598391175f, 0.598467987f, 0.598544793f, 0.598621594f,
0.598698389f, 0.598775179f, 0.598851963f, 0.598928742f, 0.599005515f,
0.599082283f, 0.599159045f, 0.599235802f, 0.599312553f, 0.599389298f,
0.599466039f, 0.599542773f, 0.599619502f, 0.599696226f, 0.599772944f,
0.599849657f, 0.599926364f, 0.600003065f, 0.600079761f, 0.600156452f,
0.600233137f, 0.600309817f, 0.600386491f, 0.600463159f, 0.600539822f,
0.600616479f, 0.600693131f, 0.600769778f, 0.600846419f, 0.600923054f,
0.600999684f, 0.601076308f, 0.601152927f, 0.601229540f, 0.601306148f,
0.601382750f, 0.601459347f, 0.601535938f, 0.601612523f, 0.601689103f,
0.601765678f, 0.601842247f, 0.601918811f, 0.601995369f, 0.602071921f,
0.602148468f, 0.602225009f, 0.602301545f, 0.602378075f, 0.602454600f,
0.602531119f, 0.602607633f, 0.602684141f, 0.602760644f, 0.602837141f,
0.602913632f, 0.602990118f, 0.603066599f, 0.603143073f, 0.603219543f,
0.603296007f, 0.603372465f, 0.603448917f, 0.603525365f, 0.603601806f,
0.603678242f, 0.603754673f, 0.603831098f, 0.603907517f, 0.603983931f,
0.604060339f, 0.604136742f, 0.604213139f, 0.604289531f, 0.604365917f,
0.604442298f, 0.604518673f, 0.604595042f, 0.604671406f, 0.604747764f,
0.604824117f, 0.604900464f, 0.604976806f, 0.605053142f, 0.605129472f,
0.605205797f, 0.605282117f, 0.605358430f, 0.605434739f, 0.605511041f,
0.605587339f, 0.605663630f, 0.605739916f, 0.605816197f, 0.605892471f,
0.605968741f, 0.606045004f, 0.606121263f, 0.606197515f, 0.606273762f,
0.606350004f, 0.606426239f, 0.606502470f, 0.606578694f, 0.606654913f,
0.606731127f, 0.606807335f, 0.606883537f, 0.606959734f, 0.607035925f,
0.607112111f, 0.607188291f, 0.607264466f, 0.607340635f, 0.607416798f,
0.607492956f, 0.607569108f, 0.607645254f, 0.607721395f, 0.607797531f,
0.607873661f, 0.607949785f, 0.608025904f, 0.608102017f, 0.608178124f,
0.608254226f, 0.608330322f, 0.608406413f, 0.608482498f, 0.608558578f,
0.608634652f, 0.608710720f, 0.608786783f, 0.608862840f, 0.608938891f,
0.609014937f, 0.609090978f, 0.609167012f, 0.609243041f, 0.609319065f,
0.609395083f, 0.609471095f, 0.609547102f, 0.609623103f, 0.609699099f,
0.609775089f, 0.609851073f, 0.609927052f, 0.610003025f, 0.610078992f,
0.610154954f, 0.610230911f, 0.610306861f, 0.610382806f, 0.610458746f,
0.610534680f, 0.610610608f, 0.610686530f, 0.610762447f, 0.610838359f,
0.610914265f, 0.610990165f, 0.611066059f, 0.611141948f, 0.611217832f,
0.611293709f, 0.611369581f, 0.611445448f, 0.611521309f, 0.611597164f,
0.611673014f, 0.611748858f, 0.611824696f, 0.611900529f, 0.611976356f,
0.612052177f, 0.612127993f, 0.612203803f, 0.612279608f, 0.612355407f,
0.612431200f, 0.612506988f, 0.612582770f, 0.612658546f, 0.612734317f,
0.612810082f, 0.612885842f, 0.612961596f, 0.613037344f, 0.613113087f,
0.613188824f, 0.613264555f, 0.613340281f, 0.613416001f, 0.613491716f,
0.613567424f, 0.613643128f, 0.613718825f, 0.613794517f, 0.613870203f,
0.613945884f, 0.614021559f, 0.614097228f, 0.614172892f, 0.614248550f,
0.614324202f, 0.614399849f, 0.614475490f, 0.614551126f, 0.614626756f,
0.614702380f, 0.614777998f, 0.614853611f, 0.614929218f, 0.615004820f,
0.615080416f, 0.615156006f, 0.615231591f, 0.615307170f, 0.615382743f,
0.615458310f, 0.615533872f, 0.615609429f, 0.615684979f, 0.615760524f,
0.615836064f, 0.615911597f, 0.615987125f, 0.616062648f, 0.616138164f,
0.616213675f, 0.616289181f, 0.616364681f, 0.616440175f, 0.616515663f,
0.616591146f, 0.616666623f, 0.616742094f, 0.616817560f, 0.616893020f,
0.616968474f, 0.617043923f, 0.617119366f, 0.617194803f, 0.617270235f,
0.617345661f, 0.617421081f, 0.617496496f, 0.617571905f, 0.617647308f,
0.617722706f, 0.617798097f, 0.617873484f, 0.617948864f, 0.618024239f,
0.618099608f, 0.618174972f, 0.618250330f, 0.618325682f, 0.618401028f,
0.618476369f, 0.618551704f, 0.618627034f, 0.618702358f, 0.618777676f,
0.618852988f, 0.618928295f, 0.619003596f, 0.619078891f, 0.619154181f,
0.619229464f, 0.619304743f, 0.619380015f, 0.619455282f, 0.619530543f,
0.619605799f, 0.619681048f, 0.619756292f, 0.619831531f, 0.619906764f,
0.619981990f, 0.620057212f, 0.620132427f, 0.620207637f, 0.620282841f,
0.620358040f, 0.620433233f, 0.620508420f, 0.620583601f, 0.620658777f,
0.620733947f, 0.620809111f, 0.620884269f, 0.620959422f, 0.621034569f,
0.621109711f, 0.621184847f, 0.621259977f, 0.621335101f, 0.621410219f,
0.621485332f, 0.621560439f, 0.621635541f, 0.621710637f, 0.621785727f,
0.621860811f, 0.621935889f, 0.622010962f, 0.622086029f, 0.622161091f,
0.622236147f, 0.622311197f, 0.622386241f, 0.622461279f, 0.622536312f,
0.622611339f, 0.622686361f, 0.622761376f, 0.622836386f, 0.622911390f,
0.622986389f, 0.623061382f, 0.623136369f, 0.623211350f, 0.623286326f,
0.623361295f, 0.623436260f, 0.623511218f, 0.623586171f, 0.623661118f,
0.623736059f, 0.623810994f, 0.623885924f, 0.623960848f, 0.624035766f,
0.624110679f, 0.624185585f, 0.624260486f, 0.624335382f, 0.624410271f,
0.624485155f, 0.624560033f, 0.624634906f, 0.624709772f, 0.624784633f,
0.624859488f, 0.624934338f, 0.625009181f, 0.625084019f, 0.625158851f,
0.625233678f, 0.625308498f, 0.625383313f, 0.625458122f, 0.625532926f,
0.625607723f, 0.625682515f, 0.625757301f, 0.625832082f, 0.625906856f,
0.625981625f, 0.626056388f, 0.626131146f, 0.626205897f, 0.626280643f,
0.626355383f, 0.626430118f, 0.626504846f, 0.626579569f, 0.626654286f,
0.626728998f, 0.626803703f, 0.626878403f, 0.626953097f, 0.627027785f,
0.627102468f, 0.627177145f, 0.627251815f, 0.627326481f, 0.627401140f,
0.627475794f, 0.627550442f, 0.627625084f, 0.627699720f, 0.627774351f,
0.627848976f, 0.627923595f, 0.627998208f, 0.628072816f, 0.628147417f,
0.628222013f, 0.628296604f, 0.628371188f, 0.628445767f, 0.628520339f,
0.628594907f, 0.628669468f, 0.628744023f, 0.628818573f, 0.628893117f,
0.628967655f, 0.629042188f, 0.629116714f, 0.629191235f, 0.629265750f,
0.629340260f, 0.629414763f, 0.629489261f, 0.629563753f, 0.629638239f,
0.629712719f, 0.629787194f, 0.629861663f, 0.629936126f, 0.630010583f,
0.630085034f, 0.630159480f, 0.630233920f, 0.630308354f, 0.630382782f,
0.630457204f, 0.630531621f, 0.630606032f, 0.630680437f, 0.630754836f,
0.630829230f, 0.630903617f, 0.630977999f, 0.631052375f, 0.631126745f,
0.631201110f, 0.631275469f, 0.631349821f, 0.631424169f, 0.631498510f,
0.631572845f, 0.631647175f, 0.631721499f, 0.631795817f, 0.631870129f,
0.631944435f, 0.632018736f, 0.632093031f, 0.632167320f, 0.632241603f,
0.632315880f, 0.632390152f, 0.632464418f, 0.632538677f, 0.632612932f,
0.632687180f, 0.632761422f, 0.632835659f, 0.632909890f, 0.632984115f,
0.633058334f, 0.633132547f, 0.633206755f, 0.633280957f, 0.633355153f,
0.633429343f, 0.633503527f, 0.633577706f, 0.633651878f, 0.633726045f,
0.633800206f, 0.633874361f, 0.633948511f, 0.634022654f, 0.634096792f,
0.634170924f, 0.634245050f, 0.634319170f, 0.634393284f, 0.634467393f,
0.634541495f, 0.634615592f, 0.634689683f, 0.634763769f, 0.634837848f,
0.634911921f, 0.634985989f, 0.635060051f, 0.635134107f, 0.635208157f,
0.635282202f, 0.635356240f, 0.635430273f, 0.635504300f, 0.635578320f,
0.635652336f, 0.635726345f, 0.635800348f, 0.635874346f, 0.635948338f,
0.636022324f, 0.636096304f, 0.636170278f, 0.636244246f, 0.636318209f,
0.636392166f, 0.636466116f, 0.636540061f, 0.636614001f, 0.636687934f,
0.636761861f, 0.636835783f, 0.636909699f, 0.636983608f, 0.637057512f,
0.637131411f, 0.637205303f, 0.637279189f, 0.637353070f, 0.637426945f,
0.637500813f, 0.637574677f, 0.637648534f, 0.637722385f, 0.637796230f,
0.637870070f, 0.637943904f, 0.638017731f, 0.638091553f, 0.638165370f,
0.638239180f, 0.638312984f, 0.638386783f, 0.638460575f, 0.638534362f,
0.638608143f, 0.638681918f, 0.638755687f, 0.638829450f, 0.638903208f,
0.638976959f, 0.639050705f, 0.639124445f, 0.639198179f, 0.639271907f,
0.639345629f, 0.639419345f, 0.639493056f, 0.639566760f, 0.639640459f,
0.639714152f, 0.639787839f, 0.639861520f, 0.639935195f, 0.640008864f,
0.640082527f, 0.640156185f, 0.640229836f, 0.640303482f, 0.640377122f,
0.640450756f, 0.640524384f, 0.640598006f, 0.640671622f, 0.640745233f,
0.640818837f, 0.640892436f, 0.640966029f, 0.641039616f, 0.641113197f,
0.641186772f, 0.641260341f, 0.641333904f, 0.641407461f, 0.641481013f,
0.641554558f, 0.641628098f, 0.641701632f, 0.641775160f, 0.641848682f,
0.641922198f, 0.641995708f, 0.642069212f, 0.642142711f, 0.642216203f,
0.642289690f, 0.642363170f, 0.642436645f, 0.642510114f, 0.642583577f,
0.642657034f, 0.642730485f, 0.642803930f, 0.642877370f, 0.642950803f,
0.643024231f, 0.643097652f, 0.643171068f, 0.643244478f, 0.643317881f,
0.643391279f, 0.643464671f, 0.643538058f, 0.643611438f, 0.643684812f,
0.643758180f, 0.643831543f, 0.643904899f, 0.643978250f, 0.644051595f,
0.644124934f, 0.644198266f, 0.644271593f, 0.644344914f, 0.644418229f,
0.644491539f, 0.644564842f, 0.644638139f, 0.644711431f, 0.644784716f,
0.644857996f, 0.644931269f, 0.645004537f, 0.645077799f, 0.645151054f,
0.645224304f, 0.645297548f, 0.645370786f, 0.645444018f, 0.645517245f,
0.645590465f, 0.645663679f, 0.645736887f, 0.645810090f, 0.645883286f,
0.645956477f, 0.646029662f, 0.646102840f, 0.646176013f, 0.646249180f,
0.646322341f, 0.646395496f, 0.646468645f, 0.646541788f, 0.646614925f,
0.646688056f, 0.646761181f, 0.646834300f, 0.646907414f, 0.646980521f,
0.647053622f, 0.647126718f, 0.647199807f, 0.647272891f, 0.647345969f,
0.647419040f, 0.647492106f, 0.647565166f, 0.647638220f, 0.647711268f,
0.647784309f, 0.647857345f, 0.647930375f, 0.648003399f, 0.648076418f,
0.648149430f, 0.648222436f, 0.648295436f, 0.648368430f, 0.648441419f,
0.648514401f, 0.648587377f, 0.648660348f, 0.648733312f, 0.648806271f,
0.648879223f, 0.648952170f, 0.649025110f, 0.649098045f, 0.649170974f,
0.649243897f, 0.649316813f, 0.649389724f, 0.649462629f, 0.649535528f,
0.649608421f, 0.649681307f, 0.649754188f, 0.649827063f, 0.649899932f,
0.649972795f, 0.650045652f, 0.650118503f, 0.650191348f, 0.650264187f,
0.650337021f, 0.650409848f, 0.650482669f, 0.650555484f, 0.650628293f,
0.650701096f, 0.650773894f, 0.650846685f, 0.650919470f, 0.650992250f,
0.651065023f, 0.651137790f, 0.651210552f, 0.651283307f, 0.651356056f,
0.651428800f, 0.651501537f, 0.651574268f, 0.651646994f, 0.651719713f,
0.651792427f, 0.651865134f, 0.651937836f, 0.652010531f, 0.652083221f,
0.652155904f, 0.652228582f, 0.652301253f, 0.652373918f, 0.652446578f,
0.652519231f, 0.652591879f, 0.652664520f, 0.652737156f, 0.652809785f,
0.652882409f, 0.652955026f, 0.653027638f, 0.653100243f, 0.653172843f,
0.653245436f, 0.653318024f, 0.653390605f, 0.653463181f, 0.653535750f,
0.653608314f, 0.653680871f, 0.653753423f, 0.653825968f, 0.653898508f,
0.653971041f, 0.654043568f, 0.654116090f, 0.654188605f, 0.654261114f,
0.654333618f, 0.654406115f, 0.654478606f, 0.654551092f, 0.654623571f,
0.654696044f, 0.654768512f, 0.654840973f, 0.654913428f, 0.654985877f,
0.655058320f, 0.655130758f, 0.655203189f, 0.655275614f, 0.655348033f,
0.655420446f, 0.655492853f, 0.655565254f, 0.655637649f, 0.655710038f,
0.655782421f, 0.655854798f, 0.655927169f, 0.655999534f, 0.656071892f,
0.656144245f, 0.656216592f, 0.656288933f, 0.656361267f, 0.656433596f,
0.656505919f, 0.656578235f, 0.656650546f, 0.656722850f, 0.656795149f,
0.656867441f, 0.656939728f, 0.657012008f, 0.657084282f, 0.657156551f,
0.657228813f, 0.657301069f, 0.657373319f, 0.657445563f, 0.657517801f,
0.657590033f, 0.657662259f, 0.657734479f, 0.657806693f, 0.657878901f,
0.657951103f, 0.658023299f, 0.658095488f, 0.658167672f, 0.658239850f,
0.658312021f, 0.658384187f, 0.658456346f, 0.658528500f, 0.658600647f,
0.658672788f, 0.658744924f, 0.658817053f, 0.658889176f, 0.658961293f,
0.659033404f, 0.659105509f, 0.659177608f, 0.659249701f, 0.659321788f,
0.659393868f, 0.659465943f, 0.659538012f, 0.659610074f, 0.659682131f,
0.659754181f, 0.659826225f, 0.659898264f, 0.659970296f, 0.660042322f,
0.660114342f, 0.660186356f, 0.660258364f, 0.660330366f, 0.660402362f,
0.660474351f, 0.660546335f, 0.660618313f, 0.660690284f, 0.660762250f,
0.660834209f, 0.660906162f, 0.660978110f, 0.661050051f, 0.661121986f,
0.661193915f, 0.661265838f, 0.661337755f, 0.661409665f, 0.661481570f,
0.661553469f, 0.661625361f, 0.661697248f, 0.661769128f, 0.661841002f,
0.661912871f, 0.661984733f, 0.662056589f, 0.662128439f, 0.662200283f,
0.662272120f, 0.662343952f, 0.662415778f, 0.662487597f, 0.662559411f,
0.662631218f, 0.662703019f, 0.662774814f, 0.662846603f, 0.662918386f,
0.662990163f, 0.663061934f, 0.663133699f, 0.663205457f, 0.663277210f,
0.663348956f, 0.663420696f, 0.663492431f, 0.663564159f, 0.663635881f,
0.663707597f, 0.663779306f, 0.663851010f, 0.663922708f, 0.663994399f,
0.664066084f, 0.664137764f, 0.664209437f, 0.664281104f, 0.664352765f,
0.664424420f, 0.664496069f, 0.664567711f, 0.664639348f, 0.664710978f,
0.664782603f, 0.664854221f, 0.664925833f, 0.664997439f, 0.665069039f,
0.665140632f, 0.665212220f, 0.665283802f, 0.665355377f, 0.665426946f,
0.665498510f, 0.665570067f, 0.665641618f, 0.665713162f, 0.665784701f,
0.665856234f, 0.665927760f, 0.665999280f, 0.666070795f, 0.666142303f,
0.666213805f, 0.666285301f, 0.666356790f, 0.666428274f, 0.666499751f,
0.666571223f, 0.666642688f, 0.666714147f, 0.666785600f, 0.666857047f,
0.666928488f, 0.666999922f, 0.667071351f, 0.667142773f, 0.667214189f,
0.667285599f, 0.667357003f, 0.667428401f, 0.667499793f, 0.667571178f,
0.667642558f, 0.667713931f, 0.667785298f, 0.667856659f, 0.667928014f,
0.667999362f, 0.668070705f, 0.668142041f, 0.668213372f, 0.668284696f,
0.668356014f, 0.668427326f, 0.668498631f, 0.668569931f, 0.668641224f,
0.668712512f, 0.668783793f, 0.668855068f, 0.668926336f, 0.668997599f,
0.669068856f, 0.669140106f, 0.669211350f, 0.669282588f, 0.669353820f,
0.669425046f, 0.669496266f, 0.669567479f, 0.669638686f, 0.669709888f,
0.669781083f, 0.669852271f, 0.669923454f, 0.669994631f, 0.670065801f,
0.670136965f, 0.670208123f, 0.670279275f, 0.670350421f, 0.670421560f,
0.670492694f, 0.670563821f, 0.670634942f, 0.670706057f, 0.670777166f,
0.670848268f, 0.670919365f, 0.670990455f, 0.671061539f, 0.671132617f,
0.671203689f, 0.671274754f, 0.671345814f, 0.671416867f, 0.671487914f,
0.671558955f, 0.671629990f, 0.671701018f, 0.671772040f, 0.671843057f,
0.671914067f, 0.671985071f, 0.672056068f, 0.672127060f, 0.672198045f,
0.672269024f, 0.672339997f, 0.672410964f, 0.672481924f, 0.672552879f,
0.672623827f, 0.672694769f, 0.672765705f, 0.672836635f, 0.672907558f,
0.672978475f, 0.673049387f, 0.673120291f, 0.673191190f, 0.673262083f,
0.673332969f, 0.673403849f, 0.673474723f, 0.673545591f, 0.673616453f,
0.673687308f, 0.673758157f, 0.673829000f, 0.673899837f, 0.673970668f,
0.674041492f, 0.674112311f, 0.674183123f, 0.674253928f, 0.674324728f,
0.674395522f, 0.674466309f, 0.674537090f, 0.674607865f, 0.674678633f,
0.674749396f, 0.674820152f, 0.674890902f, 0.674961646f, 0.675032384f,
0.675103115f, 0.675173840f, 0.675244559f, 0.675315272f, 0.675385979f,
0.675456679f, 0.675527374f, 0.675598062f, 0.675668743f, 0.675739419f,
0.675810088f, 0.675880751f, 0.675951408f, 0.676022059f, 0.676092704f,
0.676163342f, 0.676233974f, 0.676304600f, 0.676375219f, 0.676445833f,
0.676516440f, 0.676587041f, 0.676657636f, 0.676728224f, 0.676798807f,
0.676869383f, 0.676939953f, 0.677010516f, 0.677081074f, 0.677151625f,
0.677222170f, 0.677292709f, 0.677363241f, 0.677433768f, 0.677504288f,
0.677574802f, 0.677645309f, 0.677715811f, 0.677786306f, 0.677856795f,
0.677927278f, 0.677997754f, 0.678068224f, 0.678138688f, 0.678209146f,
0.678279598f, 0.678350043f, 0.678420482f, 0.678490915f, 0.678561342f,
0.678631762f, 0.678702176f, 0.678772584f, 0.678842986f, 0.678913381f,
0.678983770f, 0.679054153f, 0.679124530f, 0.679194900f, 0.679265265f,
0.679335623f, 0.679405974f, 0.679476320f, 0.679546659f, 0.679616992f,
0.679687319f, 0.679757639f, 0.679827954f, 0.679898262f, 0.679968563f,
0.680038859f, 0.680109148f, 0.680179431f, 0.680249708f, 0.680319978f,
0.680390243f, 0.680460501f, 0.680530752f, 0.680600998f, 0.680671237f,
0.680741470f, 0.680811697f, 0.680881917f, 0.680952131f, 0.681022339f,
0.681092541f, 0.681162736f, 0.681232925f, 0.681303108f, 0.681373285f,
0.681443455f, 0.681513619f, 0.681583777f, 0.681653929f, 0.681724074f,
0.681794213f, 0.681864346f, 0.681934472f, 0.682004593f, 0.682074707f,
0.682144814f, 0.682214916f, 0.682285011f, 0.682355100f, 0.682425182f,
0.682495259f, 0.682565329f, 0.682635393f, 0.682705450f, 0.682775501f,
0.682845546f, 0.682915585f, 0.682985617f, 0.683055644f, 0.683125663f,
0.683195677f, 0.683265684f, 0.683335685f, 0.683405680f, 0.683475669f,
0.683545651f, 0.683615627f, 0.683685596f, 0.683755560f, 0.683825517f,
0.683895467f, 0.683965412f, 0.684035350f, 0.684105282f, 0.684175207f,
0.684245127f, 0.684315040f, 0.684384947f, 0.684454847f, 0.684524741f,
0.684594629f, 0.684664511f, 0.684734386f, 0.684804255f, 0.684874117f,
0.684943974f, 0.685013824f, 0.685083668f, 0.685153505f, 0.685223336f,
0.685293161f, 0.685362980f, 0.685432792f, 0.685502598f, 0.685572398f,
0.685642191f, 0.685711978f, 0.685781759f, 0.685851534f, 0.685921302f,
0.685991064f, 0.686060819f, 0.686130569f, 0.686200312f, 0.686270048f,
0.686339779f, 0.686409503f, 0.686479220f, 0.686548932f, 0.686618637f,
0.686688336f, 0.686758028f, 0.686827714f, 0.686897394f, 0.686967068f,
0.687036735f, 0.687106396f, 0.687176051f, 0.687245699f, 0.687315341f,
0.687384977f, 0.687454606f, 0.687524229f, 0.687593846f, 0.687663456f,
0.687733060f, 0.687802658f, 0.687872249f, 0.687941834f, 0.688011413f,
0.688080985f, 0.688150552f, 0.688220111f, 0.688289665f, 0.688359212f,
0.688428753f, 0.688498287f, 0.688567815f, 0.688637337f, 0.688706853f,
0.688776362f, 0.688845865f, 0.688915361f, 0.688984851f, 0.689054335f,
0.689123813f, 0.689193284f, 0.689262749f, 0.689332207f, 0.689401659f,
0.689471105f, 0.689540545f, 0.689609978f, 0.689679405f, 0.689748825f,
0.689818239f, 0.689887647f, 0.689957049f, 0.690026444f, 0.690095832f,
0.690165215f, 0.690234591f, 0.690303961f, 0.690373324f, 0.690442681f,
0.690512032f, 0.690581376f, 0.690650714f, 0.690720046f, 0.690789371f,
0.690858690f, 0.690928003f, 0.690997309f, 0.691066609f, 0.691135902f,
0.691205190f, 0.691274470f, 0.691343745f, 0.691413013f, 0.691482275f,
0.691551530f, 0.691620779f, 0.691690022f, 0.691759258f, 0.691828488f,
0.691897712f, 0.691966929f, 0.692036140f, 0.692105345f, 0.692174543f,
0.692243735f, 0.692312920f, 0.692382099f, 0.692451272f, 0.692520438f,
0.692589598f, 0.692658752f, 0.692727899f, 0.692797040f, 0.692866175f,
0.692935303f, 0.693004425f, 0.693073540f, 0.693142649f, 0.693211752f,
0.693280848f, 0.693349938f, 0.693419022f, 0.693488099f, 0.693557170f,
0.693626234f, 0.693695292f, 0.693764344f, 0.693833389f, 0.693902428f,
0.693971461f, 0.694040487f, 0.694109507f, 0.694178520f, 0.694247527f,
0.694316528f, 0.694385522f, 0.694454510f, 0.694523492f, 0.694592467f,
0.694661436f, 0.694730398f, 0.694799354f, 0.694868304f, 0.694937247f,
0.695006184f, 0.695075114f, 0.695144038f, 0.695212956f, 0.695281867f,
0.695350772f, 0.695419670f, 0.695488562f, 0.695557448f, 0.695626327f,
0.695695200f, 0.695764067f, 0.695832927f, 0.695901781f, 0.695970628f,
0.696039469f, 0.696108303f, 0.696177131f, 0.696245953f, 0.696314769f,
0.696383577f, 0.696452380f, 0.696521176f, 0.696589966f, 0.696658749f,
0.696727526f, 0.696796297f, 0.696865061f, 0.696933818f, 0.697002570f,
0.697071315f, 0.697140053f, 0.697208785f, 0.697277511f, 0.697346230f,
0.697414943f, 0.697483649f, 0.697552349f, 0.697621043f, 0.697689730f,
0.697758411f, 0.697827085f, 0.697895753f, 0.697964415f, 0.698033070f,
0.698101719f, 0.698170361f, 0.698238997f, 0.698307626f, 0.698376249f,
0.698444866f, 0.698513476f, 0.698582080f, 0.698650677f, 0.698719268f,
0.698787853f, 0.698856431f, 0.698925003f, 0.698993568f, 0.699062127f,
0.699130679f, 0.699199225f, 0.699267765f, 0.699336298f, 0.699404824f,
0.699473345f, 0.699541858f, 0.699610366f, 0.699678867f, 0.699747361f,
0.699815849f, 0.699884331f, 0.699952806f, 0.700021275f, 0.700089738f,
0.700158194f, 0.700226643f, 0.700295086f, 0.700363523f, 0.700431953f,
0.700500377f, 0.700568794f, 0.700637205f, 0.700705609f, 0.700774007f,
0.700842399f, 0.700910784f, 0.700979163f, 0.701047535f, 0.701115901f,
0.701184260f, 0.701252613f, 0.701320959f, 0.701389299f, 0.701457633f,
0.701525960f, 0.701594281f, 0.701662595f, 0.701730902f, 0.701799204f,
0.701867499f, 0.701935787f, 0.702004069f, 0.702072345f, 0.702140614f,
0.702208876f, 0.702277132f, 0.702345382f, 0.702413625f, 0.702481862f,
0.702550092f, 0.702618316f, 0.702686534f, 0.702754744f, 0.702822949f,
0.702891147f, 0.702959339f, 0.703027524f, 0.703095702f, 0.703163874f,
0.703232040f, 0.703300199f, 0.703368352f, 0.703436498f, 0.703504638f,
0.703572772f, 0.703640899f, 0.703709019f, 0.703777133f, 0.703845241f,
0.703913342f, 0.703981436f, 0.704049524f, 0.704117606f, 0.704185681f,
0.704253750f, 0.704321812f, 0.704389868f, 0.704457917f, 0.704525960f,
0.704593996f, 0.704662026f, 0.704730049f, 0.704798066f, 0.704866076f,
0.704934080f, 0.705002078f, 0.705070069f, 0.705138053f, 0.705206031f,
0.705274003f, 0.705341968f, 0.705409926f, 0.705477878f, 0.705545824f,
0.705613763f, 0.705681696f, 0.705749622f, 0.705817541f, 0.705885455f,
0.705953361f, 0.706021261f, 0.706089155f, 0.706157042f, 0.706224923f,
0.706292797f, 0.706360665f, 0.706428526f, 0.706496381f, 0.706564229f,
0.706632071f, 0.706699906f, 0.706767735f, 0.706835557f, 0.706903373f,
0.706971182f, 0.707038985f, 0.707106781f, 0.707174571f, 0.707242354f,
0.707310131f, 0.707377901f, 0.707445665f, 0.707513422f, 0.707581173f,
0.707648917f, 0.707716655f, 0.707784386f, 0.707852111f, 0.707919829f,
0.707987541f, 0.708055246f, 0.708122945f, 0.708190637f, 0.708258323f,
0.708326002f, 0.708393675f, 0.708461341f, 0.708529000f, 0.708596653f,
0.708664300f, 0.708731940f, 0.708799574f, 0.708867201f, 0.708934821f,
0.709002435f, 0.709070043f, 0.709137644f, 0.709205238f, 0.709272826f,
0.709340408f, 0.709407983f, 0.709475551f, 0.709543113f, 0.709610668f,
0.709678217f, 0.709745760f, 0.709813295f, 0.709880825f, 0.709948347f,
0.710015864f, 0.710083373f, 0.710150877f, 0.710218373f, 0.710285863f,
0.710353347f, 0.710420824f, 0.710488294f, 0.710555758f, 0.710623216f,
0.710690667f, 0.710758111f, 0.710825549f, 0.710892980f, 0.710960405f,
0.711027823f, 0.711095235f, 0.711162640f, 0.711230039f, 0.711297431f,
0.711364817f, 0.711432196f, 0.711499568f, 0.711566934f, 0.711634294f,
0.711701646f, 0.711768993f, 0.711836333f, 0.711903666f, 0.711970993f,
0.712038313f, 0.712105626f, 0.712172933f, 0.712240234f, 0.712307528f,
0.712374815f, 0.712442096f, 0.712509371f, 0.712576638f, 0.712643900f,
0.712711154f, 0.712778402f, 0.712845644f, 0.712912879f, 0.712980107f,
0.713047329f, 0.713114545f, 0.713181754f, 0.713248956f, 0.713316152f,
0.713383341f, 0.713450523f, 0.713517699f, 0.713584869f, 0.713652032f,
0.713719188f, 0.713786338f, 0.713853481f, 0.713920618f, 0.713987748f,
0.714054871f, 0.714121988f, 0.714189099f, 0.714256203f, 0.714323300f,
0.714390391f, 0.714457475f, 0.714524552f, 0.714591623f, 0.714658688f,
0.714725746f, 0.714792797f, 0.714859842f, 0.714926880f, 0.714993912f,
0.715060937f, 0.715127955f, 0.715194967f, 0.715261972f, 0.715328971f,
0.715395963f, 0.715462949f, 0.715529928f, 0.715596900f, 0.715663866f,
0.715730825f, 0.715797778f, 0.715864724f, 0.715931664f, 0.715998597f,
0.716065523f, 0.716132443f, 0.716199356f, 0.716266263f, 0.716333163f,
0.716400056f, 0.716466943f, 0.716533823f, 0.716600697f, 0.716667564f,
0.716734425f, 0.716801279f, 0.716868126f, 0.716934967f, 0.717001801f,
0.717068628f, 0.717135449f, 0.717202264f, 0.717269072f, 0.717335873f,
0.717402667f, 0.717469455f, 0.717536237f, 0.717603012f, 0.717669780f,
0.717736542f, 0.717803297f, 0.717870045f, 0.717936787f, 0.718003522f,
0.718070251f, 0.718136973f, 0.718203688f, 0.718270397f, 0.718337099f,
0.718403795f, 0.718470484f, 0.718537166f, 0.718603842f, 0.718670512f,
0.718737174f, 0.718803830f, 0.718870480f, 0.718937122f, 0.719003759f,
0.719070388f, 0.719137011f, 0.719203627f, 0.719270237f, 0.719336840f,
0.719403437f, 0.719470027f, 0.719536610f, 0.719603187f, 0.719669757f,
0.719736320f, 0.719802877f, 0.719869427f, 0.719935971f, 0.720002508f,
0.720069038f, 0.720135562f, 0.720202079f, 0.720268590f, 0.720335094f,
0.720401591f, 0.720468082f, 0.720534566f, 0.720601043f, 0.720667514f,
0.720733978f, 0.720800435f, 0.720866886f, 0.720933331f, 0.720999768f,
0.721066199f, 0.721132624f, 0.721199041f, 0.721265453f, 0.721331857f,
0.721398255f, 0.721464646f, 0.721531031f, 0.721597409f, 0.721663780f,
0.721730145f, 0.721796503f, 0.721862854f, 0.721929199f, 0.721995537f,
0.722061869f, 0.722128194f, 0.722194512f, 0.722260824f, 0.722327129f,
0.722393427f, 0.722459719f, 0.722526004f, 0.722592282f, 0.722658554f,
0.722724819f, 0.722791078f, 0.722857330f, 0.722923575f, 0.722989813f,
0.723056045f, 0.723122271f, 0.723188489f, 0.723254701f, 0.723320907f,
0.723387105f, 0.723453297f, 0.723519483f, 0.723585661f, 0.723651834f,
0.723717999f, 0.723784158f, 0.723850310f, 0.723916455f, 0.723982594f,
0.724048726f, 0.724114852f, 0.724180971f, 0.724247083f, 0.724313188f,
0.724379287f, 0.724445380f, 0.724511465f, 0.724577544f, 0.724643616f,
0.724709682f, 0.724775741f, 0.724841793f, 0.724907839f, 0.724973878f,
0.725039910f, 0.725105936f, 0.725171954f, 0.725237967f, 0.725303972f,
0.725369971f, 0.725435964f, 0.725501949f, 0.725567928f, 0.725633900f,
0.725699866f, 0.725765825f, 0.725831777f, 0.725897723f, 0.725963662f,
0.726029594f, 0.726095520f, 0.726161438f, 0.726227351f, 0.726293256f,
0.726359155f, 0.726425047f, 0.726490933f, 0.726556812f, 0.726622684f,
0.726688549f, 0.726754408f, 0.726820260f, 0.726886106f, 0.726951944f,
0.727017776f, 0.727083602f, 0.727149421f, 0.727215233f, 0.727281038f,
0.727346837f, 0.727412629f, 0.727478414f, 0.727544192f, 0.727609964f,
0.727675730f, 0.727741488f, 0.727807240f, 0.727872985f, 0.727938724f,
0.728004455f, 0.728070180f, 0.728135899f, 0.728201611f, 0.728267316f,
0.728333014f, 0.728398706f, 0.728464390f, 0.728530069f, 0.728595740f,
0.728661405f, 0.728727063f, 0.728792715f, 0.728858359f, 0.728923997f,
0.728989629f, 0.729055253f, 0.729120871f, 0.729186483f, 0.729252087f,
0.729317685f, 0.729383276f, 0.729448860f, 0.729514438f, 0.729580009f,
0.729645573f, 0.729711131f, 0.729776682f, 0.729842226f, 0.729907764f,
0.729973294f, 0.730038818f, 0.730104336f, 0.730169846f, 0.730235350f,
0.730300848f, 0.730366338f, 0.730431822f, 0.730497299f, 0.730562769f,
0.730628233f, 0.730693690f, 0.730759140f, 0.730824583f, 0.730890020f,
0.730955450f, 0.731020874f, 0.731086290f, 0.731151700f, 0.731217103f,
0.731282500f, 0.731347890f, 0.731413273f, 0.731478649f, 0.731544018f,
0.731609381f, 0.731674737f, 0.731740087f, 0.731805429f, 0.731870765f,
0.731936095f, 0.732001417f, 0.732066733f, 0.732132042f, 0.732197344f,
0.732262640f, 0.732327928f, 0.732393211f, 0.732458486f, 0.732523755f,
0.732589017f, 0.732654272f, 0.732719520f, 0.732784762f, 0.732849997f,
0.732915225f, 0.732980446f, 0.733045661f, 0.733110869f, 0.733176071f,
0.733241265f, 0.733306453f, 0.733371634f, 0.733436808f, 0.733501976f,
0.733567137f, 0.733632291f, 0.733697438f, 0.733762579f, 0.733827713f,
0.733892840f, 0.733957960f, 0.734023074f, 0.734088181f, 0.734153281f,
0.734218374f, 0.734283461f, 0.734348541f, 0.734413614f, 0.734478680f,
0.734543740f, 0.734608793f, 0.734673839f, 0.734738878f, 0.734803911f,
0.734868937f, 0.734933956f, 0.734998968f, 0.735063974f, 0.735128972f,
0.735193965f, 0.735258950f, 0.735323928f, 0.735388900f, 0.735453865f,
0.735518824f, 0.735583775f, 0.735648720f, 0.735713658f, 0.735778589f,
0.735843514f, 0.735908431f, 0.735973342f, 0.736038247f, 0.736103144f,
0.736168035f, 0.736232918f, 0.736297796f, 0.736362666f, 0.736427530f,
0.736492386f, 0.736557236f, 0.736622080f, 0.736686916f, 0.736751746f,
0.736816569f, 0.736881385f, 0.736946194f, 0.737010997f, 0.737075793f,
0.737140582f, 0.737205364f, 0.737270140f, 0.737334909f, 0.737399671f,
0.737464426f, 0.737529174f, 0.737593916f, 0.737658651f, 0.737723379f,
0.737788100f, 0.737852815f, 0.737917523f, 0.737982223f, 0.738046918f,
0.738111605f, 0.738176286f, 0.738240960f, 0.738305627f, 0.738370287f,
0.738434940f, 0.738499587f, 0.738564227f, 0.738628860f, 0.738693486f,
0.738758106f, 0.738822719f, 0.738887324f, 0.738951924f, 0.739016516f,
0.739081102f, 0.739145680f, 0.739210252f, 0.739274817f, 0.739339376f,
0.739403927f, 0.739468472f, 0.739533010f, 0.739597541f, 0.739662066f,
0.739726583f, 0.739791094f, 0.739855598f, 0.739920095f, 0.739984586f,
0.740049069f, 0.740113546f, 0.740178016f, 0.740242479f, 0.740306936f,
0.740371385f, 0.740435828f, 0.740500264f, 0.740564693f, 0.740629116f,
0.740693531f, 0.740757940f, 0.740822342f, 0.740886737f, 0.740951125f,
0.741015507f, 0.741079882f, 0.741144249f, 0.741208610f, 0.741272965f,
0.741337312f, 0.741401653f, 0.741465987f, 0.741530314f, 0.741594634f,
0.741658947f, 0.741723254f, 0.741787553f, 0.741851846f, 0.741916132f,
0.741980412f, 0.742044684f, 0.742108950f, 0.742173209f, 0.742237461f,
0.742301706f, 0.742365944f, 0.742430176f, 0.742494400f, 0.742558618f,
0.742622829f, 0.742687033f, 0.742751231f, 0.742815421f, 0.742879605f,
0.742943782f, 0.743007952f, 0.743072115f, 0.743136272f, 0.743200421f,
0.743264564f, 0.743328700f, 0.743392829f, 0.743456951f, 0.743521067f,
0.743585175f, 0.743649277f, 0.743713372f, 0.743777460f, 0.743841541f,
0.743905616f, 0.743969683f, 0.744033744f, 0.744097798f, 0.744161845f,
0.744225885f, 0.744289919f, 0.744353945f, 0.744417965f, 0.744481978f,
0.744545984f, 0.744609983f, 0.744673975f, 0.744737961f, 0.744801939f,
0.744865911f, 0.744929876f, 0.744993834f, 0.745057785f, 0.745121730f,
0.745185667f, 0.745249598f, 0.745313522f, 0.745377439f, 0.745441349f,
0.745505252f, 0.745569149f, 0.745633038f, 0.745696921f, 0.745760797f,
0.745824666f, 0.745888528f, 0.745952383f, 0.746016232f, 0.746080074f,
0.746143908f, 0.746207736f, 0.746271557f, 0.746335371f, 0.746399179f,
0.746462979f, 0.746526773f, 0.746590559f, 0.746654339f, 0.746718112f,
0.746781878f, 0.746845638f, 0.746909390f, 0.746973136f, 0.747036874f,
0.747100606f, 0.747164331f, 0.747228049f, 0.747291760f, 0.747355465f,
0.747419162f, 0.747482853f, 0.747546536f, 0.747610213f, 0.747673883f,
0.747737546f, 0.747801202f, 0.747864852f, 0.747928494f, 0.747992130f,
0.748055759f, 0.748119380f, 0.748182995f, 0.748246604f, 0.748310205f,
0.748373799f, 0.748437387f, 0.748500967f, 0.748564541f, 0.748628108f,
0.748691668f, 0.748755221f, 0.748818767f, 0.748882306f, 0.748945839f,
0.749009364f, 0.749072883f, 0.749136395f, 0.749199899f, 0.749263397f,
0.749326888f, 0.749390373f, 0.749453850f, 0.749517320f, 0.749580784f,
0.749644241f, 0.749707690f, 0.749771133f, 0.749834569f, 0.749897998f,
0.749961421f, 0.750024836f, 0.750088244f, 0.750151646f, 0.750215040f,
0.750278428f, 0.750341809f, 0.750405183f, 0.750468550f, 0.750531910f,
0.750595263f, 0.750658610f, 0.750721949f, 0.750785282f, 0.750848607f,
0.750911926f, 0.750975238f, 0.751038543f, 0.751101841f, 0.751165132f,
0.751228416f, 0.751291693f, 0.751354964f, 0.751418227f, 0.751481484f,
0.751544734f, 0.751607976f, 0.751671212f, 0.751734441f, 0.751797663f,
0.751860878f, 0.751924087f, 0.751987288f, 0.752050482f, 0.752113670f,
0.752176850f, 0.752240024f, 0.752303191f, 0.752366351f, 0.752429504f,
0.752492650f, 0.752555789f, 0.752618921f, 0.752682046f, 0.752745164f,
0.752808276f, 0.752871380f, 0.752934478f, 0.752997569f, 0.753060652f,
0.753123729f, 0.753186799f, 0.753249862f, 0.753312918f, 0.753375967f,
0.753439009f, 0.753502045f, 0.753565073f, 0.753628094f, 0.753691109f,
0.753754116f, 0.753817117f, 0.753880111f, 0.753943098f, 0.754006077f,
0.754069050f, 0.754132016f, 0.754194975f, 0.754257927f, 0.754320873f,
0.754383811f, 0.754446742f, 0.754509667f, 0.754572584f, 0.754635495f,
0.754698398f, 0.754761295f, 0.754824184f, 0.754887067f, 0.754949943f,
0.755012812f, 0.755075674f, 0.755138529f, 0.755201377f, 0.755264218f,
0.755327052f, 0.755389879f, 0.755452700f, 0.755515513f, 0.755578319f,
0.755641119f, 0.755703911f, 0.755766697f, 0.755829476f, 0.755892247f,
0.755955012f, 0.756017770f, 0.756080521f, 0.756143264f, 0.756206001f,
0.756268731f, 0.756331454f, 0.756394170f, 0.756456880f, 0.756519582f,
0.756582277f, 0.756644965f, 0.756707647f, 0.756770321f, 0.756832988f,
0.756895649f, 0.756958302f, 0.757020949f, 0.757083588f, 0.757146221f,
0.757208847f, 0.757271465f, 0.757334077f, 0.757396682f, 0.757459279f,
0.757521870f, 0.757584454f, 0.757647031f, 0.757709601f, 0.757772164f,
0.757834720f, 0.757897269f, 0.757959811f, 0.758022346f, 0.758084874f,
0.758147396f, 0.758209910f, 0.758272417f, 0.758334917f, 0.758397411f,
0.758459897f, 0.758522376f, 0.758584849f, 0.758647314f, 0.758709773f,
0.758772224f, 0.758834669f, 0.758897106f, 0.758959537f, 0.759021960f,
0.759084377f, 0.759146786f, 0.759209189f, 0.759271585f, 0.759333973f,
0.759396355f, 0.759458730f, 0.759521097f, 0.759583458f, 0.759645812f,
0.759708159f, 0.759770499f, 0.759832831f, 0.759895157f, 0.759957476f,
0.760019788f, 0.760082093f, 0.760144391f, 0.760206682f, 0.760268966f,
0.760331243f, 0.760393512f, 0.760455775f, 0.760518031f, 0.760580280f,
0.760642522f, 0.760704757f, 0.760766985f, 0.760829206f, 0.760891420f,
0.760953627f, 0.761015827f, 0.761078020f, 0.761140206f, 0.761202385f,
0.761264558f, 0.761326723f, 0.761388881f, 0.761451032f, 0.761513176f,
0.761575313f, 0.761637443f, 0.761699566f, 0.761761682f, 0.761823791f,
0.761885893f, 0.761947988f, 0.762010076f, 0.762072157f, 0.762134231f,
0.762196298f, 0.762258358f, 0.762320411f, 0.762382457f, 0.762444496f,
0.762506528f, 0.762568553f, 0.762630571f, 0.762692582f, 0.762754586f,
0.762816583f, 0.762878573f, 0.762940556f, 0.763002532f, 0.763064501f,
0.763126462f, 0.763188417f, 0.763250365f, 0.763312306f, 0.763374240f,
0.763436167f, 0.763498086f, 0.763559999f, 0.763621905f, 0.763683804f,
0.763745695f, 0.763807580f, 0.763869458f, 0.763931328f, 0.763993192f,
0.764055048f, 0.764116898f, 0.764178741f, 0.764240576f, 0.764302405f,
0.764364226f, 0.764426040f, 0.764487848f, 0.764549648f, 0.764611442f,
0.764673228f, 0.764735007f, 0.764796780f, 0.764858545f, 0.764920303f,
0.764982054f, 0.765043798f, 0.765105536f, 0.765167266f, 0.765228989f,
0.765290705f, 0.765352414f, 0.765414116f, 0.765475811f, 0.765537498f,
0.765599179f, 0.765660853f, 0.765722520f, 0.765784180f, 0.765845832f,
0.765907478f, 0.765969117f, 0.766030748f, 0.766092373f, 0.766153990f,
0.766215601f, 0.766277204f, 0.766338800f, 0.766400390f, 0.766461972f,
0.766523547f, 0.766585115f, 0.766646677f, 0.766708231f, 0.766769778f,
0.766831318f, 0.766892851f, 0.766954377f, 0.767015895f, 0.767077407f,
0.767138912f, 0.767200410f, 0.767261900f, 0.767323384f, 0.767384860f,
0.767446330f, 0.767507792f, 0.767569248f, 0.767630696f, 0.767692137f,
0.767753571f, 0.767814999f, 0.767876419f, 0.767937832f, 0.767999238f,
0.768060637f, 0.768122029f, 0.768183413f, 0.768244791f, 0.768306162f,
0.768367525f, 0.768428882f, 0.768490231f, 0.768551574f, 0.768612909f,
0.768674237f, 0.768735559f, 0.768796873f, 0.768858180f, 0.768919480f,
0.768980773f, 0.769042059f, 0.769103338f, 0.769164609f, 0.769225874f,
0.769287132f, 0.769348382f, 0.769409626f, 0.769470862f, 0.769532091f,
0.769593314f, 0.769654529f, 0.769715737f, 0.769776938f, 0.769838132f,
0.769899319f, 0.769960499f, 0.770021671f, 0.770082837f, 0.770143996f,
0.770205147f, 0.770266291f, 0.770327429f, 0.770388559f, 0.770449682f,
0.770510798f, 0.770571907f, 0.770633009f, 0.770694104f, 0.770755192f,
0.770816272f, 0.770877346f, 0.770938413f, 0.770999472f, 0.771060524f,
0.771121569f, 0.771182608f, 0.771243639f, 0.771304663f, 0.771365680f,
0.771426689f, 0.771487692f, 0.771548688f, 0.771609676f, 0.771670658f,
0.771731632f, 0.771792599f, 0.771853559f, 0.771914512f, 0.771975458f,
0.772036397f, 0.772097329f, 0.772158254f, 0.772219171f, 0.772280082f,
0.772340985f, 0.772401881f, 0.772462770f, 0.772523652f, 0.772584527f,
0.772645395f, 0.772706256f, 0.772767110f, 0.772827956f, 0.772888796f,
0.772949628f, 0.773010453f, 0.773071272f, 0.773132083f, 0.773192886f,
0.773253683f, 0.773314473f, 0.773375256f, 0.773436031f, 0.773496799f,
0.773557561f, 0.773618315f, 0.773679062f, 0.773739802f, 0.773800535f,
0.773861261f, 0.773921979f, 0.773982691f, 0.774043395f, 0.774104092f,
0.774164782f, 0.774225465f, 0.774286141f, 0.774346810f, 0.774407472f,
0.774468126f, 0.774528774f, 0.774589414f, 0.774650047f, 0.774710673f,
0.774771292f, 0.774831904f, 0.774892509f, 0.774953107f, 0.775013697f,
0.775074280f, 0.775134857f, 0.775195426f, 0.775255988f, 0.775316543f,
0.775377090f, 0.775437631f, 0.775498164f, 0.775558691f, 0.775619210f,
0.775679722f, 0.775740227f, 0.775800725f, 0.775861215f, 0.775921699f,
0.775982175f, 0.776042645f, 0.776103107f, 0.776163562f, 0.776224010f,
0.776284451f, 0.776344884f, 0.776405311f, 0.776465730f, 0.776526142f,
0.776586547f, 0.776646945f, 0.776707336f, 0.776767720f, 0.776828096f,
0.776888466f, 0.776948828f, 0.777009183f, 0.777069531f, 0.777129872f,
0.777190205f, 0.777250532f, 0.777310851f, 0.777371164f, 0.777431469f,
0.777491767f, 0.777552057f, 0.777612341f, 0.777672618f, 0.777732887f,
0.777793149f, 0.777853404f, 0.777913652f, 0.777973893f, 0.778034126f,
0.778094353f, 0.778154572f, 0.778214784f, 0.778274989f, 0.778335187f,
0.778395378f, 0.778455561f, 0.778515738f, 0.778575907f, 0.778636069f,
0.778696224f, 0.778756372f, 0.778816512f, 0.778876646f, 0.778936772f,
0.778996891f, 0.779057003f, 0.779117108f, 0.779177206f, 0.779237296f,
0.779297379f, 0.779357456f, 0.779417524f, 0.779477586f, 0.779537641f,
0.779597688f, 0.779657729f, 0.779717762f, 0.779777788f, 0.779837807f,
0.779897818f, 0.779957823f, 0.780017820f, 0.780077810f, 0.780137793f,
0.780197769f, 0.780257738f, 0.780317699f, 0.780377653f, 0.780437601f,
0.780497541f, 0.780557473f, 0.780617399f, 0.780677317f, 0.780737229f,
0.780797133f, 0.780857030f, 0.780916919f, 0.780976802f, 0.781036677f,
0.781096545f, 0.781156406f, 0.781216260f, 0.781276107f, 0.781335946f,
0.781395778f, 0.781455604f, 0.781515421f, 0.781575232f, 0.781635036f,
0.781694832f, 0.781754621f, 0.781814403f, 0.781874178f, 0.781933946f,
0.781993706f, 0.782053459f, 0.782113205f, 0.782172944f, 0.782232676f,
0.782292400f, 0.782352118f, 0.782411828f, 0.782471531f, 0.782531226f,
0.782590915f, 0.782650596f, 0.782710270f, 0.782769937f, 0.782829597f,
0.782889250f, 0.782948895f, 0.783008533f, 0.783068164f, 0.783127788f,
0.783187404f, 0.783247014f, 0.783306616f, 0.783366211f, 0.783425799f,
0.783485379f, 0.783544952f, 0.783604519f, 0.783664078f, 0.783723629f,
0.783783174f, 0.783842711f, 0.783902241f, 0.783961764f, 0.784021280f,
0.784080789f, 0.784140290f, 0.784199784f, 0.784259271f, 0.784318751f,
0.784378223f, 0.784437688f, 0.784497146f, 0.784556597f, 0.784616041f,
0.784675477f, 0.784734906f, 0.784794328f, 0.784853743f, 0.784913151f,
0.784972551f, 0.785031944f, 0.785091330f, 0.785150709f, 0.785210080f,
0.785269445f, 0.785328802f, 0.785388152f, 0.785447494f, 0.785506830f,
0.785566158f, 0.785625479f, 0.785684792f, 0.785744099f, 0.785803398f,
0.785862690f, 0.785921975f, 0.785981253f, 0.786040523f, 0.786099786f,
0.786159042f, 0.786218291f, 0.786277532f, 0.786336767f, 0.786395994f,
0.786455214f, 0.786514426f, 0.786573632f, 0.786632830f, 0.786692021f,
0.786751204f, 0.786810381f, 0.786869550f, 0.786928712f, 0.786987867f,
0.787047014f, 0.787106154f, 0.787165287f, 0.787224413f, 0.787283532f,
0.787342643f, 0.787401747f, 0.787460844f, 0.787519933f, 0.787579016f,
0.787638091f, 0.787697159f, 0.787756220f, 0.787815273f, 0.787874319f,
0.787933358f, 0.787992390f, 0.788051414f, 0.788110431f, 0.788169441f,
0.788228444f, 0.788287439f, 0.788346428f, 0.788405409f, 0.788464382f,
0.788523349f, 0.788582308f, 0.788641260f, 0.788700205f, 0.788759142f,
0.788818072f, 0.788876995f, 0.788935911f, 0.788994820f, 0.789053721f,
0.789112615f, 0.789171502f, 0.789230381f, 0.789289253f, 0.789348118f,
0.789406976f, 0.789465826f, 0.789524669f, 0.789583505f, 0.789642334f,
0.789701155f, 0.789759970f, 0.789818776f, 0.789877576f, 0.789936368f,
0.789995154f, 0.790053931f, 0.790112702f, 0.790171465f, 0.790230221f,
0.790288970f, 0.790347712f, 0.790406446f, 0.790465173f, 0.790523893f,
0.790582605f, 0.790641310f, 0.790700008f, 0.790758699f, 0.790817382f,
0.790876059f, 0.790934727f, 0.790993389f, 0.791052043f, 0.791110690f,
0.791169330f, 0.791227963f, 0.791286588f, 0.791345206f, 0.791403817f,
0.791462420f, 0.791521016f, 0.791579605f, 0.791638187f, 0.791696761f,
0.791755328f, 0.791813888f, 0.791872440f, 0.791930985f, 0.791989523f,
0.792048054f, 0.792106577f, 0.792165093f, 0.792223602f, 0.792282104f,
0.792340598f, 0.792399085f, 0.792457565f, 0.792516037f, 0.792574502f,
0.792632960f, 0.792691410f, 0.792749854f, 0.792808290f, 0.792866718f,
0.792925140f, 0.792983554f, 0.793041960f, 0.793100360f, 0.793158752f,
0.793217137f, 0.793275515f, 0.793333885f, 0.793392248f, 0.793450604f,
0.793508952f, 0.793567294f, 0.793625627f, 0.793683954f, 0.793742273f,
0.793800585f, 0.793858890f, 0.793917187f, 0.793975478f, 0.794033760f,
0.794092036f, 0.794150304f, 0.794208565f, 0.794266819f, 0.794325065f,
0.794383304f, 0.794441536f, 0.794499760f, 0.794557977f, 0.794616187f,
0.794674389f, 0.794732585f, 0.794790772f, 0.794848953f, 0.794907126f,
0.794965292f, 0.795023451f, 0.795081602f, 0.795139746f, 0.795197883f,
0.795256012f, 0.795314135f, 0.795372249f, 0.795430357f, 0.795488457f,
0.795546550f, 0.795604636f, 0.795662714f, 0.795720785f, 0.795778848f,
0.795836905f, 0.795894954f, 0.795952995f, 0.796011030f, 0.796069057f,
0.796127076f, 0.796185089f, 0.796243094f, 0.796301092f, 0.796359082f,
0.796417065f, 0.796475041f, 0.796533009f, 0.796590971f, 0.796648924f,
0.796706871f, 0.796764810f, 0.796822742f, 0.796880667f, 0.796938584f,
0.796996494f, 0.797054396f, 0.797112292f, 0.797170179f, 0.797228060f,
0.797285933f, 0.797343799f, 0.797401658f, 0.797459509f, 0.797517353f,
0.797575190f, 0.797633019f, 0.797690841f, 0.797748656f, 0.797806463f,
0.797864263f, 0.797922055f, 0.797979841f, 0.798037619f, 0.798095389f,
0.798153153f, 0.798210908f, 0.798268657f, 0.798326398f, 0.798384132f,
0.798441859f, 0.798499578f, 0.798557290f, 0.798614995f, 0.798672692f,
0.798730382f, 0.798788064f, 0.798845740f, 0.798903407f, 0.798961068f,
0.799018721f, 0.799076367f, 0.799134005f, 0.799191637f, 0.799249260f,
0.799306877f, 0.799364486f, 0.799422088f, 0.799479682f, 0.799537269f,
0.799594849f, 0.799652421f, 0.799709986f, 0.799767544f, 0.799825094f,
0.799882637f, 0.799940173f, 0.799997701f, 0.800055222f, 0.800112735f,
0.800170242f, 0.800227740f, 0.800285232f, 0.800342716f, 0.800400193f,
0.800457662f, 0.800515124f, 0.800572579f, 0.800630026f, 0.800687466f,
0.800744899f, 0.800802324f, 0.800859742f, 0.800917153f, 0.800974556f,
0.801031952f, 0.801089340f, 0.801146721f, 0.801204095f, 0.801261461f,
0.801318820f, 0.801376172f, 0.801433516f, 0.801490853f, 0.801548182f,
0.801605505f, 0.801662819f, 0.801720127f, 0.801777427f, 0.801834719f,
0.801892005f, 0.801949283f, 0.802006553f, 0.802063816f, 0.802121072f,
0.802178321f, 0.802235562f, 0.802292796f, 0.802350022f, 0.802407241f,
0.802464452f, 0.802521657f, 0.802578853f, 0.802636043f, 0.802693225f,
0.802750400f, 0.802807567f, 0.802864727f, 0.802921879f, 0.802979025f,
0.803036162f, 0.803093293f, 0.803150416f, 0.803207531f, 0.803264640f,
0.803321741f, 0.803378834f, 0.803435920f, 0.803492999f, 0.803550070f,
0.803607134f, 0.803664191f, 0.803721240f, 0.803778282f, 0.803835316f,
0.803892343f, 0.803949363f, 0.804006375f, 0.804063380f, 0.804120377f,
0.804177367f, 0.804234350f, 0.804291325f, 0.804348293f, 0.804405254f,
0.804462207f, 0.804519153f, 0.804576091f, 0.804633022f, 0.804689945f,
0.804746861f, 0.804803770f, 0.804860672f, 0.804917565f, 0.804974452f,
0.805031331f, 0.805088203f, 0.805145067f, 0.805201924f, 0.805258774f,
0.805315616f, 0.805372451f, 0.805429278f, 0.805486098f, 0.805542910f,
0.805599715f, 0.805656513f, 0.805713303f, 0.805770086f, 0.805826862f,
0.805883630f, 0.805940391f, 0.805997144f, 0.806053890f, 0.806110628f,
0.806167359f, 0.806224083f, 0.806280799f, 0.806337508f, 0.806394209f,
0.806450903f, 0.806507590f, 0.806564269f, 0.806620941f, 0.806677605f,
0.806734262f, 0.806790911f, 0.806847554f, 0.806904188f, 0.806960815f,
0.807017435f, 0.807074048f, 0.807130653f, 0.807187250f, 0.807243840f,
0.807300423f, 0.807356999f, 0.807413566f, 0.807470127f, 0.807526680f,
0.807583226f, 0.807639764f, 0.807696295f, 0.807752818f, 0.807809334f,
0.807865842f, 0.807922343f, 0.807978837f, 0.808035323f, 0.808091802f,
0.808148274f, 0.808204737f, 0.808261194f, 0.808317643f, 0.808374085f,
0.808430519f, 0.808486946f, 0.808543365f, 0.808599777f, 0.808656182f,
0.808712579f, 0.808768968f, 0.808825350f, 0.808881725f, 0.808938093f,
0.808994452f, 0.809050805f, 0.809107150f, 0.809163488f, 0.809219818f,
0.809276140f, 0.809332456f, 0.809388764f, 0.809445064f, 0.809501357f,
0.809557642f, 0.809613920f, 0.809670191f, 0.809726454f, 0.809782710f,
0.809838958f, 0.809895199f, 0.809951433f, 0.810007659f, 0.810063877f,
0.810120088f, 0.810176292f, 0.810232488f, 0.810288677f, 0.810344858f,
0.810401032f, 0.810457198f, 0.810513357f, 0.810569509f, 0.810625653f,
0.810681789f, 0.810737918f, 0.810794040f, 0.810850154f, 0.810906261f,
0.810962360f, 0.811018452f, 0.811074537f, 0.811130614f, 0.811186683f,
0.811242745f, 0.811298800f, 0.811354847f, 0.811410887f, 0.811466919f,
0.811522944f, 0.811578961f, 0.811634971f, 0.811690973f, 0.811746968f,
0.811802956f, 0.811858936f, 0.811914908f, 0.811970873f, 0.812026831f,
0.812082781f, 0.812138724f, 0.812194659f, 0.812250587f, 0.812306507f,
0.812362420f, 0.812418325f, 0.812474223f, 0.812530113f, 0.812585996f,
0.812641872f, 0.812697740f, 0.812753600f, 0.812809453f, 0.812865299f,
0.812921137f, 0.812976968f, 0.813032791f, 0.813088607f, 0.813144415f,
0.813200216f, 0.813256009f, 0.813311795f, 0.813367573f, 0.813423344f,
0.813479107f, 0.813534863f, 0.813590612f, 0.813646353f, 0.813702086f,
0.813757812f, 0.813813530f, 0.813869242f, 0.813924945f, 0.813980641f,
0.814036330f, 0.814092011f, 0.814147684f, 0.814203351f, 0.814259009f,
0.814314660f, 0.814370304f, 0.814425940f, 0.814481569f, 0.814537190f,
0.814592804f, 0.814648410f, 0.814704009f, 0.814759600f, 0.814815184f,
0.814870760f, 0.814926329f, 0.814981890f, 0.815037444f, 0.815092991f,
0.815148529f, 0.815204061f, 0.815259585f, 0.815315101f, 0.815370610f,
0.815426111f, 0.815481605f, 0.815537091f, 0.815592570f, 0.815648042f,
0.815703506f, 0.815758962f, 0.815814411f, 0.815869852f, 0.815925286f,
0.815980712f, 0.816036131f, 0.816091543f, 0.816146947f, 0.816202343f,
0.816257732f, 0.816313113f, 0.816368487f, 0.816423854f, 0.816479212f,
0.816534564f, 0.816589908f, 0.816645244f, 0.816700573f, 0.816755894f,
0.816811208f, 0.816866514f, 0.816921813f, 0.816977104f, 0.817032388f,
0.817087665f, 0.817142933f, 0.817198195f, 0.817253448f, 0.817308695f,
0.817363933f, 0.817419165f, 0.817474388f, 0.817529604f, 0.817584813f,
0.817640014f, 0.817695208f, 0.817750394f, 0.817805573f, 0.817860744f,
0.817915907f, 0.817971063f, 0.818026212f, 0.818081353f, 0.818136487f,
0.818191612f, 0.818246731f, 0.818301842f, 0.818356945f, 0.818412041f,
0.818467130f, 0.818522210f, 0.818577284f, 0.818632350f, 0.818687408f,
0.818742459f, 0.818797502f, 0.818852538f, 0.818907566f, 0.818962586f,
0.819017599f, 0.819072605f, 0.819127603f, 0.819182594f, 0.819237577f,
0.819292552f, 0.819347520f, 0.819402480f, 0.819457433f, 0.819512379f,
0.819567317f, 0.819622247f, 0.819677170f, 0.819732085f, 0.819786992f,
0.819841893f, 0.819896785f, 0.819951670f, 0.820006548f, 0.820061418f,
0.820116280f, 0.820171135f, 0.820225983f, 0.820280822f, 0.820335655f,
0.820390479f, 0.820445297f, 0.820500106f, 0.820554909f, 0.820609703f,
0.820664490f, 0.820719270f, 0.820774042f, 0.820828806f, 0.820883563f,
0.820938312f, 0.820993054f, 0.821047788f, 0.821102515f, 0.821157234f,
0.821211946f, 0.821266650f, 0.821321346f, 0.821376035f, 0.821430717f,
0.821485390f, 0.821540057f, 0.821594716f, 0.821649367f, 0.821704010f,
0.821758646f, 0.821813275f, 0.821867896f, 0.821922509f, 0.821977115f,
0.822031714f, 0.822086304f, 0.822140888f, 0.822195463f, 0.822250031f,
0.822304592f, 0.822359145f, 0.822413690f, 0.822468228f, 0.822522758f,
0.822577281f, 0.822631796f, 0.822686304f, 0.822740804f, 0.822795296f,
0.822849781f, 0.822904259f, 0.822958729f, 0.823013191f, 0.823067645f,
0.823122093f, 0.823176532f, 0.823230964f, 0.823285388f, 0.823339805f,
0.823394215f, 0.823448616f, 0.823503010f, 0.823557397f, 0.823611776f,
0.823666147f, 0.823720511f, 0.823774868f, 0.823829216f, 0.823883557f,
0.823937891f, 0.823992217f, 0.824046535f, 0.824100846f, 0.824155149f,
0.824209445f, 0.824263733f, 0.824318014f, 0.824372287f, 0.824426552f,
0.824480810f, 0.824535060f, 0.824589303f, 0.824643538f, 0.824697765f,
0.824751985f, 0.824806198f, 0.824860402f, 0.824914599f, 0.824968789f,
0.825022971f, 0.825077145f, 0.825131312f, 0.825185472f, 0.825239623f,
0.825293767f, 0.825347904f, 0.825402033f, 0.825456154f, 0.825510268f,
0.825564374f, 0.825618472f, 0.825672563f, 0.825726647f, 0.825780723f,
0.825834791f, 0.825888851f, 0.825942904f, 0.825996950f, 0.826050988f,
0.826105018f, 0.826159040f, 0.826213056f, 0.826267063f, 0.826321063f,
0.826375055f, 0.826429040f, 0.826483017f, 0.826536986f, 0.826590948f,
0.826644902f, 0.826698849f, 0.826752788f, 0.826806720f, 0.826860644f,
0.826914560f, 0.826968469f, 0.827022370f, 0.827076263f, 0.827130149f,
0.827184027f, 0.827237898f, 0.827291761f, 0.827345616f, 0.827399464f,
0.827453305f, 0.827507137f, 0.827560962f, 0.827614780f, 0.827668590f,
0.827722392f, 0.827776186f, 0.827829973f, 0.827883753f, 0.827937525f,
0.827991289f, 0.828045045f, 0.828098794f, 0.828152536f, 0.828206269f,
0.828259995f, 0.828313714f, 0.828367425f, 0.828421128f, 0.828474824f,
0.828528512f, 0.828582192f, 0.828635865f, 0.828689530f, 0.828743188f,
0.828796838f, 0.828850480f, 0.828904115f, 0.828957742f, 0.829011361f,
0.829064973f, 0.829118577f, 0.829172174f, 0.829225763f, 0.829279344f,
0.829332918f, 0.829386484f, 0.829440043f, 0.829493594f, 0.829547137f,
0.829600673f, 0.829654201f, 0.829707721f, 0.829761234f, 0.829814739f,
0.829868236f, 0.829921726f, 0.829975209f, 0.830028683f, 0.830082150f,
0.830135610f, 0.830189061f, 0.830242505f, 0.830295942f, 0.830349371f,
0.830402792f, 0.830456205f, 0.830509611f, 0.830563010f, 0.830616400f,
0.830669783f, 0.830723159f, 0.830776526f, 0.830829887f, 0.830883239f,
0.830936584f, 0.830989921f, 0.831043251f, 0.831096573f, 0.831149887f,
0.831203194f, 0.831256493f, 0.831309784f, 0.831363068f, 0.831416344f,
0.831469612f, 0.831522873f, 0.831576126f, 0.831629372f, 0.831682610f,
0.831735840f, 0.831789062f, 0.831842277f, 0.831895485f, 0.831948684f,
0.832001876f, 0.832055061f, 0.832108237f, 0.832161406f, 0.832214568f,
0.832267722f, 0.832320868f, 0.832374006f, 0.832427137f, 0.832480260f,
0.832533376f, 0.832586484f, 0.832639584f, 0.832692676f, 0.832745761f,
0.832798838f, 0.832851908f, 0.832904970f, 0.832958024f, 0.833011071f,
0.833064110f, 0.833117141f, 0.833170165f, 0.833223181f, 0.833276189f,
0.833329190f, 0.833382183f, 0.833435168f, 0.833488146f, 0.833541116f,
0.833594078f, 0.833647033f, 0.833699980f, 0.833752919f, 0.833805851f,
0.833858775f, 0.833911691f, 0.833964600f, 0.834017501f, 0.834070394f,
0.834123280f, 0.834176158f, 0.834229029f, 0.834281891f, 0.834334746f,
0.834387594f, 0.834440433f, 0.834493266f, 0.834546090f, 0.834598907f,
0.834651716f, 0.834704517f, 0.834757311f, 0.834810097f, 0.834862875f,
0.834915646f, 0.834968409f, 0.835021164f, 0.835073912f, 0.835126652f,
0.835179384f, 0.835232108f, 0.835284825f, 0.835337535f, 0.835390236f,
0.835442930f, 0.835495616f, 0.835548295f, 0.835600966f, 0.835653629f,
0.835706284f, 0.835758932f, 0.835811572f, 0.835864205f, 0.835916830f,
0.835969447f, 0.836022056f, 0.836074658f, 0.836127252f, 0.836179838f,
0.836232417f, 0.836284988f, 0.836337551f, 0.836390107f, 0.836442654f,
0.836495195f, 0.836547727f, 0.836600252f, 0.836652769f, 0.836705279f,
0.836757780f, 0.836810275f, 0.836862761f, 0.836915240f, 0.836967711f,
0.837020174f, 0.837072630f, 0.837125077f, 0.837177518f, 0.837229950f,
0.837282375f, 0.837334792f, 0.837387202f, 0.837439603f, 0.837491997f,
0.837544384f, 0.837596762f, 0.837649133f, 0.837701497f, 0.837753852f,
0.837806200f, 0.837858540f, 0.837910873f, 0.837963197f, 0.838015514f,
0.838067824f, 0.838120125f, 0.838172419f, 0.838224706f, 0.838276984f,
0.838329255f, 0.838381518f, 0.838433773f, 0.838486021f, 0.838538261f,
0.838590493f, 0.838642718f, 0.838694935f, 0.838747144f, 0.838799345f,
0.838851539f, 0.838903725f, 0.838955904f, 0.839008074f, 0.839060237f,
0.839112392f, 0.839164540f, 0.839216679f, 0.839268812f, 0.839320936f,
0.839373052f, 0.839425161f, 0.839477263f, 0.839529356f, 0.839581442f,
0.839633520f, 0.839685590f, 0.839737653f, 0.839789708f, 0.839841755f,
0.839893794f, 0.839945826f, 0.839997850f, 0.840049866f, 0.840101875f,
0.840153876f, 0.840205869f, 0.840257854f, 0.840309832f, 0.840361802f,
0.840413764f, 0.840465718f, 0.840517665f, 0.840569604f, 0.840621536f,
0.840673459f, 0.840725375f, 0.840777283f, 0.840829184f, 0.840881076f,
0.840932961f, 0.840984838f, 0.841036708f, 0.841088570f, 0.841140424f,
0.841192270f, 0.841244108f, 0.841295939f, 0.841347762f, 0.841399578f,
0.841451385f, 0.841503185f, 0.841554977f, 0.841606762f, 0.841658539f,
0.841710307f, 0.841762069f, 0.841813822f, 0.841865568f, 0.841917306f,
0.841969036f, 0.842020759f, 0.842072474f, 0.842124181f, 0.842175880f,
0.842227571f, 0.842279255f, 0.842330931f, 0.842382600f, 0.842434260f,
0.842485913f, 0.842537558f, 0.842589196f, 0.842640825f, 0.842692447f,
0.842744061f, 0.842795668f, 0.842847266f, 0.842898857f, 0.842950440f,
0.843002016f, 0.843053583f, 0.843105143f, 0.843156695f, 0.843208240f,
0.843259776f, 0.843311305f, 0.843362826f, 0.843414340f, 0.843465845f,
0.843517343f, 0.843568833f, 0.843620316f, 0.843671790f, 0.843723257f,
0.843774716f, 0.843826168f, 0.843877611f, 0.843929047f, 0.843980475f,
0.844031895f, 0.844083308f, 0.844134713f, 0.844186110f, 0.844237499f,
0.844288881f, 0.844340254f, 0.844391621f, 0.844442979f, 0.844494329f,
0.844545672f, 0.844597007f, 0.844648334f, 0.844699654f, 0.844750965f,
0.844802269f, 0.844853565f, 0.844904854f, 0.844956134f, 0.845007407f,
0.845058672f, 0.845109929f, 0.845161179f, 0.845212421f, 0.845263655f,
0.845314881f, 0.845366099f, 0.845417310f, 0.845468513f, 0.845519708f,
0.845570896f, 0.845622075f, 0.845673247f, 0.845724411f, 0.845775567f,
0.845826716f, 0.845877857f, 0.845928990f, 0.845980115f, 0.846031232f,
0.846082342f, 0.846133444f, 0.846184538f, 0.846235624f, 0.846286702f,
0.846337773f, 0.846388836f, 0.846439891f, 0.846490939f, 0.846541978f,
0.846593010f, 0.846644034f, 0.846695051f, 0.846746059f, 0.846797060f,
0.846848053f, 0.846899038f, 0.846950015f, 0.847000985f, 0.847051947f,
0.847102901f, 0.847153847f, 0.847204785f, 0.847255716f, 0.847306639f,
0.847357554f, 0.847408461f, 0.847459361f, 0.847510252f, 0.847561136f,
0.847612012f, 0.847662881f, 0.847713741f, 0.847764594f, 0.847815439f,
0.847866276f, 0.847917105f, 0.847967927f, 0.848018741f, 0.848069547f,
0.848120345f, 0.848171135f, 0.848221918f, 0.848272693f, 0.848323460f,
0.848374219f, 0.848424970f, 0.848475714f, 0.848526450f, 0.848577178f,
0.848627898f, 0.848678610f, 0.848729315f, 0.848780012f, 0.848830701f,
0.848881382f, 0.848932055f, 0.848982721f, 0.849033379f, 0.849084029f,
0.849134671f, 0.849185305f, 0.849235932f, 0.849286550f, 0.849337161f,
0.849387765f, 0.849438360f, 0.849488947f, 0.849539527f, 0.849590099f,
0.849640663f, 0.849691220f, 0.849741768f, 0.849792309f, 0.849842842f,
0.849893367f, 0.849943884f, 0.849994393f, 0.850044895f, 0.850095389f,
0.850145875f, 0.850196353f, 0.850246823f, 0.850297286f, 0.850347741f,
0.850398187f, 0.850448627f, 0.850499058f, 0.850549481f, 0.850599897f,
0.850650305f, 0.850700705f, 0.850751097f, 0.850801481f, 0.850851858f,
0.850902227f, 0.850952587f, 0.851002941f, 0.851053286f, 0.851103623f,
0.851153953f, 0.851204275f, 0.851254589f, 0.851304895f, 0.851355193f,
0.851405484f, 0.851455766f, 0.851506041f, 0.851556308f, 0.851606567f,
0.851656819f, 0.851707062f, 0.851757298f, 0.851807526f, 0.851857746f,
0.851907958f, 0.851958162f, 0.852008359f, 0.852058548f, 0.852108729f,
0.852158902f, 0.852209067f, 0.852259224f, 0.852309374f, 0.852359516f,
0.852409649f, 0.852459775f, 0.852509894f, 0.852560004f, 0.852610107f,
0.852660201f, 0.852710288f, 0.852760367f, 0.852810438f, 0.852860502f,
0.852910557f, 0.852960605f, 0.853010645f, 0.853060677f, 0.853110701f,
0.853160717f, 0.853210726f, 0.853260726f, 0.853310719f, 0.853360704f,
0.853410681f, 0.853460650f, 0.853510612f, 0.853560565f, 0.853610511f,
0.853660449f, 0.853710379f, 0.853760301f, 0.853810215f, 0.853860122f,
0.853910021f, 0.853959911f, 0.854009794f, 0.854059669f, 0.854109537f,
0.854159396f, 0.854209248f, 0.854259091f, 0.854308927f, 0.854358755f,
0.854408575f, 0.854458387f, 0.854508192f, 0.854557988f, 0.854607777f,
0.854657558f, 0.854707331f, 0.854757096f, 0.854806853f, 0.854856603f,
0.854906344f, 0.854956078f, 0.855005804f, 0.855055522f, 0.855105232f,
0.855154934f, 0.855204629f, 0.855254315f, 0.855303994f, 0.855353665f,
0.855403328f, 0.855452983f, 0.855502630f, 0.855552269f, 0.855601901f,
0.855651525f, 0.855701140f, 0.855750748f, 0.855800348f, 0.855849940f,
0.855899525f, 0.855949101f, 0.855998670f, 0.856048231f, 0.856097783f,
0.856147328f, 0.856196865f, 0.856246395f, 0.856295916f, 0.856345430f,
0.856394935f, 0.856444433f, 0.856493923f, 0.856543405f, 0.856592879f,
0.856642345f, 0.856691804f, 0.856741254f, 0.856790697f, 0.856840132f,
0.856889558f, 0.856938977f, 0.856988389f, 0.857037792f, 0.857087187f,
0.857136575f, 0.857185954f, 0.857235326f, 0.857284690f, 0.857334046f,
0.857383394f, 0.857432734f, 0.857482067f, 0.857531391f, 0.857580708f,
0.857630016f, 0.857679317f, 0.857728610f, 0.857777895f, 0.857827172f,
0.857876441f, 0.857925703f, 0.857974956f, 0.858024202f, 0.858073440f,
0.858122670f, 0.858171891f, 0.858221106f, 0.858270312f, 0.858319510f,
0.858368700f, 0.858417883f, 0.858467058f, 0.858516224f, 0.858565383f,
0.858614534f, 0.858663677f, 0.858712812f, 0.858761940f, 0.858811059f,
0.858860170f, 0.858909274f, 0.858958370f, 0.859007457f, 0.859056537f,
0.859105609f, 0.859154673f, 0.859203730f, 0.859252778f, 0.859301818f,
0.859350851f, 0.859399875f, 0.859448892f, 0.859497901f, 0.859546902f,
0.859595895f, 0.859644880f, 0.859693857f, 0.859742827f, 0.859791788f,
0.859840741f, 0.859889687f, 0.859938625f, 0.859987555f, 0.860036476f,
0.860085390f, 0.860134297f, 0.860183195f, 0.860232085f, 0.860280967f,
0.860329842f, 0.860378708f, 0.860427567f, 0.860476418f, 0.860525260f,
0.860574095f, 0.860622922f, 0.860671741f, 0.860720553f, 0.860769356f,
0.860818151f, 0.860866939f, 0.860915718f, 0.860964490f, 0.861013253f,
0.861062009f, 0.861110757f, 0.861159497f, 0.861208229f, 0.861256953f,
0.861305669f, 0.861354378f, 0.861403078f, 0.861451771f, 0.861500455f,
0.861549132f, 0.861597800f, 0.861646461f, 0.861695114f, 0.861743759f,
0.861792396f, 0.861841025f, 0.861889646f, 0.861938259f, 0.861986865f,
0.862035462f, 0.862084052f, 0.862132633f, 0.862181207f, 0.862229773f,
0.862278330f, 0.862326880f, 0.862375422f, 0.862423956f, 0.862472482f,
0.862521000f, 0.862569511f, 0.862618013f, 0.862666507f, 0.862714994f,
0.862763472f, 0.862811943f, 0.862860405f, 0.862908860f, 0.862957307f,
0.863005746f, 0.863054177f, 0.863102600f, 0.863151015f, 0.863199422f,
0.863247821f, 0.863296212f, 0.863344595f, 0.863392971f, 0.863441338f,
0.863489698f, 0.863538049f, 0.863586393f, 0.863634729f, 0.863683056f,
0.863731376f, 0.863779688f, 0.863827992f, 0.863876288f, 0.863924576f,
0.863972856f, 0.864021128f, 0.864069393f, 0.864117649f, 0.864165897f,
0.864214138f, 0.864262370f, 0.864310594f, 0.864358811f, 0.864407020f,
0.864455220f, 0.864503413f, 0.864551598f, 0.864599775f, 0.864647944f,
0.864696105f, 0.864744258f, 0.864792403f, 0.864840540f, 0.864888669f,
0.864936790f, 0.864984903f, 0.865033009f, 0.865081106f, 0.865129195f,
0.865177277f, 0.865225350f, 0.865273416f, 0.865321473f, 0.865369523f,
0.865417565f, 0.865465598f, 0.865513624f, 0.865561642f, 0.865609652f,
0.865657654f, 0.865705648f, 0.865753634f, 0.865801612f, 0.865849582f,
0.865897544f, 0.865945498f, 0.865993444f, 0.866041382f, 0.866089313f,
0.866137235f, 0.866185149f, 0.866233056f, 0.866280954f, 0.866328844f,
0.866376727f, 0.866424602f, 0.866472468f, 0.866520327f, 0.866568177f,
0.866616020f, 0.866663855f, 0.866711681f, 0.866759500f, 0.866807311f,
0.866855114f, 0.866902909f, 0.866950696f, 0.866998475f, 0.867046246f,
0.867094009f, 0.867141764f, 0.867189511f, 0.867237250f, 0.867284981f,
0.867332704f, 0.867380419f, 0.867428126f, 0.867475826f, 0.867523517f,
0.867571200f, 0.867618875f, 0.867666543f, 0.867714202f, 0.867761853f,
0.867809497f, 0.867857132f, 0.867904760f, 0.867952379f, 0.867999991f,
0.868047594f, 0.868095190f, 0.868142777f, 0.868190357f, 0.868237928f,
0.868285492f, 0.868333048f, 0.868380595f, 0.868428135f, 0.868475667f,
0.868523190f, 0.868570706f, 0.868618214f, 0.868665713f, 0.868713205f,
0.868760689f, 0.868808165f, 0.868855633f, 0.868903092f, 0.868950544f,
0.868997988f, 0.869045424f, 0.869092852f, 0.869140272f, 0.869187684f,
0.869235088f, 0.869282483f, 0.869329871f, 0.869377251f, 0.869424623f,
0.869471987f, 0.869519343f, 0.869566691f, 0.869614031f, 0.869661363f,
0.869708687f, 0.869756003f, 0.869803311f, 0.869850611f, 0.869897903f,
0.869945187f, 0.869992463f, 0.870039731f, 0.870086991f, 0.870134243f,
0.870181487f, 0.870228723f, 0.870275951f, 0.870323171f, 0.870370383f,
0.870417587f, 0.870464783f, 0.870511971f, 0.870559151f, 0.870606323f,
0.870653487f, 0.870700643f, 0.870747791f, 0.870794931f, 0.870842063f,
0.870889187f, 0.870936303f, 0.870983411f, 0.871030511f, 0.871077603f,
0.871124687f, 0.871171763f, 0.871218831f, 0.871265891f, 0.871312943f,
0.871359987f, 0.871407023f, 0.871454051f, 0.871501071f, 0.871548083f,
0.871595087f, 0.871642083f, 0.871689070f, 0.871736050f, 0.871783022f,
0.871829986f, 0.871876942f, 0.871923889f, 0.871970829f, 0.872017761f,
0.872064685f, 0.872111600f, 0.872158508f, 0.872205408f, 0.872252300f,
0.872299183f, 0.872346059f, 0.872392927f, 0.872439786f, 0.872486638f,
0.872533481f, 0.872580317f, 0.872627144f, 0.872673964f, 0.872720775f,
0.872767579f, 0.872814374f, 0.872861162f, 0.872907941f, 0.872954712f,
0.873001476f, 0.873048231f, 0.873094978f, 0.873141718f, 0.873188449f,
0.873235172f, 0.873281887f, 0.873328595f, 0.873375294f, 0.873421985f,
0.873468668f, 0.873515343f, 0.873562010f, 0.873608669f, 0.873655320f,
0.873701963f, 0.873748598f, 0.873795225f, 0.873841843f, 0.873888454f,
0.873935057f, 0.873981652f, 0.874028239f, 0.874074817f, 0.874121388f,
0.874167950f, 0.874214505f, 0.874261052f, 0.874307590f, 0.874354121f,
0.874400643f, 0.874447157f, 0.874493664f, 0.874540162f, 0.874586652f,
0.874633135f, 0.874679609f, 0.874726075f, 0.874772533f, 0.874818983f,
0.874865425f, 0.874911859f, 0.874958285f, 0.875004703f, 0.875051113f,
0.875097515f, 0.875143908f, 0.875190294f, 0.875236672f, 0.875283042f,
0.875329403f, 0.875375757f, 0.875422102f, 0.875468440f, 0.875514769f,
0.875561090f, 0.875607404f, 0.875653709f, 0.875700006f, 0.875746295f,
0.875792577f, 0.875838850f, 0.875885115f, 0.875931372f, 0.875977621f,
0.876023861f, 0.876070094f, 0.876116319f, 0.876162536f, 0.876208744f,
0.876254945f, 0.876301137f, 0.876347322f, 0.876393498f, 0.876439667f,
0.876485827f, 0.876531979f, 0.876578124f, 0.876624260f, 0.876670388f,
0.876716508f, 0.876762620f, 0.876808724f, 0.876854820f, 0.876900907f,
0.876946987f, 0.876993059f, 0.877039123f, 0.877085178f, 0.877131226f,
0.877177265f, 0.877223296f, 0.877269320f, 0.877315335f, 0.877361342f,
0.877407341f, 0.877453332f, 0.877499315f, 0.877545290f, 0.877591257f,
0.877637216f, 0.877683167f, 0.877729109f, 0.877775044f, 0.877820970f,
0.877866889f, 0.877912799f, 0.877958701f, 0.878004596f, 0.878050482f,
0.878096360f, 0.878142230f, 0.878188092f, 0.878233946f, 0.878279792f,
0.878325629f, 0.878371459f, 0.878417281f, 0.878463094f, 0.878508900f,
0.878554697f, 0.878600486f, 0.878646267f, 0.878692041f, 0.878737806f,
0.878783563f, 0.878829312f, 0.878875052f, 0.878920785f, 0.878966510f,
0.879012226f, 0.879057935f, 0.879103635f, 0.879149328f, 0.879195012f,
0.879240688f, 0.879286356f, 0.879332016f, 0.879377668f, 0.879423312f,
0.879468948f, 0.879514576f, 0.879560195f, 0.879605807f, 0.879651410f,
0.879697006f, 0.879742593f, 0.879788172f, 0.879833743f, 0.879879306f,
0.879924861f, 0.879970408f, 0.880015947f, 0.880061477f, 0.880107000f,
0.880152514f, 0.880198021f, 0.880243519f, 0.880289009f, 0.880334491f,
0.880379965f, 0.880425431f, 0.880470889f, 0.880516339f, 0.880561780f,
0.880607214f, 0.880652639f, 0.880698057f, 0.880743466f, 0.880788867f,
0.880834260f, 0.880879645f, 0.880925022f, 0.880970391f, 0.881015752f,
0.881061104f, 0.881106449f, 0.881151785f, 0.881197113f, 0.881242434f,
0.881287746f, 0.881333050f, 0.881378346f, 0.881423633f, 0.881468913f,
0.881514185f, 0.881559448f, 0.881604704f, 0.881649951f, 0.881695190f,
0.881740421f, 0.881785644f, 0.881830859f, 0.881876066f, 0.881921264f,
0.881966455f, 0.882011637f, 0.882056812f, 0.882101978f, 0.882147136f,
0.882192286f, 0.882237428f, 0.882282562f, 0.882327687f, 0.882372805f,
0.882417914f, 0.882463016f, 0.882508109f, 0.882553194f, 0.882598271f,
0.882643340f, 0.882688401f, 0.882733453f, 0.882778498f, 0.882823534f,
0.882868563f, 0.882913583f, 0.882958595f, 0.883003599f, 0.883048595f,
0.883093583f, 0.883138562f, 0.883183534f, 0.883228497f, 0.883273452f,
0.883318400f, 0.883363339f, 0.883408270f, 0.883453192f, 0.883498107f,
0.883543014f, 0.883587912f, 0.883632802f, 0.883677685f, 0.883722559f,
0.883767425f, 0.883812282f, 0.883857132f, 0.883901974f, 0.883946807f,
0.883991632f, 0.884036450f, 0.884081259f, 0.884126060f, 0.884170852f,
0.884215637f, 0.884260414f, 0.884305182f, 0.884349942f, 0.884394695f,
0.884439439f, 0.884484175f, 0.884528902f, 0.884573622f, 0.884618334f,
0.884663037f, 0.884707732f, 0.884752419f, 0.884797098f, 0.884841769f,
0.884886432f, 0.884931087f, 0.884975733f, 0.885020371f, 0.885065002f,
0.885109624f, 0.885154238f, 0.885198843f, 0.885243441f, 0.885288031f,
0.885332612f, 0.885377185f, 0.885421750f, 0.885466307f, 0.885510856f,
0.885555397f, 0.885599929f, 0.885644454f, 0.885688970f, 0.885733478f,
0.885777978f, 0.885822470f, 0.885866954f, 0.885911429f, 0.885955897f,
0.886000356f, 0.886044807f, 0.886089250f, 0.886133685f, 0.886178112f,
0.886222530f, 0.886266941f, 0.886311343f, 0.886355737f, 0.886400123f,
0.886444501f, 0.886488870f, 0.886533232f, 0.886577585f, 0.886621930f,
0.886666268f, 0.886710596f, 0.886754917f, 0.886799230f, 0.886843534f,
0.886887831f, 0.886932119f, 0.886976399f, 0.887020671f, 0.887064934f,
0.887109190f, 0.887153437f, 0.887197677f, 0.887241908f, 0.887286131f,
0.887330345f, 0.887374552f, 0.887418750f, 0.887462941f, 0.887507123f,
0.887551297f, 0.887595463f, 0.887639620f, 0.887683770f, 0.887727911f,
0.887772044f, 0.887816170f, 0.887860286f, 0.887904395f, 0.887948496f,
0.887992588f, 0.888036672f, 0.888080748f, 0.888124816f, 0.888168876f,
0.888212928f, 0.888256971f, 0.888301006f, 0.888345033f, 0.888389052f,
0.888433063f, 0.888477066f, 0.888521060f, 0.888565046f, 0.888609024f,
0.888652994f, 0.888696956f, 0.888740910f, 0.888784855f, 0.888828792f,
0.888872721f, 0.888916642f, 0.888960555f, 0.889004459f, 0.889048356f,
0.889092244f, 0.889136124f, 0.889179996f, 0.889223860f, 0.889267715f,
0.889311563f, 0.889355402f, 0.889399233f, 0.889443056f, 0.889486870f,
0.889530677f, 0.889574475f, 0.889618265f, 0.889662047f, 0.889705821f,
0.889749586f, 0.889793344f, 0.889837093f, 0.889880834f, 0.889924567f,
0.889968292f, 0.890012008f, 0.890055716f, 0.890099417f, 0.890143109f,
0.890186792f, 0.890230468f, 0.890274135f, 0.890317795f, 0.890361446f,
0.890405089f, 0.890448723f, 0.890492350f, 0.890535968f, 0.890579578f,
0.890623180f, 0.890666774f, 0.890710359f, 0.890753937f, 0.890797506f,
0.890841067f, 0.890884620f, 0.890928164f, 0.890971701f, 0.891015229f,
0.891058749f, 0.891102261f, 0.891145765f, 0.891189260f, 0.891232748f,
0.891276227f, 0.891319698f, 0.891363160f, 0.891406615f, 0.891450061f,
0.891493499f, 0.891536929f, 0.891580351f, 0.891623765f, 0.891667170f,
0.891710567f, 0.891753956f, 0.891797337f, 0.891840709f, 0.891884074f,
0.891927430f, 0.891970778f, 0.892014118f, 0.892057449f, 0.892100773f,
0.892144088f, 0.892187395f, 0.892230694f, 0.892273984f, 0.892317267f,
0.892360541f, 0.892403807f, 0.892447064f, 0.892490314f, 0.892533555f,
0.892576789f, 0.892620014f, 0.892663230f, 0.892706439f, 0.892749639f,
0.892792831f, 0.892836015f, 0.892879191f, 0.892922358f, 0.892965518f,
0.893008669f, 0.893051812f, 0.893094946f, 0.893138073f, 0.893181191f,
0.893224301f, 0.893267403f, 0.893310497f, 0.893353582f, 0.893396659f,
0.893439728f, 0.893482789f, 0.893525842f, 0.893568886f, 0.893611922f,
0.893654950f, 0.893697970f, 0.893740981f, 0.893783985f, 0.893826980f,
0.893869967f, 0.893912945f, 0.893955916f, 0.893998878f, 0.894041832f,
0.894084778f, 0.894127715f, 0.894170644f, 0.894213566f, 0.894256478f,
0.894299383f, 0.894342280f, 0.894385168f, 0.894428048f, 0.894470920f,
0.894513783f, 0.894556639f, 0.894599486f, 0.894642325f, 0.894685155f,
0.894727978f, 0.894770792f, 0.894813598f, 0.894856396f, 0.894899185f,
0.894941967f, 0.894984740f, 0.895027505f, 0.895070261f, 0.895113010f,
0.895155750f, 0.895198482f, 0.895241206f, 0.895283921f, 0.895326628f,
0.895369327f, 0.895412018f, 0.895454701f, 0.895497375f, 0.895540041f,
0.895582699f, 0.895625349f, 0.895667990f, 0.895710623f, 0.895753248f,
0.895795865f, 0.895838474f, 0.895881074f, 0.895923666f, 0.895966250f,
0.896008825f, 0.896051393f, 0.896093952f, 0.896136503f, 0.896179045f,
0.896221580f, 0.896264106f, 0.896306624f, 0.896349133f, 0.896391635f,
0.896434128f, 0.896476613f, 0.896519090f, 0.896561558f, 0.896604018f,
0.896646470f, 0.896688914f, 0.896731349f, 0.896773777f, 0.896816196f,
0.896858606f, 0.896901009f, 0.896943403f, 0.896985789f, 0.897028167f,
0.897070537f, 0.897112898f, 0.897155251f, 0.897197596f, 0.897239932f,
0.897282261f, 0.897324581f, 0.897366893f, 0.897409196f, 0.897451491f,
0.897493778f, 0.897536057f, 0.897578328f, 0.897620590f, 0.897662844f,
0.897705090f, 0.897747328f, 0.897789557f, 0.897831778f, 0.897873991f,
0.897916195f, 0.897958392f, 0.898000580f, 0.898042760f, 0.898084931f,
0.898127094f, 0.898169249f, 0.898211396f, 0.898253535f, 0.898295665f,
0.898337787f, 0.898379901f, 0.898422006f, 0.898464103f, 0.898506192f,
0.898548273f, 0.898590346f, 0.898632410f, 0.898674466f, 0.898716513f,
0.898758553f, 0.898800584f, 0.898842607f, 0.898884621f, 0.898926628f,
0.898968626f, 0.899010616f, 0.899052597f, 0.899094571f, 0.899136536f,
0.899178492f, 0.899220441f, 0.899262381f, 0.899304313f, 0.899346237f,
0.899388152f, 0.899430060f, 0.899471959f, 0.899513849f, 0.899555732f,
0.899597606f, 0.899639472f, 0.899681329f, 0.899723178f, 0.899765019f,
0.899806852f, 0.899848677f, 0.899890493f, 0.899932301f, 0.899974101f,
0.900015892f, 0.900057675f, 0.900099450f, 0.900141217f, 0.900182975f,
0.900224725f, 0.900266467f, 0.900308200f, 0.900349925f, 0.900391642f,
0.900433351f, 0.900475051f, 0.900516744f, 0.900558427f, 0.900600103f,
0.900641770f, 0.900683429f, 0.900725080f, 0.900766722f, 0.900808357f,
0.900849982f, 0.900891600f, 0.900933209f, 0.900974810f, 0.901016403f,
0.901057988f, 0.901099564f, 0.901141132f, 0.901182691f, 0.901224243f,
0.901265786f, 0.901307321f, 0.901348847f, 0.901390365f, 0.901431875f,
0.901473377f, 0.901514870f, 0.901556355f, 0.901597832f, 0.901639300f,
0.901680761f, 0.901722213f, 0.901763656f, 0.901805092f, 0.901846519f,
0.901887937f, 0.901929348f, 0.901970750f, 0.902012144f, 0.902053529f,
0.902094907f, 0.902136276f, 0.902177637f, 0.902218989f, 0.902260333f,
0.902301669f, 0.902342996f, 0.902384316f, 0.902425627f, 0.902466929f,
0.902508224f, 0.902549510f, 0.902590788f, 0.902632057f, 0.902673318f,
0.902714571f, 0.902755816f, 0.902797052f, 0.902838280f, 0.902879500f,
0.902920711f, 0.902961914f, 0.903003109f, 0.903044295f, 0.903085474f,
0.903126644f, 0.903167805f, 0.903208958f, 0.903250103f, 0.903291240f,
0.903332368f, 0.903373489f, 0.903414600f, 0.903455704f, 0.903496799f,
0.903537886f, 0.903578964f, 0.903620035f, 0.903661097f, 0.903702150f,
0.903743196f, 0.903784233f, 0.903825261f, 0.903866282f, 0.903907294f,
0.903948298f, 0.903989293f, 0.904030280f, 0.904071259f, 0.904112230f,
0.904153192f, 0.904194146f, 0.904235092f, 0.904276029f, 0.904316958f,
0.904357879f, 0.904398791f, 0.904439695f, 0.904480591f, 0.904521478f,
0.904562357f, 0.904603228f, 0.904644091f, 0.904684945f, 0.904725791f,
0.904766628f, 0.904807457f, 0.904848278f, 0.904889091f, 0.904929895f,
0.904970691f, 0.905011479f, 0.905052258f, 0.905093029f, 0.905133792f,
0.905174546f, 0.905215292f, 0.905256030f, 0.905296759f, 0.905337480f,
0.905378193f, 0.905418898f, 0.905459594f, 0.905500282f, 0.905540961f,
0.905581632f, 0.905622295f, 0.905662949f, 0.905703596f, 0.905744233f,
0.905784863f, 0.905825484f, 0.905866097f, 0.905906702f, 0.905947298f,
0.905987886f, 0.906028465f, 0.906069036f, 0.906109599f, 0.906150154f,
0.906190700f, 0.906231238f, 0.906271768f, 0.906312289f, 0.906352802f,
0.906393307f, 0.906433803f, 0.906474291f, 0.906514770f, 0.906555242f,
0.906595705f, 0.906636159f, 0.906676605f, 0.906717043f, 0.906757473f,
0.906797894f, 0.906838307f, 0.906878712f, 0.906919108f, 0.906959496f,
0.906999875f, 0.907040247f, 0.907080610f, 0.907120964f, 0.907161310f,
0.907201648f, 0.907241978f, 0.907282299f, 0.907322612f, 0.907362917f,
0.907403213f, 0.907443501f, 0.907483780f, 0.907524051f, 0.907564314f,
0.907604569f, 0.907644815f, 0.907685053f, 0.907725282f, 0.907765503f,
0.907805716f, 0.907845920f, 0.907886116f, 0.907926304f, 0.907966484f,
0.908006655f, 0.908046817f, 0.908086972f, 0.908127118f, 0.908167255f,
0.908207385f, 0.908247506f, 0.908287618f, 0.908327723f, 0.908367819f,
0.908407906f, 0.908447985f, 0.908488056f, 0.908528119f, 0.908568173f,
0.908608219f, 0.908648256f, 0.908688285f, 0.908728306f, 0.908768318f,
0.908808323f, 0.908848318f, 0.908888306f, 0.908928285f, 0.908968255f,
0.909008218f, 0.909048171f, 0.909088117f, 0.909128054f, 0.909167983f,
0.909207904f, 0.909247816f, 0.909287720f, 0.909327615f, 0.909367502f,
0.909407381f, 0.909447251f, 0.909487113f, 0.909526967f, 0.909566812f,
0.909606649f, 0.909646477f, 0.909686298f, 0.909726110f, 0.909765913f,
0.909805708f, 0.909845495f, 0.909885273f, 0.909925043f, 0.909964805f,
0.910004558f, 0.910044303f, 0.910084040f, 0.910123768f, 0.910163488f,
0.910203199f, 0.910242902f, 0.910282597f, 0.910322283f, 0.910361961f,
0.910401631f, 0.910441292f, 0.910480945f, 0.910520590f, 0.910560226f,
0.910599854f, 0.910639473f, 0.910679084f, 0.910718687f, 0.910758281f,
0.910797867f, 0.910837445f, 0.910877014f, 0.910916575f, 0.910956127f,
0.910995671f, 0.911035207f, 0.911074734f, 0.911114253f, 0.911153764f,
0.911193266f, 0.911232760f, 0.911272245f, 0.911311722f, 0.911351191f,
0.911390651f, 0.911430103f, 0.911469547f, 0.911508982f, 0.911548409f,
0.911587827f, 0.911627237f, 0.911666639f, 0.911706032f, 0.911745417f,
0.911784793f, 0.911824162f, 0.911863521f, 0.911902873f, 0.911942216f,
0.911981550f, 0.912020877f, 0.912060194f, 0.912099504f, 0.912138805f,
0.912178098f, 0.912217382f, 0.912256658f, 0.912295925f, 0.912335185f,
0.912374435f, 0.912413678f, 0.912452912f, 0.912492137f, 0.912531355f,
0.912570563f, 0.912609764f, 0.912648956f, 0.912688140f, 0.912727315f,
0.912766482f, 0.912805640f, 0.912844790f, 0.912883932f, 0.912923065f,
0.912962190f, 0.913001307f, 0.913040415f, 0.913079515f, 0.913118606f,
0.913157689f, 0.913196764f, 0.913235830f, 0.913274888f, 0.913313937f,
0.913352978f, 0.913392011f, 0.913431035f, 0.913470051f, 0.913509058f,
0.913548057f, 0.913587048f, 0.913626030f, 0.913665004f, 0.913703969f,
0.913742926f, 0.913781875f, 0.913820815f, 0.913859747f, 0.913898671f,
0.913937586f, 0.913976492f, 0.914015391f, 0.914054280f, 0.914093162f,
0.914132035f, 0.914170899f, 0.914209756f, 0.914248604f, 0.914287443f,
0.914326274f, 0.914365097f, 0.914403911f, 0.914442717f, 0.914481514f,
0.914520303f, 0.914559084f, 0.914597856f, 0.914636619f, 0.914675375f,
0.914714122f, 0.914752860f, 0.914791591f, 0.914830312f, 0.914869026f,
0.914907730f, 0.914946427f, 0.914985115f, 0.915023795f, 0.915062466f,
0.915101129f, 0.915139783f, 0.915178429f, 0.915217067f, 0.915255696f,
0.915294317f, 0.915332929f, 0.915371533f, 0.915410129f, 0.915448716f,
0.915487295f, 0.915525865f, 0.915564427f, 0.915602981f, 0.915641526f,
0.915680062f, 0.915718590f, 0.915757110f, 0.915795622f, 0.915834125f,
0.915872619f, 0.915911105f, 0.915949583f, 0.915988052f, 0.916026513f,
0.916064966f, 0.916103410f, 0.916141845f, 0.916180273f, 0.916218691f,
0.916257102f, 0.916295504f, 0.916333897f, 0.916372282f, 0.916410659f,
0.916449027f, 0.916487387f, 0.916525739f, 0.916564082f, 0.916602416f,
0.916640742f, 0.916679060f, 0.916717369f, 0.916755670f, 0.916793962f,
0.916832246f, 0.916870522f, 0.916908789f, 0.916947048f, 0.916985298f,
0.917023540f, 0.917061773f, 0.917099998f, 0.917138215f, 0.917176423f,
0.917214623f, 0.917252814f, 0.917290997f, 0.917329171f, 0.917367337f,
0.917405495f, 0.917443644f, 0.917481785f, 0.917519917f, 0.917558041f,
0.917596156f, 0.917634263f, 0.917672362f, 0.917710452f, 0.917748533f,
0.917786607f, 0.917824671f, 0.917862728f, 0.917900776f, 0.917938815f,
0.917976846f, 0.918014869f, 0.918052883f, 0.918090889f, 0.918128886f,
0.918166875f, 0.918204855f, 0.918242827f, 0.918280791f, 0.918318746f,
0.918356692f, 0.918394630f, 0.918432560f, 0.918470481f, 0.918508394f,
0.918546299f, 0.918584195f, 0.918622082f, 0.918659961f, 0.918697832f,
0.918735694f, 0.918773548f, 0.918811393f, 0.918849230f, 0.918887059f,
0.918924879f, 0.918962690f, 0.919000493f, 0.919038288f, 0.919076074f,
0.919113852f, 0.919151621f, 0.919189382f, 0.919227134f, 0.919264878f,
0.919302614f, 0.919340341f, 0.919378059f, 0.919415769f, 0.919453471f,
0.919491164f, 0.919528849f, 0.919566525f, 0.919604193f, 0.919641853f,
0.919679504f, 0.919717146f, 0.919754780f, 0.919792406f, 0.919830023f,
0.919867632f, 0.919905232f, 0.919942824f, 0.919980407f, 0.920017982f,
0.920055549f, 0.920093107f, 0.920130656f, 0.920168197f, 0.920205730f,
0.920243254f, 0.920280769f, 0.920318277f, 0.920355775f, 0.920393266f,
0.920430748f, 0.920468221f, 0.920505686f, 0.920543142f, 0.920580590f,
0.920618030f, 0.920655461f, 0.920692884f, 0.920730298f, 0.920767703f,
0.920805101f, 0.920842489f, 0.920879870f, 0.920917242f, 0.920954605f,
0.920991960f, 0.921029306f, 0.921066644f, 0.921103974f, 0.921141295f,
0.921178607f, 0.921215911f, 0.921253207f, 0.921290494f, 0.921327773f,
0.921365043f, 0.921402305f, 0.921439558f, 0.921476803f, 0.921514039f,
0.921551267f, 0.921588487f, 0.921625698f, 0.921662900f, 0.921700094f,
0.921737280f, 0.921774457f, 0.921811625f, 0.921848785f, 0.921885937f,
0.921923080f, 0.921960215f, 0.921997341f, 0.922034459f, 0.922071568f,
0.922108669f, 0.922145761f, 0.922182845f, 0.922219920f, 0.922256987f,
0.922294046f, 0.922331095f, 0.922368137f, 0.922405170f, 0.922442194f,
0.922479210f, 0.922516218f, 0.922553217f, 0.922590208f, 0.922627190f,
0.922664163f, 0.922701128f, 0.922738085f, 0.922775033f, 0.922811973f,
0.922848904f, 0.922885827f, 0.922922741f, 0.922959647f, 0.922996544f,
0.923033433f, 0.923070313f, 0.923107185f, 0.923144048f, 0.923180903f,
0.923217749f, 0.923254587f, 0.923291417f, 0.923328238f, 0.923365050f,
0.923401854f, 0.923438649f, 0.923475436f, 0.923512215f, 0.923548985f,
0.923585746f, 0.923622499f, 0.923659244f, 0.923695980f, 0.923732707f,
0.923769426f, 0.923806137f, 0.923842839f, 0.923879533f, 0.923916218f,
0.923952894f, 0.923989562f, 0.924026222f, 0.924062873f, 0.924099516f,
0.924136150f, 0.924172775f, 0.924209392f, 0.924246001f, 0.924282601f,
0.924319193f, 0.924355776f, 0.924392351f, 0.924428917f, 0.924465474f,
0.924502023f, 0.924538564f, 0.924575096f, 0.924611620f, 0.924648135f,
0.924684642f, 0.924721140f, 0.924757630f, 0.924794111f, 0.924830583f,
0.924867048f, 0.924903503f, 0.924939950f, 0.924976389f, 0.925012819f,
0.925049241f, 0.925085654f, 0.925122059f, 0.925158455f, 0.925194842f,
0.925231221f, 0.925267592f, 0.925303954f, 0.925340308f, 0.925376653f,
0.925412990f, 0.925449318f, 0.925485637f, 0.925521948f, 0.925558251f,
0.925594545f, 0.925630831f, 0.925667108f, 0.925703376f, 0.925739636f,
0.925775888f, 0.925812131f, 0.925848365f, 0.925884591f, 0.925920809f,
0.925957018f, 0.925993218f, 0.926029410f, 0.926065594f, 0.926101768f,
0.926137935f, 0.926174093f, 0.926210242f, 0.926246383f, 0.926282515f,
0.926318639f, 0.926354755f, 0.926390861f, 0.926426960f, 0.926463049f,
0.926499131f, 0.926535203f, 0.926571268f, 0.926607323f, 0.926643371f,
0.926679409f, 0.926715440f, 0.926751461f, 0.926787474f, 0.926823479f,
0.926859475f, 0.926895463f, 0.926931442f, 0.926967412f, 0.927003374f,
0.927039328f, 0.927075273f, 0.927111209f, 0.927147137f, 0.927183056f,
0.927218967f, 0.927254870f, 0.927290764f, 0.927326649f, 0.927362526f,
0.927398394f, 0.927434254f, 0.927470105f, 0.927505948f, 0.927541782f,
0.927577607f, 0.927613425f, 0.927649233f, 0.927685033f, 0.927720825f,
0.927756608f, 0.927792382f, 0.927828148f, 0.927863906f, 0.927899654f,
0.927935395f, 0.927971127f, 0.928006850f, 0.928042565f, 0.928078271f,
0.928113969f, 0.928149658f, 0.928185339f, 0.928221011f, 0.928256674f,
0.928292329f, 0.928327976f, 0.928363614f, 0.928399243f, 0.928434864f,
0.928470477f, 0.928506080f, 0.928541676f, 0.928577263f, 0.928612841f,
0.928648411f, 0.928683972f, 0.928719524f, 0.928755068f, 0.928790604f,
0.928826131f, 0.928861650f, 0.928897160f, 0.928932661f, 0.928968154f,
0.929003638f, 0.929039114f, 0.929074581f, 0.929110040f, 0.929145490f,
0.929180932f, 0.929216365f, 0.929251789f, 0.929287205f, 0.929322613f,
0.929358012f, 0.929393402f, 0.929428784f, 0.929464157f, 0.929499522f,
0.929534878f, 0.929570226f, 0.929605565f, 0.929640896f, 0.929676218f,
0.929711531f, 0.929746836f, 0.929782133f, 0.929817421f, 0.929852700f,
0.929887971f, 0.929923233f, 0.929958487f, 0.929993732f, 0.930028968f,
0.930064196f, 0.930099416f, 0.930134627f, 0.930169829f, 0.930205023f,
0.930240208f, 0.930275385f, 0.930310553f, 0.930345713f, 0.930380864f,
0.930416006f, 0.930451140f, 0.930486266f, 0.930521383f, 0.930556491f,
0.930591591f, 0.930626682f, 0.930661764f, 0.930696839f, 0.930731904f,
0.930766961f, 0.930802010f, 0.930837049f, 0.930872081f, 0.930907103f,
0.930942118f, 0.930977123f, 0.931012120f, 0.931047109f, 0.931082089f,
0.931117060f, 0.931152023f, 0.931186977f, 0.931221923f, 0.931256860f,
0.931291789f, 0.931326709f, 0.931361621f, 0.931396524f, 0.931431418f,
0.931466304f, 0.931501181f, 0.931536050f, 0.931570910f, 0.931605761f,
0.931640604f, 0.931675439f, 0.931710265f, 0.931745082f, 0.931779891f,
0.931814691f, 0.931849483f, 0.931884266f, 0.931919040f, 0.931953806f,
0.931988563f, 0.932023312f, 0.932058052f, 0.932092784f, 0.932127507f,
0.932162222f, 0.932196928f, 0.932231625f, 0.932266314f, 0.932300994f,
0.932335666f, 0.932370329f, 0.932404983f, 0.932439629f, 0.932474267f,
0.932508895f, 0.932543516f, 0.932578127f, 0.932612731f, 0.932647325f,
0.932681911f, 0.932716488f, 0.932751057f, 0.932785617f, 0.932820169f,
0.932854712f, 0.932889247f, 0.932923773f, 0.932958290f, 0.932992799f,
0.933027299f, 0.933061791f, 0.933096274f, 0.933130748f, 0.933165214f,
0.933199671f, 0.933234120f, 0.933268560f, 0.933302992f, 0.933337415f,
0.933371829f, 0.933406235f, 0.933440633f, 0.933475021f, 0.933509401f,
0.933543773f, 0.933578136f, 0.933612490f, 0.933646836f, 0.933681173f,
0.933715502f, 0.933749822f, 0.933784133f, 0.933818436f, 0.933852731f,
0.933887016f, 0.933921294f, 0.933955562f, 0.933989822f, 0.934024073f,
0.934058316f, 0.934092550f, 0.934126776f, 0.934160993f, 0.934195202f,
0.934229401f, 0.934263593f, 0.934297775f, 0.934331949f, 0.934366115f,
0.934400272f, 0.934434420f, 0.934468560f, 0.934502691f, 0.934536814f,
0.934570928f, 0.934605033f, 0.934639130f, 0.934673218f, 0.934707298f,
0.934741369f, 0.934775431f, 0.934809485f, 0.934843530f, 0.934877567f,
0.934911595f, 0.934945614f, 0.934979625f, 0.935013627f, 0.935047621f,
0.935081606f, 0.935115583f, 0.935149551f, 0.935183510f, 0.935217461f,
0.935251403f, 0.935285336f, 0.935319261f, 0.935353177f, 0.935387085f,
0.935420984f, 0.935454875f, 0.935488757f, 0.935522630f, 0.935556495f,
0.935590351f, 0.935624198f, 0.935658037f, 0.935691868f, 0.935725689f,
0.935759503f, 0.935793307f, 0.935827103f, 0.935860890f, 0.935894669f,
0.935928439f, 0.935962201f, 0.935995954f, 0.936029698f, 0.936063434f,
0.936097161f, 0.936130879f, 0.936164589f, 0.936198290f, 0.936231983f,
0.936265667f, 0.936299343f, 0.936333010f, 0.936366668f, 0.936400317f,
0.936433958f, 0.936467591f, 0.936501215f, 0.936534830f, 0.936568437f,
0.936602035f, 0.936635624f, 0.936669205f, 0.936702777f, 0.936736340f,
0.936769895f, 0.936803442f, 0.936836979f, 0.936870509f, 0.936904029f,
0.936937541f, 0.936971044f, 0.937004539f, 0.937038025f, 0.937071502f,
0.937104971f, 0.937138432f, 0.937171883f, 0.937205326f, 0.937238760f,
0.937272186f, 0.937305603f, 0.937339012f, 0.937372412f, 0.937405803f,
0.937439186f, 0.937472560f, 0.937505925f, 0.937539282f, 0.937572630f,
0.937605970f, 0.937639301f, 0.937672623f, 0.937705937f, 0.937739242f,
0.937772539f, 0.937805827f, 0.937839106f, 0.937872376f, 0.937905638f,
0.937938892f, 0.937972137f, 0.938005373f, 0.938038600f, 0.938071819f,
0.938105030f, 0.938138231f, 0.938171424f, 0.938204609f, 0.938237784f,
0.938270952f, 0.938304110f, 0.938337260f, 0.938370401f, 0.938403534f,
0.938436658f, 0.938469774f, 0.938502880f, 0.938535978f, 0.938569068f,
0.938602149f, 0.938635221f, 0.938668285f, 0.938701340f, 0.938734386f,
0.938767424f, 0.938800453f, 0.938833474f, 0.938866486f, 0.938899489f,
0.938932484f, 0.938965470f, 0.938998447f, 0.939031416f, 0.939064376f,
0.939097327f, 0.939130270f, 0.939163204f, 0.939196130f, 0.939229047f,
0.939261955f, 0.939294855f, 0.939327746f, 0.939360628f, 0.939393502f,
0.939426367f, 0.939459224f, 0.939492071f, 0.939524911f, 0.939557741f,
0.939590563f, 0.939623377f, 0.939656181f, 0.939688977f, 0.939721765f,
0.939754543f, 0.939787314f, 0.939820075f, 0.939852828f, 0.939885572f,
0.939918308f, 0.939951035f, 0.939983753f, 0.940016463f, 0.940049164f,
0.940081856f, 0.940114540f, 0.940147215f, 0.940179881f, 0.940212539f,
0.940245188f, 0.940277829f, 0.940310461f, 0.940343084f, 0.940375699f,
0.940408305f, 0.940440902f, 0.940473491f, 0.940506071f, 0.940538642f,
0.940571205f, 0.940603759f, 0.940636304f, 0.940668841f, 0.940701369f,
0.940733889f, 0.940766400f, 0.940798902f, 0.940831395f, 0.940863880f,
0.940896356f, 0.940928824f, 0.940961283f, 0.940993733f, 0.941026175f,
0.941058608f, 0.941091032f, 0.941123448f, 0.941155855f, 0.941188254f,
0.941220643f, 0.941253025f, 0.941285397f, 0.941317761f, 0.941350116f,
0.941382462f, 0.941414800f, 0.941447130f, 0.941479450f, 0.941511762f,
0.941544065f, 0.941576360f, 0.941608646f, 0.941640923f, 0.941673192f,
0.941705452f, 0.941737703f, 0.941769946f, 0.941802179f, 0.941834405f,
0.941866622f, 0.941898830f, 0.941931029f, 0.941963220f, 0.941995402f,
0.942027575f, 0.942059740f, 0.942091896f, 0.942124043f, 0.942156182f,
0.942188312f, 0.942220434f, 0.942252546f, 0.942284650f, 0.942316746f,
0.942348833f, 0.942380911f, 0.942412980f, 0.942445041f, 0.942477093f,
0.942509137f, 0.942541171f, 0.942573198f, 0.942605215f, 0.942637224f,
0.942669224f, 0.942701216f, 0.942733198f, 0.942765173f, 0.942797138f,
0.942829095f, 0.942861043f, 0.942892983f, 0.942924913f, 0.942956836f,
0.942988749f, 0.943020654f, 0.943052550f, 0.943084437f, 0.943116316f,
0.943148186f, 0.943180048f, 0.943211901f, 0.943243745f, 0.943275580f,
0.943307407f, 0.943339225f, 0.943371035f, 0.943402836f, 0.943434628f,
0.943466411f, 0.943498186f, 0.943529952f, 0.943561709f, 0.943593458f,
0.943625198f, 0.943656930f, 0.943688652f, 0.943720366f, 0.943752072f,
0.943783769f, 0.943815457f, 0.943847136f, 0.943878807f, 0.943910469f,
0.943942122f, 0.943973767f, 0.944005403f, 0.944037030f, 0.944068649f,
0.944100258f, 0.944131860f, 0.944163452f, 0.944195036f, 0.944226612f,
0.944258178f, 0.944289736f, 0.944321285f, 0.944352826f, 0.944384357f,
0.944415881f, 0.944447395f, 0.944478901f, 0.944510398f, 0.944541886f,
0.944573366f, 0.944604837f, 0.944636300f, 0.944667753f, 0.944699198f,
0.944730635f, 0.944762062f, 0.944793481f, 0.944824892f, 0.944856293f,
0.944887686f, 0.944919070f, 0.944950446f, 0.944981813f, 0.945013171f,
0.945044520f, 0.945075861f, 0.945107193f, 0.945138517f, 0.945169831f,
0.945201137f, 0.945232435f, 0.945263724f, 0.945295004f, 0.945326275f,
0.945357537f, 0.945388791f, 0.945420037f, 0.945451273f, 0.945482501f,
0.945513720f, 0.945544931f, 0.945576132f, 0.945607325f, 0.945638510f,
0.945669685f, 0.945700852f, 0.945732011f, 0.945763160f, 0.945794301f,
0.945825434f, 0.945856557f, 0.945887672f, 0.945918778f, 0.945949876f,
0.945980964f, 0.946012044f, 0.946043116f, 0.946074178f, 0.946105232f,
0.946136278f, 0.946167314f, 0.946198342f, 0.946229361f, 0.946260372f,
0.946291374f, 0.946322367f, 0.946353351f, 0.946384327f, 0.946415294f,
0.946446252f, 0.946477202f, 0.946508143f, 0.946539075f, 0.946569998f,
0.946600913f, 0.946631819f, 0.946662717f, 0.946693605f, 0.946724485f,
0.946755357f, 0.946786219f, 0.946817073f, 0.946847918f, 0.946878755f,
0.946909582f, 0.946940402f, 0.946971212f, 0.947002014f, 0.947032807f,
0.947063591f, 0.947094366f, 0.947125133f, 0.947155891f, 0.947186641f,
0.947217381f, 0.947248114f, 0.947278837f, 0.947309551f, 0.947340257f,
0.947370955f, 0.947401643f, 0.947432323f, 0.947462994f, 0.947493656f,
0.947524310f, 0.947554955f, 0.947585591f, 0.947616219f, 0.947646837f,
0.947677447f, 0.947708049f, 0.947738642f, 0.947769225f, 0.947799801f,
0.947830367f, 0.947860925f, 0.947891474f, 0.947922015f, 0.947952546f,
0.947983069f, 0.948013584f, 0.948044089f, 0.948074586f, 0.948105074f,
0.948135553f, 0.948166024f, 0.948196486f, 0.948226939f, 0.948257384f,
0.948287820f, 0.948318247f, 0.948348665f, 0.948379075f, 0.948409476f,
0.948439868f, 0.948470252f, 0.948500626f, 0.948530993f, 0.948561350f,
0.948591699f, 0.948622038f, 0.948652370f, 0.948682692f, 0.948713006f,
0.948743311f, 0.948773607f, 0.948803895f, 0.948834174f, 0.948864444f,
0.948894705f, 0.948924958f, 0.948955202f, 0.948985437f, 0.949015664f,
0.949045882f, 0.949076091f, 0.949106291f, 0.949136483f, 0.949166666f,
0.949196840f, 0.949227006f, 0.949257162f, 0.949287310f, 0.949317450f,
0.949347580f, 0.949377702f, 0.949407815f, 0.949437920f, 0.949468015f,
0.949498102f, 0.949528181f, 0.949558250f, 0.949588311f, 0.949618363f,
0.949648406f, 0.949678441f, 0.949708467f, 0.949738484f, 0.949768492f,
0.949798492f, 0.949828483f, 0.949858465f, 0.949888438f, 0.949918403f,
0.949948359f, 0.949978306f, 0.950008245f, 0.950038175f, 0.950068096f,
0.950098008f, 0.950127912f, 0.950157807f, 0.950187693f, 0.950217570f,
0.950247439f, 0.950277299f, 0.950307150f, 0.950336993f, 0.950366826f,
0.950396651f, 0.950426468f, 0.950456275f, 0.950486074f, 0.950515864f,
0.950545645f, 0.950575418f, 0.950605182f, 0.950634937f, 0.950664683f,
0.950694421f, 0.950724150f, 0.950753870f, 0.950783581f, 0.950813284f,
0.950842978f, 0.950872663f, 0.950902340f, 0.950932007f, 0.950961666f,
0.950991317f, 0.951020958f, 0.951050591f, 0.951080215f, 0.951109830f,
0.951139437f, 0.951169034f, 0.951198623f, 0.951228204f, 0.951257775f,
0.951287338f, 0.951316892f, 0.951346437f, 0.951375974f, 0.951405502f,
0.951435021f, 0.951464531f, 0.951494033f, 0.951523526f, 0.951553010f,
0.951582485f, 0.951611952f, 0.951641410f, 0.951670859f, 0.951700299f,
0.951729731f, 0.951759154f, 0.951788568f, 0.951817973f, 0.951847370f,
0.951876758f, 0.951906137f, 0.951935507f, 0.951964869f, 0.951994222f,
0.952023566f, 0.952052901f, 0.952082228f, 0.952111546f, 0.952140855f,
0.952170155f, 0.952199447f, 0.952228730f, 0.952258004f, 0.952287269f,
0.952316526f, 0.952345774f, 0.952375013f, 0.952404243f, 0.952433465f,
0.952462677f, 0.952491882f, 0.952521077f, 0.952550263f, 0.952579441f,
0.952608610f, 0.952637771f, 0.952666922f, 0.952696065f, 0.952725199f,
0.952754324f, 0.952783441f, 0.952812549f, 0.952841648f, 0.952870738f,
0.952899819f, 0.952928892f, 0.952957956f, 0.952987011f, 0.953016058f,
0.953045095f, 0.953074124f, 0.953103144f, 0.953132156f, 0.953161159f,
0.953190152f, 0.953219138f, 0.953248114f, 0.953277082f, 0.953306040f,
0.953334990f, 0.953363932f, 0.953392864f, 0.953421788f, 0.953450703f,
0.953479609f, 0.953508507f, 0.953537396f, 0.953566276f, 0.953595147f,
0.953624009f, 0.953652863f, 0.953681708f, 0.953710544f, 0.953739371f,
0.953768190f, 0.953797000f, 0.953825801f, 0.953854593f, 0.953883377f,
0.953912151f, 0.953940917f, 0.953969675f, 0.953998423f, 0.954027163f,
0.954055894f, 0.954084616f, 0.954113329f, 0.954142034f, 0.954170730f,
0.954199417f, 0.954228095f, 0.954256765f, 0.954285425f, 0.954314077f,
0.954342721f, 0.954371355f, 0.954399981f, 0.954428598f, 0.954457206f,
0.954485805f, 0.954514396f, 0.954542978f, 0.954571551f, 0.954600115f,
0.954628670f, 0.954657217f, 0.954685755f, 0.954714284f, 0.954742804f,
0.954771316f, 0.954799819f, 0.954828313f, 0.954856798f, 0.954885275f,
0.954913742f, 0.954942201f, 0.954970652f, 0.954999093f, 0.955027526f,
0.955055949f, 0.955084365f, 0.955112771f, 0.955141168f, 0.955169557f,
0.955197937f, 0.955226308f, 0.955254671f, 0.955283024f, 0.955311369f,
0.955339705f, 0.955368032f, 0.955396351f, 0.955424660f, 0.955452961f,
0.955481253f, 0.955509537f, 0.955537811f, 0.955566077f, 0.955594334f,
0.955622582f, 0.955650822f, 0.955679052f, 0.955707274f, 0.955735487f,
0.955763692f, 0.955791887f, 0.955820074f, 0.955848252f, 0.955876421f,
0.955904581f, 0.955932733f, 0.955960876f, 0.955989010f, 0.956017135f,
0.956045251f, 0.956073359f, 0.956101458f, 0.956129548f, 0.956157629f,
0.956185702f, 0.956213765f, 0.956241820f, 0.956269866f, 0.956297904f,
0.956325932f, 0.956353952f, 0.956381963f, 0.956409965f, 0.956437959f,
0.956465943f, 0.956493919f, 0.956521886f, 0.956549844f, 0.956577794f,
0.956605734f, 0.956633666f, 0.956661589f, 0.956689503f, 0.956717409f,
0.956745305f, 0.956773193f, 0.956801072f, 0.956828943f, 0.956856804f,
0.956884657f, 0.956912501f, 0.956940336f, 0.956968162f, 0.956995980f,
0.957023788f, 0.957051588f, 0.957079379f, 0.957107162f, 0.957134935f,
0.957162700f, 0.957190456f, 0.957218203f, 0.957245941f, 0.957273671f,
0.957301391f, 0.957329103f, 0.957356806f, 0.957384501f, 0.957412186f,
0.957439863f, 0.957467531f, 0.957495190f, 0.957522840f, 0.957550482f,
0.957578115f, 0.957605739f, 0.957633354f, 0.957660960f, 0.957688558f,
0.957716146f, 0.957743726f, 0.957771297f, 0.957798860f, 0.957826413f,
0.957853958f, 0.957881494f, 0.957909021f, 0.957936539f, 0.957964048f,
0.957991549f, 0.958019041f, 0.958046524f, 0.958073998f, 0.958101464f,
0.958128920f, 0.958156368f, 0.958183807f, 0.958211237f, 0.958238659f,
0.958266071f, 0.958293475f, 0.958320870f, 0.958348256f, 0.958375634f,
0.958403002f, 0.958430362f, 0.958457713f, 0.958485055f, 0.958512388f,
0.958539713f, 0.958567029f, 0.958594335f, 0.958621634f, 0.958648923f,
0.958676203f, 0.958703475f, 0.958730738f, 0.958757992f, 0.958785237f,
0.958812473f, 0.958839701f, 0.958866920f, 0.958894130f, 0.958921331f,
0.958948523f, 0.958975707f, 0.959002881f, 0.959030047f, 0.959057204f,
0.959084352f, 0.959111492f, 0.959138622f, 0.959165744f, 0.959192857f,
0.959219961f, 0.959247057f, 0.959274143f, 0.959301221f, 0.959328290f,
0.959355350f, 0.959382401f, 0.959409444f, 0.959436477f, 0.959463502f,
0.959490518f, 0.959517525f, 0.959544524f, 0.959571513f, 0.959598494f,
0.959625466f, 0.959652429f, 0.959679383f, 0.959706328f, 0.959733265f,
0.959760193f, 0.959787112f, 0.959814022f, 0.959840923f, 0.959867816f,
0.959894699f, 0.959921574f, 0.959948440f, 0.959975297f, 0.960002146f,
0.960028985f, 0.960055816f, 0.960082638f, 0.960109451f, 0.960136255f,
0.960163051f, 0.960189837f, 0.960216615f, 0.960243384f, 0.960270144f,
0.960296895f, 0.960323638f, 0.960350371f, 0.960377096f, 0.960403812f,
0.960430519f, 0.960457218f, 0.960483907f, 0.960510588f, 0.960537260f,
0.960563923f, 0.960590577f, 0.960617222f, 0.960643859f, 0.960670487f,
0.960697105f, 0.960723715f, 0.960750317f, 0.960776909f, 0.960803493f,
0.960830067f, 0.960856633f, 0.960883190f, 0.960909738f, 0.960936278f,
0.960962808f, 0.960989330f, 0.961015843f, 0.961042347f, 0.961068842f,
0.961095329f, 0.961121806f, 0.961148275f, 0.961174735f, 0.961201186f,
0.961227628f, 0.961254061f, 0.961280486f, 0.961306902f, 0.961333308f,
0.961359706f, 0.961386096f, 0.961412476f, 0.961438847f, 0.961465210f,
0.961491564f, 0.961517909f, 0.961544245f, 0.961570572f, 0.961596891f,
0.961623201f, 0.961649501f, 0.961675793f, 0.961702077f, 0.961728351f,
0.961754616f, 0.961780873f, 0.961807121f, 0.961833360f, 0.961859590f,
0.961885811f, 0.961912023f, 0.961938227f, 0.961964422f, 0.961990608f,
0.962016785f, 0.962042953f, 0.962069112f, 0.962095263f, 0.962121404f,
0.962147537f, 0.962173661f, 0.962199776f, 0.962225882f, 0.962251980f,
0.962278069f, 0.962304148f, 0.962330219f, 0.962356281f, 0.962382334f,
0.962408379f, 0.962434414f, 0.962460441f, 0.962486459f, 0.962512468f,
0.962538468f, 0.962564459f, 0.962590442f, 0.962616415f, 0.962642380f,
0.962668336f, 0.962694283f, 0.962720221f, 0.962746151f, 0.962772071f,
0.962797983f, 0.962823886f, 0.962849780f, 0.962875665f, 0.962901541f,
0.962927408f, 0.962953267f, 0.962979117f, 0.963004957f, 0.963030789f,
0.963056613f, 0.963082427f, 0.963108232f, 0.963134029f, 0.963159817f,
0.963185596f, 0.963211366f, 0.963237127f, 0.963262879f, 0.963288623f,
0.963314357f, 0.963340083f, 0.963365800f, 0.963391508f, 0.963417207f,
0.963442897f, 0.963468579f, 0.963494251f, 0.963519915f, 0.963545570f,
0.963571216f, 0.963596853f, 0.963622482f, 0.963648101f, 0.963673712f,
0.963699314f, 0.963724907f, 0.963750491f, 0.963776066f, 0.963801632f,
0.963827190f, 0.963852738f, 0.963878278f, 0.963903809f, 0.963929331f,
0.963954844f, 0.963980348f, 0.964005844f, 0.964031330f, 0.964056808f,
0.964082277f, 0.964107737f, 0.964133188f, 0.964158631f, 0.964184064f,
0.964209489f, 0.964234904f, 0.964260311f, 0.964285709f, 0.964311098f,
0.964336478f, 0.964361850f, 0.964387212f, 0.964412566f, 0.964437911f,
0.964463247f, 0.964488574f, 0.964513892f, 0.964539201f, 0.964564502f,
0.964589793f, 0.964615076f, 0.964640350f, 0.964665615f, 0.964690871f,
0.964716118f, 0.964741357f, 0.964766586f, 0.964791807f, 0.964817019f,
0.964842222f, 0.964867416f, 0.964892601f, 0.964917777f, 0.964942945f,
0.964968103f, 0.964993253f, 0.965018394f, 0.965043526f, 0.965068649f,
0.965093763f, 0.965118868f, 0.965143965f, 0.965169052f, 0.965194131f,
0.965219201f, 0.965244262f, 0.965269314f, 0.965294357f, 0.965319392f,
0.965344417f, 0.965369434f, 0.965394442f, 0.965419441f, 0.965444431f,
0.965469412f, 0.965494384f, 0.965519347f, 0.965544302f, 0.965569248f,
0.965594184f, 0.965619112f, 0.965644031f, 0.965668941f, 0.965693843f,
0.965718735f, 0.965743618f, 0.965768493f, 0.965793359f, 0.965818216f,
0.965843064f, 0.965867903f, 0.965892733f, 0.965917554f, 0.965942367f,
0.965967171f, 0.965991965f, 0.966016751f, 0.966041528f, 0.966066296f,
0.966091055f, 0.966115806f, 0.966140547f, 0.966165280f, 0.966190003f,
0.966214718f, 0.966239424f, 0.966264121f, 0.966288809f, 0.966313489f,
0.966338159f, 0.966362821f, 0.966387473f, 0.966412117f, 0.966436752f,
0.966461378f, 0.966485995f, 0.966510603f, 0.966535202f, 0.966559793f,
0.966584374f, 0.966608947f, 0.966633511f, 0.966658066f, 0.966682612f,
0.966707149f, 0.966731677f, 0.966756197f, 0.966780707f, 0.966805209f,
0.966829701f, 0.966854185f, 0.966878660f, 0.966903126f, 0.966927583f,
0.966952032f, 0.966976471f, 0.967000902f, 0.967025323f, 0.967049736f,
0.967074140f, 0.967098535f, 0.967122921f, 0.967147298f, 0.967171666f,
0.967196025f, 0.967220376f, 0.967244718f, 0.967269050f, 0.967293374f,
0.967317689f, 0.967341995f, 0.967366292f, 0.967390580f, 0.967414860f,
0.967439130f, 0.967463392f, 0.967487645f, 0.967511888f, 0.967536123f,
0.967560349f, 0.967584566f, 0.967608775f, 0.967632974f, 0.967657164f,
0.967681346f, 0.967705519f, 0.967729682f, 0.967753837f, 0.967777983f,
0.967802120f, 0.967826248f, 0.967850368f, 0.967874478f, 0.967898579f,
0.967922672f, 0.967946756f, 0.967970830f, 0.967994896f, 0.968018953f,
0.968043001f, 0.968067041f, 0.968091071f, 0.968115092f, 0.968139105f,
0.968163108f, 0.968187103f, 0.968211089f, 0.968235066f, 0.968259034f,
0.968282993f, 0.968306943f, 0.968330884f, 0.968354817f, 0.968378740f,
0.968402655f, 0.968426561f, 0.968450457f, 0.968474345f, 0.968498224f,
0.968522094f, 0.968545955f, 0.968569808f, 0.968593651f, 0.968617486f,
0.968641311f, 0.968665128f, 0.968688936f, 0.968712734f, 0.968736524f,
0.968760305f, 0.968784078f, 0.968807841f, 0.968831595f, 0.968855341f,
0.968879077f, 0.968902805f, 0.968926523f, 0.968950233f, 0.968973934f,
0.968997626f, 0.969021309f, 0.969044983f, 0.969068649f, 0.969092305f,
0.969115953f, 0.969139591f, 0.969163221f, 0.969186842f, 0.969210453f,
0.969234056f, 0.969257650f, 0.969281235f, 0.969304812f, 0.969328379f,
0.969351937f, 0.969375487f, 0.969399027f, 0.969422559f, 0.969446082f,
0.969469595f, 0.969493100f, 0.969516596f, 0.969540083f, 0.969563562f,
0.969587031f, 0.969610491f, 0.969633943f, 0.969657385f, 0.969680819f,
0.969704243f, 0.969727659f, 0.969751066f, 0.969774464f, 0.969797853f,
0.969821233f, 0.969844604f, 0.969867967f, 0.969891320f, 0.969914665f,
0.969938000f, 0.969961327f, 0.969984644f, 0.970007953f, 0.970031253f,
0.970054544f, 0.970077826f, 0.970101099f, 0.970124364f, 0.970147619f,
0.970170865f, 0.970194103f, 0.970217331f, 0.970240551f, 0.970263762f,
0.970286963f, 0.970310156f, 0.970333340f, 0.970356515f, 0.970379681f,
0.970402839f, 0.970425987f, 0.970449126f, 0.970472257f, 0.970495378f,
0.970518491f, 0.970541595f, 0.970564689f, 0.970587775f, 0.970610852f,
0.970633920f, 0.970656979f, 0.970680029f, 0.970703071f, 0.970726103f,
0.970749126f, 0.970772141f, 0.970795146f, 0.970818143f, 0.970841131f,
0.970864109f, 0.970887079f, 0.970910040f, 0.970932992f, 0.970955935f,
0.970978869f, 0.971001795f, 0.971024711f, 0.971047618f, 0.971070517f,
0.971093406f, 0.971116287f, 0.971139158f, 0.971162021f, 0.971184875f,
0.971207720f, 0.971230556f, 0.971253383f, 0.971276201f, 0.971299010f,
0.971321810f, 0.971344602f, 0.971367384f, 0.971390158f, 0.971412922f,
0.971435678f, 0.971458424f, 0.971481162f, 0.971503891f, 0.971526611f,
0.971549322f, 0.971572024f, 0.971594717f, 0.971617401f, 0.971640076f,
0.971662743f, 0.971685400f, 0.971708048f, 0.971730688f, 0.971753319f,
0.971775940f, 0.971798553f, 0.971821157f, 0.971843752f, 0.971866337f,
0.971888914f, 0.971911483f, 0.971934042f, 0.971956592f, 0.971979133f,
0.972001665f, 0.972024189f, 0.972046703f, 0.972069209f, 0.972091705f,
0.972114193f, 0.972136672f, 0.972159141f, 0.972181602f, 0.972204054f,
0.972226497f, 0.972248931f, 0.972271356f, 0.972293772f, 0.972316180f,
0.972338578f, 0.972360967f, 0.972383348f, 0.972405719f, 0.972428082f,
0.972450435f, 0.972472780f, 0.972495115f, 0.972517442f, 0.972539760f,
0.972562069f, 0.972584369f, 0.972606660f, 0.972628942f, 0.972651215f,
0.972673479f, 0.972695735f, 0.972717981f, 0.972740218f, 0.972762447f,
0.972784666f, 0.972806877f, 0.972829078f, 0.972851271f, 0.972873455f,
0.972895629f, 0.972917795f, 0.972939952f, 0.972962100f, 0.972984239f,
0.973006369f, 0.973028490f, 0.973050603f, 0.973072706f, 0.973094800f,
0.973116885f, 0.973138962f, 0.973161029f, 0.973183088f, 0.973205137f,
0.973227178f, 0.973249210f, 0.973271232f, 0.973293246f, 0.973315251f,
0.973337247f, 0.973359234f, 0.973381212f, 0.973403181f, 0.973425141f,
0.973447092f, 0.973469034f, 0.973490967f, 0.973512892f, 0.973534807f,
0.973556714f, 0.973578611f, 0.973600499f, 0.973622379f, 0.973644250f,
0.973666111f, 0.973687964f, 0.973709808f, 0.973731643f, 0.973753468f,
0.973775285f, 0.973797093f, 0.973818892f, 0.973840682f, 0.973862464f,
0.973884236f, 0.973905999f, 0.973927753f, 0.973949498f, 0.973971235f,
0.973992962f, 0.974014681f, 0.974036390f, 0.974058091f, 0.974079782f,
0.974101465f, 0.974123139f, 0.974144803f, 0.974166459f, 0.974188106f,
0.974209744f, 0.974231373f, 0.974252993f, 0.974274604f, 0.974296206f,
0.974317799f, 0.974339383f, 0.974360958f, 0.974382524f, 0.974404081f,
0.974425630f, 0.974447169f, 0.974468699f, 0.974490221f, 0.974511733f,
0.974533237f, 0.974554731f, 0.974576217f, 0.974597694f, 0.974619161f,
0.974640620f, 0.974662070f, 0.974683511f, 0.974704943f, 0.974726365f,
0.974747779f, 0.974769184f, 0.974790580f, 0.974811967f, 0.974833345f,
0.974854715f, 0.974876075f, 0.974897426f, 0.974918768f, 0.974940102f,
0.974961426f, 0.974982741f, 0.975004048f, 0.975025345f, 0.975046634f,
0.975067913f, 0.975089184f, 0.975110445f, 0.975131698f, 0.975152941f,
0.975174176f, 0.975195402f, 0.975216619f, 0.975237827f, 0.975259025f,
0.975280215f, 0.975301396f, 0.975322568f, 0.975343731f, 0.975364885f,
0.975386030f, 0.975407166f, 0.975428293f, 0.975449412f, 0.975470521f,
0.975491621f, 0.975512712f, 0.975533795f, 0.975554868f, 0.975575932f,
0.975596988f, 0.975618034f, 0.975639071f, 0.975660100f, 0.975681119f,
0.975702130f, 0.975723132f, 0.975744124f, 0.975765108f, 0.975786083f,
0.975807048f, 0.975828005f, 0.975848953f, 0.975869892f, 0.975890821f,
0.975911742f, 0.975932654f, 0.975953557f, 0.975974451f, 0.975995336f,
0.976016212f, 0.976037079f, 0.976057937f, 0.976078786f, 0.976099626f,
0.976120457f, 0.976141280f, 0.976162093f, 0.976182897f, 0.976203692f,
0.976224479f, 0.976245256f, 0.976266024f, 0.976286784f, 0.976307534f,
0.976328275f, 0.976349008f, 0.976369731f, 0.976390446f, 0.976411151f,
0.976431848f, 0.976452535f, 0.976473214f, 0.976493884f, 0.976514544f,
0.976535196f, 0.976555839f, 0.976576472f, 0.976597097f, 0.976617713f,
0.976638320f, 0.976658917f, 0.976679506f, 0.976700086f, 0.976720657f,
0.976741219f, 0.976761772f, 0.976782316f, 0.976802851f, 0.976823377f,
0.976843894f, 0.976864402f, 0.976884901f, 0.976905391f, 0.976925872f,
0.976946344f, 0.976966807f, 0.976987261f, 0.977007706f, 0.977028143f,
0.977048570f, 0.977068988f, 0.977089397f, 0.977109798f, 0.977130189f,
0.977150571f, 0.977170944f, 0.977191309f, 0.977211664f, 0.977232011f,
0.977252348f, 0.977272676f, 0.977292996f, 0.977313306f, 0.977333608f,
0.977353900f, 0.977374184f, 0.977394458f, 0.977414724f, 0.977434980f,
0.977455228f, 0.977475466f, 0.977495696f, 0.977515917f, 0.977536128f,
0.977556331f, 0.977576524f, 0.977596709f, 0.977616885f, 0.977637051f,
0.977657209f, 0.977677358f, 0.977697498f, 0.977717628f, 0.977737750f,
0.977757863f, 0.977777967f, 0.977798061f, 0.977818147f, 0.977838224f,
0.977858292f, 0.977878351f, 0.977898401f, 0.977918441f, 0.977938473f,
0.977958496f, 0.977978510f, 0.977998515f, 0.978018511f, 0.978038498f,
0.978058476f, 0.978078445f, 0.978098405f, 0.978118356f, 0.978138298f,
0.978158231f, 0.978178155f, 0.978198070f, 0.978217976f, 0.978237873f,
0.978257761f, 0.978277640f, 0.978297510f, 0.978317371f, 0.978337223f,
0.978357066f, 0.978376900f, 0.978396725f, 0.978416541f, 0.978436348f,
0.978456146f, 0.978475935f, 0.978495715f, 0.978515487f, 0.978535249f,
0.978555002f, 0.978574746f, 0.978594481f, 0.978614207f, 0.978633924f,
0.978653633f, 0.978673332f, 0.978693022f, 0.978712703f, 0.978732375f,
0.978752038f, 0.978771693f, 0.978791338f, 0.978810974f, 0.978830601f,
0.978850219f, 0.978869829f, 0.978889429f, 0.978909020f, 0.978928602f,
0.978948175f, 0.978967740f, 0.978987295f, 0.979006841f, 0.979026378f,
0.979045906f, 0.979065426f, 0.979084936f, 0.979104437f, 0.979123929f,
0.979143412f, 0.979162887f, 0.979182352f, 0.979201808f, 0.979221255f,
0.979240693f, 0.979260123f, 0.979279543f, 0.979298954f, 0.979318356f,
0.979337749f, 0.979357134f, 0.979376509f, 0.979395875f, 0.979415232f,
0.979434580f, 0.979453920f, 0.979473250f, 0.979492571f, 0.979511883f,
0.979531186f, 0.979550481f, 0.979569766f, 0.979589042f, 0.979608309f,
0.979627567f, 0.979646816f, 0.979666056f, 0.979685288f, 0.979704510f,
0.979723723f, 0.979742927f, 0.979762122f, 0.979781308f, 0.979800485f,
0.979819653f, 0.979838813f, 0.979857963f, 0.979877104f, 0.979896236f,
0.979915359f, 0.979934473f, 0.979953578f, 0.979972674f, 0.979991761f,
0.980010839f, 0.980029908f, 0.980048968f, 0.980068019f, 0.980087061f,
0.980106094f, 0.980125118f, 0.980144133f, 0.980163139f, 0.980182136f,
0.980201124f, 0.980220103f, 0.980239073f, 0.980258034f, 0.980276986f,
0.980295928f, 0.980314862f, 0.980333787f, 0.980352703f, 0.980371610f,
0.980390508f, 0.980409397f, 0.980428276f, 0.980447147f, 0.980466009f,
0.980484862f, 0.980503706f, 0.980522540f, 0.980541366f, 0.980560183f,
0.980578990f, 0.980597789f, 0.980616579f, 0.980635360f, 0.980654131f,
0.980672894f, 0.980691647f, 0.980710392f, 0.980729128f, 0.980747854f,
0.980766572f, 0.980785280f, 0.980803980f, 0.980822670f, 0.980841352f,
0.980860024f, 0.980878688f, 0.980897342f, 0.980915988f, 0.980934624f,
0.980953252f, 0.980971870f, 0.980990480f, 0.981009080f, 0.981027671f,
0.981046254f, 0.981064827f, 0.981083391f, 0.981101946f, 0.981120493f,
0.981139030f, 0.981157558f, 0.981176077f, 0.981194588f, 0.981213089f,
0.981231581f, 0.981250064f, 0.981268538f, 0.981287003f, 0.981305459f,
0.981323906f, 0.981342344f, 0.981360773f, 0.981379193f, 0.981397604f,
0.981416006f, 0.981434399f, 0.981452783f, 0.981471158f, 0.981489524f,
0.981507881f, 0.981526228f, 0.981544567f, 0.981562897f, 0.981581218f,
0.981599530f, 0.981617832f, 0.981636126f, 0.981654411f, 0.981672686f,
0.981690953f, 0.981709210f, 0.981727459f, 0.981745699f, 0.981763929f,
0.981782151f, 0.981800363f, 0.981818566f, 0.981836761f, 0.981854946f,
0.981873123f, 0.981891290f, 0.981909448f, 0.981927598f, 0.981945738f,
0.981963869f, 0.981981991f, 0.982000105f, 0.982018209f, 0.982036304f,
0.982054390f, 0.982072467f, 0.982090535f, 0.982108594f, 0.982126644f,
0.982144685f, 0.982162717f, 0.982180740f, 0.982198754f, 0.982216759f,
0.982234755f, 0.982252741f, 0.982270719f, 0.982288688f, 0.982306648f,
0.982324598f, 0.982342540f, 0.982360473f, 0.982378396f, 0.982396311f,
0.982414216f, 0.982432113f, 0.982450000f, 0.982467879f, 0.982485748f,
0.982503609f, 0.982521460f, 0.982539302f, 0.982557136f, 0.982574960f,
0.982592775f, 0.982610581f, 0.982628378f, 0.982646167f, 0.982663946f,
0.982681716f, 0.982699477f, 0.982717229f, 0.982734972f, 0.982752706f,
0.982770431f, 0.982788147f, 0.982805853f, 0.982823551f, 0.982841240f,
0.982858920f, 0.982876590f, 0.982894252f, 0.982911905f, 0.982929548f,
0.982947183f, 0.982964808f, 0.982982425f, 0.983000032f, 0.983017631f,
0.983035220f, 0.983052801f, 0.983070372f, 0.983087934f, 0.983105487f,
0.983123032f, 0.983140567f, 0.983158093f, 0.983175610f, 0.983193118f,
0.983210617f, 0.983228107f, 0.983245588f, 0.983263060f, 0.983280523f,
0.983297977f, 0.983315422f, 0.983332857f, 0.983350284f, 0.983367702f,
0.983385110f, 0.983402510f, 0.983419900f, 0.983437282f, 0.983454655f,
0.983472018f, 0.983489372f, 0.983506718f, 0.983524054f, 0.983541381f,
0.983558700f, 0.983576009f, 0.983593309f, 0.983610600f, 0.983627882f,
0.983645155f, 0.983662419f, 0.983679674f, 0.983696920f, 0.983714157f,
0.983731385f, 0.983748604f, 0.983765813f, 0.983783014f, 0.983800206f,
0.983817388f, 0.983834562f, 0.983851726f, 0.983868882f, 0.983886028f,
0.983903166f, 0.983920294f, 0.983937413f, 0.983954524f, 0.983971625f,
0.983988717f, 0.984005800f, 0.984022874f, 0.984039939f, 0.984056995f,
0.984074042f, 0.984091080f, 0.984108109f, 0.984125129f, 0.984142140f,
0.984159141f, 0.984176134f, 0.984193118f, 0.984210092f, 0.984227058f,
0.984244014f, 0.984260962f, 0.984277900f, 0.984294830f, 0.984311750f,
0.984328661f, 0.984345563f, 0.984362457f, 0.984379341f, 0.984396216f,
0.984413082f, 0.984429939f, 0.984446787f, 0.984463626f, 0.984480455f,
0.984497276f, 0.984514088f, 0.984530891f, 0.984547684f, 0.984564469f,
0.984581244f, 0.984598011f, 0.984614768f, 0.984631517f, 0.984648256f,
0.984664986f, 0.984681707f, 0.984698420f, 0.984715123f, 0.984731817f,
0.984748502f, 0.984765178f, 0.984781845f, 0.984798503f, 0.984815151f,
0.984831791f, 0.984848422f, 0.984865043f, 0.984881656f, 0.984898260f,
0.984914854f, 0.984931440f, 0.984948016f, 0.984964583f, 0.984981142f,
0.984997691f, 0.985014231f, 0.985030762f, 0.985047284f, 0.985063797f,
0.985080301f, 0.985096796f, 0.985113282f, 0.985129759f, 0.985146226f,
0.985162685f, 0.985179135f, 0.985195575f, 0.985212007f, 0.985228429f,
0.985244843f, 0.985261247f, 0.985277642f, 0.985294029f, 0.985310406f,
0.985326774f, 0.985343133f, 0.985359483f, 0.985375824f, 0.985392156f,
0.985408479f, 0.985424792f, 0.985441097f, 0.985457393f, 0.985473679f,
0.985489957f, 0.985506226f, 0.985522485f, 0.985538735f, 0.985554977f,
0.985571209f, 0.985587432f, 0.985603646f, 0.985619851f, 0.985636047f,
0.985652234f, 0.985668412f, 0.985684581f, 0.985700741f, 0.985716891f,
0.985733033f, 0.985749166f, 0.985765289f, 0.985781404f, 0.985797509f,
0.985813606f, 0.985829693f, 0.985845771f, 0.985861840f, 0.985877900f,
0.985893951f, 0.985909993f, 0.985926026f, 0.985942050f, 0.985958065f,
0.985974071f, 0.985990067f, 0.986006055f, 0.986022033f, 0.986038003f,
0.986053963f, 0.986069915f, 0.986085857f, 0.986101790f, 0.986117714f,
0.986133629f, 0.986149535f, 0.986165432f, 0.986181320f, 0.986197199f,
0.986213069f, 0.986228930f, 0.986244781f, 0.986260624f, 0.986276457f,
0.986292282f, 0.986308097f, 0.986323904f, 0.986339701f, 0.986355489f,
0.986371268f, 0.986387038f, 0.986402799f, 0.986418551f, 0.986434294f,
0.986450028f, 0.986465752f, 0.986481468f, 0.986497175f, 0.986512872f,
0.986528561f, 0.986544240f, 0.986559910f, 0.986575572f, 0.986591224f,
0.986606867f, 0.986622501f, 0.986638126f, 0.986653742f, 0.986669349f,
0.986684946f, 0.986700535f, 0.986716115f, 0.986731685f, 0.986747247f,
0.986762799f, 0.986778342f, 0.986793877f, 0.986809402f, 0.986824918f,
0.986840425f, 0.986855923f, 0.986871412f, 0.986886892f, 0.986902363f,
0.986917824f, 0.986933277f, 0.986948720f, 0.986964155f, 0.986979580f,
0.986994997f, 0.987010404f, 0.987025802f, 0.987041191f, 0.987056571f,
0.987071942f, 0.987087304f, 0.987102657f, 0.987118001f, 0.987133335f,
0.987148661f, 0.987163978f, 0.987179285f, 0.987194583f, 0.987209873f,
0.987225153f, 0.987240424f, 0.987255686f, 0.987270939f, 0.987286183f,
0.987301418f, 0.987316644f, 0.987331861f, 0.987347068f, 0.987362267f,
0.987377456f, 0.987392637f, 0.987407808f, 0.987422970f, 0.987438124f,
0.987453268f, 0.987468403f, 0.987483529f, 0.987498646f, 0.987513753f,
0.987528852f, 0.987543942f, 0.987559022f, 0.987574094f, 0.987589156f,
0.987604210f, 0.987619254f, 0.987634289f, 0.987649315f, 0.987664332f,
0.987679340f, 0.987694339f, 0.987709329f, 0.987724310f, 0.987739281f,
0.987754244f, 0.987769197f, 0.987784142f, 0.987799077f, 0.987814003f,
0.987828920f, 0.987843828f, 0.987858727f, 0.987873617f, 0.987888498f,
0.987903370f, 0.987918233f, 0.987933086f, 0.987947931f, 0.987962766f,
0.987977593f, 0.987992410f, 0.988007218f, 0.988022017f, 0.988036807f,
0.988051588f, 0.988066360f, 0.988081123f, 0.988095876f, 0.988110621f,
0.988125357f, 0.988140083f, 0.988154800f, 0.988169509f, 0.988184208f,
0.988198898f, 0.988213579f, 0.988228251f, 0.988242914f, 0.988257568f,
0.988272212f, 0.988286848f, 0.988301475f, 0.988316092f, 0.988330700f,
0.988345300f, 0.988359890f, 0.988374471f, 0.988389043f, 0.988403606f,
0.988418160f, 0.988432705f, 0.988447240f, 0.988461767f, 0.988476284f,
0.988490793f, 0.988505292f, 0.988519782f, 0.988534264f, 0.988548736f,
0.988563199f, 0.988577653f, 0.988592097f, 0.988606533f, 0.988620960f,
0.988635377f, 0.988649786f, 0.988664185f, 0.988678576f, 0.988692957f,
0.988707329f, 0.988721692f, 0.988736046f, 0.988750391f, 0.988764727f,
0.988779053f, 0.988793371f, 0.988807679f, 0.988821979f, 0.988836269f,
0.988850550f, 0.988864822f, 0.988879086f, 0.988893340f, 0.988907584f,
0.988921820f, 0.988936047f, 0.988950265f, 0.988964473f, 0.988978672f,
0.988992863f, 0.989007044f, 0.989021216f, 0.989035379f, 0.989049533f,
0.989063678f, 0.989077814f, 0.989091941f, 0.989106058f, 0.989120167f,
0.989134266f, 0.989148357f, 0.989162438f, 0.989176510f, 0.989190573f,
0.989204627f, 0.989218672f, 0.989232708f, 0.989246734f, 0.989260752f,
0.989274760f, 0.989288760f, 0.989302750f, 0.989316731f, 0.989330704f,
0.989344667f, 0.989358621f, 0.989372565f, 0.989386501f, 0.989400428f,
0.989414345f, 0.989428254f, 0.989442153f, 0.989456043f, 0.989469925f,
0.989483797f, 0.989497660f, 0.989511514f, 0.989525358f, 0.989539194f,
0.989553021f, 0.989566838f, 0.989580647f, 0.989594446f, 0.989608236f,
0.989622017f, 0.989635790f, 0.989649552f, 0.989663306f, 0.989677051f,
0.989690787f, 0.989704513f, 0.989718231f, 0.989731939f, 0.989745638f,
0.989759329f, 0.989773010f, 0.989786682f, 0.989800344f, 0.989813998f,
0.989827643f, 0.989841278f, 0.989854905f, 0.989868522f, 0.989882131f,
0.989895730f, 0.989909320f, 0.989922901f, 0.989936473f, 0.989950036f,
0.989963589f, 0.989977134f, 0.989990669f, 0.990004196f, 0.990017713f,
0.990031221f, 0.990044720f, 0.990058210f, 0.990071691f, 0.990085163f,
0.990098626f, 0.990112079f, 0.990125524f, 0.990138959f, 0.990152385f,
0.990165803f, 0.990179211f, 0.990192610f, 0.990205999f, 0.990219380f,
0.990232752f, 0.990246115f, 0.990259468f, 0.990272812f, 0.990286148f,
0.990299474f, 0.990312791f, 0.990326099f, 0.990339398f, 0.990352687f,
0.990365968f, 0.990379240f, 0.990392502f, 0.990405755f, 0.990419000f,
0.990432235f, 0.990445461f, 0.990458678f, 0.990471886f, 0.990485084f,
0.990498274f, 0.990511454f, 0.990524626f, 0.990537788f, 0.990550941f,
0.990564085f, 0.990577220f, 0.990590346f, 0.990603463f, 0.990616571f,
0.990629669f, 0.990642759f, 0.990655839f, 0.990668910f, 0.990681972f,
0.990695025f, 0.990708069f, 0.990721104f, 0.990734130f, 0.990747147f,
0.990760154f, 0.990773152f, 0.990786142f, 0.990799122f, 0.990812093f,
0.990825055f, 0.990838008f, 0.990850952f, 0.990863886f, 0.990876812f,
0.990889728f, 0.990902635f, 0.990915534f, 0.990928423f, 0.990941303f,
0.990954174f, 0.990967035f, 0.990979888f, 0.990992732f, 0.991005566f,
0.991018391f, 0.991031208f, 0.991044015f, 0.991056813f, 0.991069602f,
0.991082381f, 0.991095152f, 0.991107914f, 0.991120666f, 0.991133410f,
0.991146144f, 0.991158869f, 0.991171585f, 0.991184292f, 0.991196990f,
0.991209678f, 0.991222358f, 0.991235028f, 0.991247690f, 0.991260342f,
0.991272985f, 0.991285619f, 0.991298244f, 0.991310860f, 0.991323467f,
0.991336064f, 0.991348653f, 0.991361232f, 0.991373802f, 0.991386363f,
0.991398915f, 0.991411458f, 0.991423992f, 0.991436517f, 0.991449032f,
0.991461539f, 0.991474036f, 0.991486524f, 0.991499003f, 0.991511473f,
0.991523934f, 0.991536386f, 0.991548829f, 0.991561262f, 0.991573687f,
0.991586102f, 0.991598508f, 0.991610905f, 0.991623293f, 0.991635672f,
0.991648042f, 0.991660402f, 0.991672754f, 0.991685096f, 0.991697430f,
0.991709754f, 0.991722069f, 0.991734375f, 0.991746671f, 0.991758959f,
0.991771238f, 0.991783507f, 0.991795768f, 0.991808019f, 0.991820261f,
0.991832494f, 0.991844718f, 0.991856933f, 0.991869138f, 0.991881335f,
0.991893522f, 0.991905700f, 0.991917870f, 0.991930030f, 0.991942181f,
0.991954322f, 0.991966455f, 0.991978579f, 0.991990693f, 0.992002799f,
0.992014895f, 0.992026982f, 0.992039060f, 0.992051129f, 0.992063189f,
0.992075239f, 0.992087281f, 0.992099313f, 0.992111336f, 0.992123351f,
0.992135356f, 0.992147352f, 0.992159338f, 0.992171316f, 0.992183285f,
0.992195244f, 0.992207194f, 0.992219136f, 0.992231068f, 0.992242991f,
0.992254905f, 0.992266809f, 0.992278705f, 0.992290591f, 0.992302469f,
0.992314337f, 0.992326196f, 0.992338046f, 0.992349887f, 0.992361719f,
0.992373541f, 0.992385355f, 0.992397159f, 0.992408955f, 0.992420741f,
0.992432518f, 0.992444286f, 0.992456044f, 0.992467794f, 0.992479535f,
0.992491266f, 0.992502988f, 0.992514701f, 0.992526406f, 0.992538100f,
0.992549786f, 0.992561463f, 0.992573130f, 0.992584789f, 0.992596438f,
0.992608078f, 0.992619709f, 0.992631331f, 0.992642944f, 0.992654548f,
0.992666142f, 0.992677728f, 0.992689304f, 0.992700871f, 0.992712429f,
0.992723978f, 0.992735518f, 0.992747049f, 0.992758570f, 0.992770083f,
0.992781586f, 0.992793080f, 0.992804565f, 0.992816041f, 0.992827508f,
0.992838966f, 0.992850414f, 0.992861854f, 0.992873284f, 0.992884705f,
0.992896117f, 0.992907520f, 0.992918914f, 0.992930299f, 0.992941674f,
0.992953041f, 0.992964398f, 0.992975746f, 0.992987085f, 0.992998415f,
0.993009736f, 0.993021048f, 0.993032350f, 0.993043644f, 0.993054928f,
0.993066203f, 0.993077469f, 0.993088726f, 0.993099974f, 0.993111212f,
0.993122442f, 0.993133662f, 0.993144873f, 0.993156076f, 0.993167269f,
0.993178452f, 0.993189627f, 0.993200793f, 0.993211949f, 0.993223097f,
0.993234235f, 0.993245364f, 0.993256484f, 0.993267595f, 0.993278696f,
0.993289789f, 0.993300872f, 0.993311947f, 0.993323012f, 0.993334068f,
0.993345115f, 0.993356153f, 0.993367181f, 0.993378201f, 0.993389211f,
0.993400212f, 0.993411205f, 0.993422188f, 0.993433161f, 0.993444126f,
0.993455082f, 0.993466028f, 0.993476966f, 0.993487894f, 0.993498813f,
0.993509723f, 0.993520624f, 0.993531515f, 0.993542398f, 0.993553271f,
0.993564136f, 0.993574991f, 0.993585837f, 0.993596674f, 0.993607501f,
0.993618320f, 0.993629129f, 0.993639930f, 0.993650721f, 0.993661503f,
0.993672276f, 0.993683040f, 0.993693795f, 0.993704540f, 0.993715277f,
0.993726004f, 0.993736722f, 0.993747431f, 0.993758131f, 0.993768822f,
0.993779503f, 0.993790176f, 0.993800839f, 0.993811493f, 0.993822138f,
0.993832774f, 0.993843401f, 0.993854019f, 0.993864627f, 0.993875227f,
0.993885817f, 0.993896398f, 0.993906970f, 0.993917533f, 0.993928087f,
0.993938631f, 0.993949167f, 0.993959693f, 0.993970210f, 0.993980718f,
0.993991217f, 0.994001707f, 0.994012187f, 0.994022659f, 0.994033121f,
0.994043574f, 0.994054019f, 0.994064453f, 0.994074879f, 0.994085296f,
0.994095704f, 0.994106102f, 0.994116491f, 0.994126871f, 0.994137242f,
0.994147604f, 0.994157957f, 0.994168300f, 0.994178635f, 0.994188960f,
0.994199276f, 0.994209583f, 0.994219881f, 0.994230170f, 0.994240449f,
0.994250720f, 0.994260981f, 0.994271233f, 0.994281476f, 0.994291710f,
0.994301935f, 0.994312151f, 0.994322357f, 0.994332555f, 0.994342743f,
0.994352922f, 0.994363092f, 0.994373253f, 0.994383404f, 0.994393547f,
0.994403680f, 0.994413804f, 0.994423919f, 0.994434025f, 0.994444122f,
0.994454210f, 0.994464288f, 0.994474358f, 0.994484418f, 0.994494469f,
0.994504511f, 0.994514544f, 0.994524567f, 0.994534582f, 0.994544587f,
0.994554584f, 0.994564571f, 0.994574549f, 0.994584518f, 0.994594477f,
0.994604428f, 0.994614369f, 0.994624301f, 0.994634225f, 0.994644138f,
0.994654043f, 0.994663939f, 0.994673826f, 0.994683703f, 0.994693571f,
0.994703430f, 0.994713280f, 0.994723121f, 0.994732953f, 0.994742775f,
0.994752589f, 0.994762393f, 0.994772188f, 0.994781974f, 0.994791751f,
0.994801519f, 0.994811277f, 0.994821026f, 0.994830767f, 0.994840498f,
0.994850220f, 0.994859933f, 0.994869636f, 0.994879331f, 0.994889016f,
0.994898692f, 0.994908359f, 0.994918017f, 0.994927666f, 0.994937306f,
0.994946936f, 0.994956558f, 0.994966170f, 0.994975773f, 0.994985367f,
0.994994952f, 0.995004527f, 0.995014094f, 0.995023651f, 0.995033199f,
0.995042738f, 0.995052268f, 0.995061789f, 0.995071301f, 0.995080803f,
0.995090297f, 0.995099781f, 0.995109256f, 0.995118722f, 0.995128178f,
0.995137626f, 0.995147064f, 0.995156494f, 0.995165914f, 0.995175325f,
0.995184727f, 0.995194119f, 0.995203503f, 0.995212877f, 0.995222243f,
0.995231599f, 0.995240946f, 0.995250283f, 0.995259612f, 0.995268932f,
0.995278242f, 0.995287543f, 0.995296835f, 0.995306118f, 0.995315392f,
0.995324657f, 0.995333912f, 0.995343158f, 0.995352396f, 0.995361624f,
0.995370843f, 0.995380052f, 0.995389253f, 0.995398444f, 0.995407627f,
0.995416800f, 0.995425964f, 0.995435119f, 0.995444264f, 0.995453401f,
0.995462528f, 0.995471646f, 0.995480755f, 0.995489855f, 0.995498946f,
0.995508028f, 0.995517100f, 0.995526164f, 0.995535218f, 0.995544263f,
0.995553299f, 0.995562325f, 0.995571343f, 0.995580352f, 0.995589351f,
0.995598341f, 0.995607322f, 0.995616294f, 0.995625256f, 0.995634210f,
0.995643154f, 0.995652089f, 0.995661016f, 0.995669932f, 0.995678840f,
0.995687739f, 0.995696628f, 0.995705509f, 0.995714380f, 0.995723242f,
0.995732095f, 0.995740938f, 0.995749773f, 0.995758598f, 0.995767414f,
0.995776222f, 0.995785019f, 0.995793808f, 0.995802588f, 0.995811358f,
0.995820120f, 0.995828872f, 0.995837615f, 0.995846349f, 0.995855073f,
0.995863789f, 0.995872495f, 0.995881193f, 0.995889881f, 0.995898560f,
0.995907229f, 0.995915890f, 0.995924542f, 0.995933184f, 0.995941817f,
0.995950441f, 0.995959056f, 0.995967662f, 0.995976258f, 0.995984846f,
0.995993424f, 0.996001993f, 0.996010553f, 0.996019104f, 0.996027645f,
0.996036178f, 0.996044701f, 0.996053215f, 0.996061720f, 0.996070216f,
0.996078703f, 0.996087180f, 0.996095648f, 0.996104108f, 0.996112558f,
0.996120999f, 0.996129430f, 0.996137853f, 0.996146266f, 0.996154671f,
0.996163066f, 0.996171452f, 0.996179829f, 0.996188196f, 0.996196555f,
0.996204904f, 0.996213244f, 0.996221575f, 0.996229897f, 0.996238210f,
0.996246513f, 0.996254808f, 0.996263093f, 0.996271369f, 0.996279636f,
0.996287894f, 0.996296142f, 0.996304382f, 0.996312612f, 0.996320833f,
0.996329045f, 0.996337248f, 0.996345442f, 0.996353626f, 0.996361802f,
0.996369968f, 0.996378125f, 0.996386273f, 0.996394411f, 0.996402541f,
0.996410661f, 0.996418773f, 0.996426875f, 0.996434968f, 0.996443051f,
0.996451126f, 0.996459191f, 0.996467248f, 0.996475295f, 0.996483333f,
0.996491362f, 0.996499381f, 0.996507392f, 0.996515393f, 0.996523385f,
0.996531368f, 0.996539342f, 0.996547307f, 0.996555262f, 0.996563209f,
0.996571146f, 0.996579074f, 0.996586993f, 0.996594902f, 0.996602803f,
0.996610694f, 0.996618577f, 0.996626450f, 0.996634314f, 0.996642168f,
0.996650014f, 0.996657850f, 0.996665678f, 0.996673496f, 0.996681305f,
0.996689105f, 0.996696895f, 0.996704677f, 0.996712449f, 0.996720212f,
0.996727966f, 0.996735711f, 0.996743447f, 0.996751173f, 0.996758890f,
0.996766599f, 0.996774298f, 0.996781987f, 0.996789668f, 0.996797340f,
0.996805002f, 0.996812655f, 0.996820299f, 0.996827934f, 0.996835560f,
0.996843176f, 0.996850784f, 0.996858382f, 0.996865971f, 0.996873551f,
0.996881122f, 0.996888683f, 0.996896236f, 0.996903779f, 0.996911313f,
0.996918838f, 0.996926354f, 0.996933860f, 0.996941358f, 0.996948846f,
0.996956325f, 0.996963795f, 0.996971256f, 0.996978707f, 0.996986150f,
0.996993583f, 0.997001007f, 0.997008422f, 0.997015828f, 0.997023225f,
0.997030612f, 0.997037990f, 0.997045360f, 0.997052720f, 0.997060070f,
0.997067412f, 0.997074744f, 0.997082068f, 0.997089382f, 0.997096687f,
0.997103983f, 0.997111269f, 0.997118547f, 0.997125815f, 0.997133074f,
0.997140324f, 0.997147565f, 0.997154797f, 0.997162019f, 0.997169233f,
0.997176437f, 0.997183632f, 0.997190818f, 0.997197994f, 0.997205162f,
0.997212320f, 0.997219469f, 0.997226609f, 0.997233740f, 0.997240862f,
0.997247974f, 0.997255078f, 0.997262172f, 0.997269257f, 0.997276333f,
0.997283399f, 0.997290457f, 0.997297505f, 0.997304544f, 0.997311574f,
0.997318595f, 0.997325607f, 0.997332609f, 0.997339602f, 0.997346587f,
0.997353562f, 0.997360527f, 0.997367484f, 0.997374432f, 0.997381370f,
0.997388299f, 0.997395219f, 0.997402130f, 0.997409032f, 0.997415924f,
0.997422807f, 0.997429682f, 0.997436546f, 0.997443402f, 0.997450249f,
0.997457086f, 0.997463915f, 0.997470734f, 0.997477544f, 0.997484345f,
0.997491136f, 0.997497919f, 0.997504692f, 0.997511456f, 0.997518211f,
0.997524957f, 0.997531694f, 0.997538421f, 0.997545139f, 0.997551848f,
0.997558548f, 0.997565239f, 0.997571921f, 0.997578593f, 0.997585256f,
0.997591910f, 0.997598555f, 0.997605191f, 0.997611818f, 0.997618435f,
0.997625043f, 0.997631642f, 0.997638232f, 0.997644813f, 0.997651385f,
0.997657947f, 0.997664500f, 0.997671044f, 0.997677579f, 0.997684105f,
0.997690621f, 0.997697129f, 0.997703627f, 0.997710116f, 0.997716596f,
0.997723067f, 0.997729528f, 0.997735981f, 0.997742424f, 0.997748858f,
0.997755283f, 0.997761698f, 0.997768105f, 0.997774502f, 0.997780890f,
0.997787269f, 0.997793639f, 0.997800000f, 0.997806351f, 0.997812693f,
0.997819026f, 0.997825350f, 0.997831665f, 0.997837971f, 0.997844267f,
0.997850554f, 0.997856833f, 0.997863101f, 0.997869361f, 0.997875612f,
0.997881853f, 0.997888085f, 0.997894309f, 0.997900522f, 0.997906727f,
0.997912923f, 0.997919109f, 0.997925286f, 0.997931454f, 0.997937613f,
0.997943763f, 0.997949903f, 0.997956035f, 0.997962157f, 0.997968270f,
0.997974374f, 0.997980468f, 0.997986554f, 0.997992630f, 0.997998697f,
0.998004755f, 0.998010804f, 0.998016843f, 0.998022874f, 0.998028895f,
0.998034907f, 0.998040910f, 0.998046904f, 0.998052888f, 0.998058864f,
0.998064830f, 0.998070787f, 0.998076735f, 0.998082673f, 0.998088603f,
0.998094523f, 0.998100434f, 0.998106336f, 0.998112229f, 0.998118113f,
0.998123987f, 0.998129853f, 0.998135709f, 0.998141556f, 0.998147393f,
0.998153222f, 0.998159041f, 0.998164852f, 0.998170653f, 0.998176445f,
0.998182227f, 0.998188001f, 0.998193765f, 0.998199521f, 0.998205267f,
0.998211003f, 0.998216731f, 0.998222450f, 0.998228159f, 0.998233859f,
0.998239550f, 0.998245232f, 0.998250904f, 0.998256568f, 0.998262222f,
0.998267867f, 0.998273503f, 0.998279130f, 0.998284747f, 0.998290356f,
0.998295955f, 0.998301545f, 0.998307126f, 0.998312697f, 0.998318260f,
0.998323813f, 0.998329357f, 0.998334892f, 0.998340418f, 0.998345935f,
0.998351442f, 0.998356941f, 0.998362430f, 0.998367910f, 0.998373380f,
0.998378842f, 0.998384294f, 0.998389737f, 0.998395171f, 0.998400596f,
0.998406012f, 0.998411418f, 0.998416816f, 0.998422204f, 0.998427583f,
0.998432953f, 0.998438313f, 0.998443665f, 0.998449007f, 0.998454340f,
0.998459664f, 0.998464979f, 0.998470284f, 0.998475581f, 0.998480868f,
0.998486146f, 0.998491415f, 0.998496674f, 0.998501925f, 0.998507166f,
0.998512398f, 0.998517621f, 0.998522835f, 0.998528039f, 0.998533235f,
0.998538421f, 0.998543598f, 0.998548766f, 0.998553925f, 0.998559074f,
0.998564215f, 0.998569346f, 0.998574468f, 0.998579581f, 0.998584684f,
0.998589779f, 0.998594864f, 0.998599940f, 0.998605007f, 0.998610065f,
0.998615113f, 0.998620152f, 0.998625183f, 0.998630204f, 0.998635216f,
0.998640218f, 0.998645212f, 0.998650196f, 0.998655171f, 0.998660137f,
0.998665094f, 0.998670041f, 0.998674980f, 0.998679909f, 0.998684829f,
0.998689740f, 0.998694642f, 0.998699534f, 0.998704417f, 0.998709291f,
0.998714156f, 0.998719012f, 0.998723859f, 0.998728696f, 0.998733524f,
0.998738344f, 0.998743153f, 0.998747954f, 0.998752746f, 0.998757528f,
0.998762301f, 0.998767065f, 0.998771820f, 0.998776566f, 0.998781302f,
0.998786029f, 0.998790747f, 0.998795456f, 0.998800156f, 0.998804846f,
0.998809528f, 0.998814200f, 0.998818863f, 0.998823517f, 0.998828161f,
0.998832797f, 0.998837423f, 0.998842040f, 0.998846648f, 0.998851247f,
0.998855836f, 0.998860417f, 0.998864988f, 0.998869550f, 0.998874103f,
0.998878646f, 0.998883181f, 0.998887706f, 0.998892222f, 0.998896729f,
0.998901227f, 0.998905715f, 0.998910195f, 0.998914665f, 0.998919126f,
0.998923578f, 0.998928020f, 0.998932454f, 0.998936878f, 0.998941293f,
0.998945699f, 0.998950096f, 0.998954483f, 0.998958862f, 0.998963231f,
0.998967591f, 0.998971942f, 0.998976283f, 0.998980616f, 0.998984939f,
0.998989253f, 0.998993558f, 0.998997854f, 0.999002140f, 0.999006418f,
0.999010686f, 0.999014945f, 0.999019195f, 0.999023435f, 0.999027667f,
0.999031889f, 0.999036102f, 0.999040306f, 0.999044501f, 0.999048686f,
0.999052863f, 0.999057030f, 0.999061188f, 0.999065336f, 0.999069476f,
0.999073607f, 0.999077728f, 0.999081840f, 0.999085943f, 0.999090036f,
0.999094121f, 0.999098196f, 0.999102262f, 0.999106319f, 0.999110367f,
0.999114406f, 0.999118435f, 0.999122455f, 0.999126466f, 0.999130468f,
0.999134461f, 0.999138444f, 0.999142419f, 0.999146384f, 0.999150340f,
0.999154287f, 0.999158224f, 0.999162153f, 0.999166072f, 0.999169982f,
0.999173883f, 0.999177774f, 0.999181657f, 0.999185530f, 0.999189394f,
0.999193249f, 0.999197095f, 0.999200931f, 0.999204759f, 0.999208577f,
0.999212386f, 0.999216186f, 0.999219976f, 0.999223758f, 0.999227530f,
0.999231293f, 0.999235047f, 0.999238792f, 0.999242527f, 0.999246253f,
0.999249971f, 0.999253679f, 0.999257377f, 0.999261067f, 0.999264747f,
0.999268419f, 0.999272081f, 0.999275733f, 0.999279377f, 0.999283012f,
0.999286637f, 0.999290253f, 0.999293860f, 0.999297458f, 0.999301046f,
0.999304626f, 0.999308196f, 0.999311757f, 0.999315309f, 0.999318851f,
0.999322385f, 0.999325909f, 0.999329424f, 0.999332930f, 0.999336426f,
0.999339914f, 0.999343392f, 0.999346861f, 0.999350321f, 0.999353772f,
0.999357214f, 0.999360646f, 0.999364069f, 0.999367483f, 0.999370888f,
0.999374284f, 0.999377670f, 0.999381048f, 0.999384416f, 0.999387775f,
0.999391124f, 0.999394465f, 0.999397796f, 0.999401118f, 0.999404431f,
0.999407735f, 0.999411030f, 0.999414315f, 0.999417591f, 0.999420859f,
0.999424116f, 0.999427365f, 0.999430605f, 0.999433835f, 0.999437056f,
0.999440268f, 0.999443471f, 0.999446664f, 0.999449849f, 0.999453024f,
0.999456190f, 0.999459347f, 0.999462494f, 0.999465633f, 0.999468762f,
0.999471882f, 0.999474993f, 0.999478094f, 0.999481187f, 0.999484270f,
0.999487344f, 0.999490409f, 0.999493465f, 0.999496512f, 0.999499549f,
0.999502577f, 0.999505596f, 0.999508606f, 0.999511607f, 0.999514598f,
0.999517580f, 0.999520553f, 0.999523517f, 0.999526472f, 0.999529418f,
0.999532354f, 0.999535281f, 0.999538199f, 0.999541108f, 0.999544007f,
0.999546898f, 0.999549779f, 0.999552651f, 0.999555514f, 0.999558367f,
0.999561212f, 0.999564047f, 0.999566873f, 0.999569690f, 0.999572498f,
0.999575296f, 0.999578085f, 0.999580865f, 0.999583636f, 0.999586398f,
0.999589151f, 0.999591894f, 0.999594628f, 0.999597353f, 0.999600069f,
0.999602776f, 0.999605473f, 0.999608161f, 0.999610840f, 0.999613510f,
0.999616171f, 0.999618822f, 0.999621465f, 0.999624098f, 0.999626722f,
0.999629337f, 0.999631942f, 0.999634538f, 0.999637126f, 0.999639704f,
0.999642272f, 0.999644832f, 0.999647382f, 0.999649924f, 0.999652456f,
0.999654979f, 0.999657492f, 0.999659997f, 0.999662492f, 0.999664978f,
0.999667455f, 0.999669923f, 0.999672381f, 0.999674831f, 0.999677271f,
0.999679702f, 0.999682124f, 0.999684536f, 0.999686940f, 0.999689334f,
0.999691719f, 0.999694095f, 0.999696461f, 0.999698819f, 0.999701167f,
0.999703506f, 0.999705836f, 0.999708157f, 0.999710468f, 0.999712770f,
0.999715064f, 0.999717348f, 0.999719622f, 0.999721888f, 0.999724144f,
0.999726391f, 0.999728629f, 0.999730858f, 0.999733078f, 0.999735288f,
0.999737489f, 0.999739682f, 0.999741864f, 0.999744038f, 0.999746203f,
0.999748358f, 0.999750504f, 0.999752641f, 0.999754769f, 0.999756887f,
0.999758996f, 0.999761097f, 0.999763188f, 0.999765269f, 0.999767342f,
0.999769405f, 0.999771460f, 0.999773505f, 0.999775540f, 0.999777567f,
0.999779584f, 0.999781593f, 0.999783592f, 0.999785582f, 0.999787562f,
0.999789534f, 0.999791496f, 0.999793449f, 0.999795393f, 0.999797328f,
0.999799254f, 0.999801170f, 0.999803077f, 0.999804975f, 0.999806864f,
0.999808743f, 0.999810614f, 0.999812475f, 0.999814327f, 0.999816170f,
0.999818004f, 0.999819828f, 0.999821643f, 0.999823449f, 0.999825246f,
0.999827034f, 0.999828812f, 0.999830582f, 0.999832342f, 0.999834093f,
0.999835835f, 0.999837567f, 0.999839291f, 0.999841005f, 0.999842710f,
0.999844405f, 0.999846092f, 0.999847770f, 0.999849438f, 0.999851097f,
0.999852747f, 0.999854387f, 0.999856019f, 0.999857641f, 0.999859254f,
0.999860858f, 0.999862453f, 0.999864038f, 0.999865615f, 0.999867182f,
0.999868740f, 0.999870288f, 0.999871828f, 0.999873358f, 0.999874879f,
0.999876391f, 0.999877894f, 0.999879388f, 0.999880872f, 0.999882347f,
0.999883813f, 0.999885270f, 0.999886718f, 0.999888156f, 0.999889586f,
0.999891006f, 0.999892417f, 0.999893818f, 0.999895211f, 0.999896594f,
0.999897968f, 0.999899333f, 0.999900689f, 0.999902036f, 0.999903373f,
0.999904701f, 0.999906020f, 0.999907330f, 0.999908630f, 0.999909922f,
0.999911204f, 0.999912477f, 0.999913741f, 0.999914996f, 0.999916241f,
0.999917477f, 0.999918704f, 0.999919922f, 0.999921131f, 0.999922330f,
0.999923521f, 0.999924702f, 0.999925874f, 0.999927036f, 0.999928190f,
0.999929334f, 0.999930470f, 0.999931596f, 0.999932712f, 0.999933820f,
0.999934918f, 0.999936007f, 0.999937087f, 0.999938158f, 0.999939220f,
0.999940272f, 0.999941316f, 0.999942350f, 0.999943375f, 0.999944390f,
0.999945397f, 0.999946394f, 0.999947382f, 0.999948361f, 0.999949331f,
0.999950291f, 0.999951243f, 0.999952185f, 0.999953118f, 0.999954041f,
0.999954956f, 0.999955861f, 0.999956758f, 0.999957645f, 0.999958522f,
0.999959391f, 0.999960250f, 0.999961101f, 0.999961942f, 0.999962774f,
0.999963596f, 0.999964410f, 0.999965214f, 0.999966009f, 0.999966795f,
0.999967572f, 0.999968339f, 0.999969097f, 0.999969846f, 0.999970586f,
0.999971317f, 0.999972039f, 0.999972751f, 0.999973454f, 0.999974148f,
0.999974833f, 0.999975509f, 0.999976175f, 0.999976832f, 0.999977480f,
0.999978119f, 0.999978749f, 0.999979369f, 0.999979980f, 0.999980582f,
0.999981175f, 0.999981759f, 0.999982333f, 0.999982899f, 0.999983455f,
0.999984002f, 0.999984539f, 0.999985068f, 0.999985587f, 0.999986097f,
0.999986598f, 0.999987090f, 0.999987573f, 0.999988046f, 0.999988510f,
0.999988965f, 0.999989411f, 0.999989848f, 0.999990275f, 0.999990693f,
0.999991102f, 0.999991502f, 0.999991893f, 0.999992274f, 0.999992647f,
0.999993010f, 0.999993364f, 0.999993708f, 0.999994044f, 0.999994370f,
0.999994687f, 0.999994995f, 0.999995294f, 0.999995583f, 0.999995864f,
0.999996135f, 0.999996397f, 0.999996650f, 0.999996893f, 0.999997128f,
0.999997353f, 0.999997569f, 0.999997776f, 0.999997973f, 0.999998162f,
0.999998341f, 0.999998511f, 0.999998672f, 0.999998823f, 0.999998966f,
0.999999099f, 0.999999223f, 0.999999338f, 0.999999444f, 0.999999540f,
0.999999628f, 0.999999706f, 0.999999775f, 0.999999835f, 0.999999885f,
0.999999926f, 0.999999959f, 0.999999982f, 0.999999995f, 1.000000000f};
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/mpc_osqp.cc | /******************************************************************************
* Copyright 2019 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/mpc_osqp.h"
namespace apollo {
namespace common {
namespace math {
MpcOsqp::MpcOsqp(const Eigen::MatrixXd &matrix_a,
const Eigen::MatrixXd &matrix_b,
const Eigen::MatrixXd &matrix_q,
const Eigen::MatrixXd &matrix_r,
const Eigen::MatrixXd &matrix_initial_x,
const Eigen::MatrixXd &matrix_u_lower,
const Eigen::MatrixXd &matrix_u_upper,
const Eigen::MatrixXd &matrix_x_lower,
const Eigen::MatrixXd &matrix_x_upper,
const Eigen::MatrixXd &matrix_x_ref, const int max_iter,
const int horizon, const double eps_abs)
: matrix_a_(matrix_a),
matrix_b_(matrix_b),
matrix_q_(matrix_q),
matrix_r_(matrix_r),
matrix_initial_x_(matrix_initial_x),
matrix_u_lower_(matrix_u_lower),
matrix_u_upper_(matrix_u_upper),
matrix_x_lower_(matrix_x_lower),
matrix_x_upper_(matrix_x_upper),
matrix_x_ref_(matrix_x_ref),
max_iteration_(max_iter),
horizon_(horizon),
eps_abs_(eps_abs) {
state_dim_ = matrix_b.rows();
control_dim_ = matrix_b.cols();
ADEBUG << "state_dim" << state_dim_;
ADEBUG << "control_dim_" << control_dim_;
num_param_ = state_dim_ * (horizon_ + 1) + control_dim_ * horizon_;
}
void MpcOsqp::CalculateKernel(std::vector<c_float> *P_data,
std::vector<c_int> *P_indices,
std::vector<c_int> *P_indptr) {
// col1:(row,val),...; col2:(row,val),....; ...
std::vector<std::vector<std::pair<c_int, c_float>>> columns;
columns.resize(num_param_);
size_t value_index = 0;
// state and terminal state
for (size_t i = 0; i <= horizon_; ++i) {
for (size_t j = 0; j < state_dim_; ++j) {
// (row, val)
columns[i * state_dim_ + j].emplace_back(i * state_dim_ + j,
matrix_q_(j, j));
++value_index;
}
}
// control
const size_t state_total_dim = state_dim_ * (horizon_ + 1);
for (size_t i = 0; i < horizon_; ++i) {
for (size_t j = 0; j < control_dim_; ++j) {
// (row, val)
columns[i * control_dim_ + j + state_total_dim].emplace_back(
state_total_dim + i * control_dim_ + j, matrix_r_(j, j));
++value_index;
}
}
CHECK_EQ(value_index, num_param_);
int ind_p = 0;
for (size_t i = 0; i < num_param_; ++i) {
// TODO(SHU) Check this
P_indptr->emplace_back(ind_p);
for (const auto &row_data_pair : columns[i]) {
P_data->emplace_back(row_data_pair.second); // val
P_indices->emplace_back(row_data_pair.first); // row
++ind_p;
}
}
P_indptr->emplace_back(ind_p);
}
// reference is always zero
void MpcOsqp::CalculateGradient() {
// populate the gradient vector
gradient_ = Eigen::VectorXd::Zero(
state_dim_ * (horizon_ + 1) + control_dim_ * horizon_, 1);
for (size_t i = 0; i < horizon_ + 1; i++) {
gradient_.block(i * state_dim_, 0, state_dim_, 1) =
-1.0 * matrix_q_ * matrix_x_ref_;
}
ADEBUG << "Gradient_mat";
ADEBUG << gradient_;
}
// equality constraints x(k+1) = A*x(k)
void MpcOsqp::CalculateEqualityConstraint(std::vector<c_float> *A_data,
std::vector<c_int> *A_indices,
std::vector<c_int> *A_indptr) {
static constexpr double kEpsilon = 1e-6;
// block matrix
Eigen::MatrixXd matrix_constraint = Eigen::MatrixXd::Zero(
state_dim_ * (horizon_ + 1) + state_dim_ * (horizon_ + 1) +
control_dim_ * horizon_,
state_dim_ * (horizon_ + 1) + control_dim_ * horizon_);
Eigen::MatrixXd state_identity_mat = Eigen::MatrixXd::Identity(
state_dim_ * (horizon_ + 1), state_dim_ * (horizon_ + 1));
ADEBUG << "state_identity_mat" << state_identity_mat;
matrix_constraint.block(0, 0, state_dim_ * (horizon_ + 1),
state_dim_ * (horizon_ + 1)) =
-1 * state_identity_mat;
ADEBUG << "matrix_constraint";
ADEBUG << matrix_constraint;
Eigen::MatrixXd control_identity_mat =
Eigen::MatrixXd::Identity(control_dim_, control_dim_);
for (size_t i = 0; i < horizon_; i++) {
matrix_constraint.block((i + 1) * state_dim_, i * state_dim_, state_dim_,
state_dim_) = matrix_a_;
}
ADEBUG << "matrix_constraint with A";
ADEBUG << matrix_constraint;
for (size_t i = 0; i < horizon_; i++) {
matrix_constraint.block((i + 1) * state_dim_,
i * control_dim_ + (horizon_ + 1) * state_dim_,
state_dim_, control_dim_) = matrix_b_;
}
ADEBUG << "matrix_constraint with B";
ADEBUG << matrix_constraint;
Eigen::MatrixXd all_identity_mat =
Eigen::MatrixXd::Identity(num_param_, num_param_);
matrix_constraint.block(state_dim_ * (horizon_ + 1), 0, num_param_,
num_param_) = all_identity_mat;
ADEBUG << "matrix_constraint with I";
ADEBUG << matrix_constraint;
std::vector<std::vector<std::pair<c_int, c_float>>> columns;
columns.resize(num_param_ + 1);
int value_index = 0;
// state and terminal state
for (size_t i = 0; i < num_param_; ++i) { // col
for (size_t j = 0; j < num_param_ + state_dim_ * (horizon_ + 1);
++j) // row
if (std::fabs(matrix_constraint(j, i)) > kEpsilon) {
// (row, val)
columns[i].emplace_back(j, matrix_constraint(j, i));
++value_index;
}
}
ADEBUG << "value_index";
ADEBUG << value_index;
int ind_A = 0;
for (size_t i = 0; i < num_param_; ++i) {
A_indptr->emplace_back(ind_A);
for (const auto &row_data_pair : columns[i]) {
A_data->emplace_back(row_data_pair.second); // value
A_indices->emplace_back(row_data_pair.first); // row
++ind_A;
}
}
A_indptr->emplace_back(ind_A);
}
void MpcOsqp::CalculateConstraintVectors() {
// evaluate the lower and the upper inequality vectors
Eigen::VectorXd lowerInequality = Eigen::MatrixXd::Zero(
state_dim_ * (horizon_ + 1) + control_dim_ * horizon_, 1);
Eigen::VectorXd upperInequality = Eigen::MatrixXd::Zero(
state_dim_ * (horizon_ + 1) + control_dim_ * horizon_, 1);
for (size_t i = 0; i < horizon_; i++) {
lowerInequality.block(control_dim_ * i + state_dim_ * (horizon_ + 1), 0,
control_dim_, 1) = matrix_u_lower_;
upperInequality.block(control_dim_ * i + state_dim_ * (horizon_ + 1), 0,
control_dim_, 1) = matrix_u_upper_;
}
ADEBUG << " matrix_u_lower_";
for (size_t i = 0; i < horizon_ + 1; i++) {
lowerInequality.block(state_dim_ * i, 0, state_dim_, 1) = matrix_x_lower_;
upperInequality.block(state_dim_ * i, 0, state_dim_, 1) = matrix_x_upper_;
}
ADEBUG << " matrix_x_lower_";
// evaluate the lower and the upper equality vectors
Eigen::VectorXd lowerEquality =
Eigen::MatrixXd::Zero(state_dim_ * (horizon_ + 1), 1);
Eigen::VectorXd upperEquality;
lowerEquality.block(0, 0, state_dim_, 1) = -1 * matrix_initial_x_;
upperEquality = lowerEquality;
lowerEquality = lowerEquality;
ADEBUG << " matrix_initial_x_";
// merge inequality and equality vectors
lowerBound_ = Eigen::MatrixXd::Zero(
2 * state_dim_ * (horizon_ + 1) + control_dim_ * horizon_, 1);
lowerBound_ << lowerEquality, lowerInequality;
ADEBUG << " lowerBound_ ";
upperBound_ = Eigen::MatrixXd::Zero(
2 * state_dim_ * (horizon_ + 1) + control_dim_ * horizon_, 1);
upperBound_ << upperEquality, upperInequality;
ADEBUG << " upperBound_";
}
OSQPSettings *MpcOsqp::Settings() {
// default setting
OSQPSettings *settings =
reinterpret_cast<OSQPSettings *>(c_malloc(sizeof(OSQPSettings)));
if (settings == nullptr) {
return nullptr;
} else {
osqp_set_default_settings(settings);
settings->polish = true;
settings->scaled_termination = true;
settings->verbose = false;
settings->max_iter = max_iteration_;
settings->eps_abs = eps_abs_;
return settings;
}
}
OSQPData *MpcOsqp::Data() {
OSQPData *data = reinterpret_cast<OSQPData *>(c_malloc(sizeof(OSQPData)));
size_t kernel_dim = state_dim_ * (horizon_ + 1) + control_dim_ * horizon_;
size_t num_affine_constraint =
2 * state_dim_ * (horizon_ + 1) + control_dim_ * horizon_;
if (data == nullptr) {
return nullptr;
} else {
data->n = kernel_dim;
data->m = num_affine_constraint;
std::vector<c_float> P_data;
std::vector<c_int> P_indices;
std::vector<c_int> P_indptr;
ADEBUG << "before CalculateKernel";
CalculateKernel(&P_data, &P_indices, &P_indptr);
ADEBUG << "CalculateKernel done";
data->P =
csc_matrix(kernel_dim, kernel_dim, P_data.size(), CopyData(P_data),
CopyData(P_indices), CopyData(P_indptr));
ADEBUG << "Get P matrix";
data->q = gradient_.data();
ADEBUG << "before CalculateEqualityConstraint";
std::vector<c_float> A_data;
std::vector<c_int> A_indices;
std::vector<c_int> A_indptr;
CalculateEqualityConstraint(&A_data, &A_indices, &A_indptr);
ADEBUG << "CalculateEqualityConstraint done";
data->A =
csc_matrix(state_dim_ * (horizon_ + 1) + state_dim_ * (horizon_ + 1) +
control_dim_ * horizon_,
kernel_dim, A_data.size(), CopyData(A_data),
CopyData(A_indices), CopyData(A_indptr));
ADEBUG << "Get A matrix";
data->l = lowerBound_.data();
data->u = upperBound_.data();
return data;
}
}
void MpcOsqp::FreeData(OSQPData *data) {
c_free(data->A);
c_free(data->P);
c_free(data);
}
bool MpcOsqp::Solve(std::vector<double> *control_cmd) {
ADEBUG << "Before Calc Gradient";
CalculateGradient();
ADEBUG << "After Calc Gradient";
CalculateConstraintVectors();
ADEBUG << "MPC2Matrix";
OSQPData *data = Data();
ADEBUG << "OSQP data done";
ADEBUG << "OSQP data n" << data->n;
ADEBUG << "OSQP data m" << data->m;
for (int i = 0; i < data->n; ++i) {
ADEBUG << "OSQP data q" << i << ":" << (data->q)[i];
}
ADEBUG << "OSQP data l" << data->l;
for (int i = 0; i < data->m; ++i) {
ADEBUG << "OSQP data l" << i << ":" << (data->l)[i];
}
ADEBUG << "OSQP data u" << data->u;
for (int i = 0; i < data->m; ++i) {
ADEBUG << "OSQP data u" << i << ":" << (data->u)[i];
}
OSQPSettings *settings = Settings();
ADEBUG << "OSQP setting done";
OSQPWorkspace *osqp_workspace = nullptr;
// osqp_setup(&osqp_workspace, data, settings);
osqp_workspace = osqp_setup(data, settings);
ADEBUG << "OSQP workspace ready";
osqp_solve(osqp_workspace);
auto status = osqp_workspace->info->status_val;
ADEBUG << "status:" << status;
// check status
if (status < 0 || (status != 1 && status != 2)) {
AERROR << "failed optimization status:\t" << osqp_workspace->info->status;
osqp_cleanup(osqp_workspace);
FreeData(data);
c_free(settings);
return false;
} else if (osqp_workspace->solution == nullptr) {
AERROR << "The solution from OSQP is nullptr";
osqp_cleanup(osqp_workspace);
FreeData(data);
c_free(settings);
return false;
}
size_t first_control = state_dim_ * (horizon_ + 1);
for (size_t i = 0; i < control_dim_; ++i) {
control_cmd->at(i) = osqp_workspace->solution->x[i + first_control];
ADEBUG << "control_cmd:" << i << ":" << control_cmd->at(i);
}
// Cleanup
osqp_cleanup(osqp_workspace);
FreeData(data);
c_free(settings);
return true;
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/math_utils.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/math_utils.h"
#include <cmath>
#include <utility>
namespace apollo {
namespace common {
namespace math {
double Sqr(const double x) { return x * x; }
double CrossProd(const Vec2d& start_point, const Vec2d& end_point_1,
const Vec2d& end_point_2) {
return (end_point_1 - start_point).CrossProd(end_point_2 - start_point);
}
double InnerProd(const Vec2d& start_point, const Vec2d& end_point_1,
const Vec2d& end_point_2) {
return (end_point_1 - start_point).InnerProd(end_point_2 - start_point);
}
double CrossProd(const double x0, const double y0, const double x1,
const double y1) {
return x0 * y1 - x1 * y0;
}
double InnerProd(const double x0, const double y0, const double x1,
const double y1) {
return x0 * x1 + y0 * y1;
}
double WrapAngle(const double angle) {
const double new_angle = std::fmod(angle, M_PI * 2.0);
return new_angle < 0 ? new_angle + M_PI * 2.0 : new_angle;
}
double NormalizeAngle(const double angle) {
double a = std::fmod(angle + M_PI, 2.0 * M_PI);
if (a < 0.0) {
a += (2.0 * M_PI);
}
return a - M_PI;
}
double AngleDiff(const double from, const double to) {
return NormalizeAngle(to - from);
}
int RandomInt(const int s, const int t, unsigned int rand_seed) {
if (s >= t) {
return s;
}
return s + rand_r(&rand_seed) % (t - s + 1);
}
double RandomDouble(const double s, const double t, unsigned int rand_seed) {
return s + (t - s) / 16383.0 * (rand_r(&rand_seed) & 16383);
}
// Gaussian
double Gaussian(const double u, const double std, const double x) {
return (1.0 / std::sqrt(2 * M_PI * std * std)) *
std::exp(-(x - u) * (x - u) / (2 * std * std));
}
Eigen::Vector2d RotateVector2d(const Eigen::Vector2d& v_in,
const double theta) {
const double cos_theta = std::cos(theta);
const double sin_theta = std::sin(theta);
auto x = cos_theta * v_in.x() - sin_theta * v_in.y();
auto y = sin_theta * v_in.x() + cos_theta * v_in.y();
return {x, y};
}
std::pair<double, double> Cartesian2Polar(double x, double y) {
double r = std::sqrt(x * x + y * y);
double theta = std::atan2(y, x);
return std::make_pair(r, theta);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/cartesian_frenet_conversion.cc | /******************************************************************************
* Copyright 2018 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/cartesian_frenet_conversion.h"
#include <cmath>
#include "cyber/common/log.h"
#include "modules/common/math/math_utils.h"
namespace apollo {
namespace common {
namespace math {
void CartesianFrenetConverter::cartesian_to_frenet(
const double rs, const double rx, const double ry, const double rtheta,
const double rkappa, const double rdkappa, const double x, const double y,
const double v, const double a, const double theta, const double kappa,
std::array<double, 3>* const ptr_s_condition,
std::array<double, 3>* const ptr_d_condition) {
const double dx = x - rx;
const double dy = y - ry;
const double cos_theta_r = std::cos(rtheta);
const double sin_theta_r = std::sin(rtheta);
const double cross_rd_nd = cos_theta_r * dy - sin_theta_r * dx;
ptr_d_condition->at(0) =
std::copysign(std::sqrt(dx * dx + dy * dy), cross_rd_nd);
const double delta_theta = theta - rtheta;
const double tan_delta_theta = std::tan(delta_theta);
const double cos_delta_theta = std::cos(delta_theta);
const double one_minus_kappa_r_d = 1 - rkappa * ptr_d_condition->at(0);
ptr_d_condition->at(1) = one_minus_kappa_r_d * tan_delta_theta;
const double kappa_r_d_prime =
rdkappa * ptr_d_condition->at(0) + rkappa * ptr_d_condition->at(1);
ptr_d_condition->at(2) =
-kappa_r_d_prime * tan_delta_theta +
one_minus_kappa_r_d / cos_delta_theta / cos_delta_theta *
(kappa * one_minus_kappa_r_d / cos_delta_theta - rkappa);
ptr_s_condition->at(0) = rs;
ptr_s_condition->at(1) = v * cos_delta_theta / one_minus_kappa_r_d;
const double delta_theta_prime =
one_minus_kappa_r_d / cos_delta_theta * kappa - rkappa;
ptr_s_condition->at(2) =
(a * cos_delta_theta -
ptr_s_condition->at(1) * ptr_s_condition->at(1) *
(ptr_d_condition->at(1) * delta_theta_prime - kappa_r_d_prime)) /
one_minus_kappa_r_d;
}
void CartesianFrenetConverter::cartesian_to_frenet(
const double rs, const double rx, const double ry, const double rtheta,
const double x, const double y, double* ptr_s, double* ptr_d) {
const double dx = x - rx;
const double dy = y - ry;
const double cos_theta_r = std::cos(rtheta);
const double sin_theta_r = std::sin(rtheta);
const double cross_rd_nd = cos_theta_r * dy - sin_theta_r * dx;
*ptr_d = std::copysign(std::sqrt(dx * dx + dy * dy), cross_rd_nd);
*ptr_s = rs;
}
void CartesianFrenetConverter::frenet_to_cartesian(
const double rs, const double rx, const double ry, const double rtheta,
const double rkappa, const double rdkappa,
const std::array<double, 3>& s_condition,
const std::array<double, 3>& d_condition, double* const ptr_x,
double* const ptr_y, double* const ptr_theta, double* const ptr_kappa,
double* const ptr_v, double* const ptr_a) {
ACHECK(std::abs(rs - s_condition[0]) < 1.0e-6)
<< "The reference point s and s_condition[0] don't match";
const double cos_theta_r = std::cos(rtheta);
const double sin_theta_r = std::sin(rtheta);
*ptr_x = rx - sin_theta_r * d_condition[0];
*ptr_y = ry + cos_theta_r * d_condition[0];
const double one_minus_kappa_r_d = 1 - rkappa * d_condition[0];
const double tan_delta_theta = d_condition[1] / one_minus_kappa_r_d;
const double delta_theta = std::atan2(d_condition[1], one_minus_kappa_r_d);
const double cos_delta_theta = std::cos(delta_theta);
*ptr_theta = NormalizeAngle(delta_theta + rtheta);
const double kappa_r_d_prime =
rdkappa * d_condition[0] + rkappa * d_condition[1];
*ptr_kappa = (((d_condition[2] + kappa_r_d_prime * tan_delta_theta) *
cos_delta_theta * cos_delta_theta) /
(one_minus_kappa_r_d) +
rkappa) *
cos_delta_theta / (one_minus_kappa_r_d);
const double d_dot = d_condition[1] * s_condition[1];
*ptr_v = std::sqrt(one_minus_kappa_r_d * one_minus_kappa_r_d *
s_condition[1] * s_condition[1] +
d_dot * d_dot);
const double delta_theta_prime =
one_minus_kappa_r_d / cos_delta_theta * (*ptr_kappa) - rkappa;
*ptr_a = s_condition[2] * one_minus_kappa_r_d / cos_delta_theta +
s_condition[1] * s_condition[1] / cos_delta_theta *
(d_condition[1] * delta_theta_prime - kappa_r_d_prime);
}
double CartesianFrenetConverter::CalculateTheta(const double rtheta,
const double rkappa,
const double l,
const double dl) {
return NormalizeAngle(rtheta + std::atan2(dl, 1 - l * rkappa));
}
double CartesianFrenetConverter::CalculateKappa(const double rkappa,
const double rdkappa,
const double l, const double dl,
const double ddl) {
double denominator = (dl * dl + (1 - l * rkappa) * (1 - l * rkappa));
if (std::fabs(denominator) < 1e-8) {
return 0.0;
}
denominator = std::pow(denominator, 1.5);
const double numerator = rkappa + ddl - 2 * l * rkappa * rkappa -
l * ddl * rkappa + l * l * rkappa * rkappa * rkappa +
l * dl * rdkappa + 2 * dl * dl * rkappa;
return numerator / denominator;
}
Vec2d CartesianFrenetConverter::CalculateCartesianPoint(const double rtheta,
const Vec2d& rpoint,
const double l) {
const double x = rpoint.x() - l * std::sin(rtheta);
const double y = rpoint.y() + l * std::cos(rtheta);
return Vec2d(x, y);
}
double CartesianFrenetConverter::CalculateLateralDerivative(
const double rtheta, const double theta, const double l,
const double rkappa) {
return (1 - rkappa * l) * std::tan(theta - rtheta);
}
double CartesianFrenetConverter::CalculateSecondOrderLateralDerivative(
const double rtheta, const double theta, const double rkappa,
const double kappa, const double rdkappa, const double l) {
const double dl = CalculateLateralDerivative(rtheta, theta, l, rkappa);
const double theta_diff = theta - rtheta;
const double cos_theta_diff = std::cos(theta_diff);
const double res = -(rdkappa * l + rkappa * dl) * std::tan(theta - rtheta) +
(1 - rkappa * l) / (cos_theta_diff * cos_theta_diff) *
(kappa * (1 - rkappa * l) / cos_theta_diff - rkappa);
if (std::isinf(res)) {
AWARN << "result is inf when calculate second order lateral "
"derivative. input values are rtheta:"
<< rtheta << " theta: " << theta << ", rkappa: " << rkappa
<< ", kappa: " << kappa << ", rdkappa: " << rdkappa << ", l: " << l
<< std::endl;
}
return res;
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/cartesian_frenet_conversion_test.cc | /******************************************************************************
* Copyright 2018 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/math/cartesian_frenet_conversion.h"
#include <array>
#include <cmath>
#include "gtest/gtest.h"
namespace apollo {
namespace common {
namespace math {
TEST(TestCartesianFrenetConversion, cartesian_to_frenet_test) {
double rs = 10.0;
double rx = 0.0;
double ry = 0.0;
double rtheta = M_PI / 4.0;
double rkappa = 0.1;
double rdkappa = 0.01;
double x = -1.0;
double y = 1.0;
double v = 2.0;
double a = 0.0;
double theta = M_PI / 3.0;
double kappa = 0.11;
std::array<double, 3> s_conditions;
std::array<double, 3> d_conditions;
CartesianFrenetConverter::cartesian_to_frenet(
rs, rx, ry, rtheta, rkappa, rdkappa, x, y, v, a, theta, kappa,
&s_conditions, &d_conditions);
double x_out;
double y_out;
double theta_out;
double kappa_out;
double v_out;
double a_out;
CartesianFrenetConverter::frenet_to_cartesian(
rs, rx, ry, rtheta, rkappa, rdkappa, s_conditions, d_conditions, &x_out,
&y_out, &theta_out, &kappa_out, &v_out, &a_out);
EXPECT_NEAR(x, x_out, 1.0e-6);
EXPECT_NEAR(y, y_out, 1.0e-6);
EXPECT_NEAR(theta, theta_out, 1.0e-6);
EXPECT_NEAR(kappa, kappa_out, 1.0e-6);
EXPECT_NEAR(v, v_out, 1.0e-6);
EXPECT_NEAR(a, a_out, 1.0e-6);
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/math/line_segment2d.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
* @brief Define the LineSegment2d class.
*/
#pragma once
#include <string>
#include "modules/common/math/vec2d.h"
/**
* @namespace apollo::common::math
* @brief apollo::common::math
*/
namespace apollo {
namespace common {
namespace math {
/**
* @class LineSegment2d
* @brief Line segment in 2-D.
*/
class LineSegment2d {
public:
/**
* @brief Empty constructor.
*/
LineSegment2d();
/**
* @brief Constructor with start point and end point.
* @param start The start point of the line segment.
* @param end The end point of the line segment.
*/
LineSegment2d(const Vec2d &start, const Vec2d &end);
/**
* @brief Get the start point.
* @return The start point of the line segment.
*/
const Vec2d &start() const { return start_; }
/**
* @brief Get the end point.
* @return The end point of the line segment.
*/
const Vec2d &end() const { return end_; }
/**
* @brief Get the unit direction from the start point to the end point.
* @return The start point of the line segment.
*/
const Vec2d &unit_direction() const { return unit_direction_; }
/**
* @brief Get the center of the line segment.
* @return The center of the line segment.
*/
Vec2d center() const { return (start_ + end_) / 2.0; }
/** @brief Get a new line-segment with the same start point, but rotated
* counterclock-wise by the given amount.
* @return The rotated line-segment's end-point.
*/
Vec2d rotate(const double angle);
/**
* @brief Get the heading of the line segment.
* @return The heading, which is the angle between unit direction and x-axis.
*/
double heading() const { return heading_; }
/**
* @brief Get the cosine of the heading.
* @return The cosine of the heading.
*/
double cos_heading() const { return unit_direction_.x(); }
/**
* @brief Get the sine of the heading.
* @return The sine of the heading.
*/
double sin_heading() const { return unit_direction_.y(); }
/**
* @brief Get the length of the line segment.
* @return The length of the line segment.
*/
double length() const;
/**
* @brief Get the square of length of the line segment.
* @return The square of length of the line segment.
*/
double length_sqr() const;
/**
* @brief Compute the shortest distance from a point on the line segment
* to a point in 2-D.
* @param point The point to compute the distance to.
* @return The shortest distance from points on the line segment to point.
*/
double DistanceTo(const Vec2d &point) const;
/**
* @brief Compute the shortest distance from a point on the line segment
* to a point in 2-D, and get the nearest point on the line segment.
* @param point The point to compute the distance to.
* @param nearest_pt The nearest point on the line segment
* to the input point.
* @return The shortest distance from points on the line segment
* to the input point.
*/
double DistanceTo(const Vec2d &point, Vec2d *const nearest_pt) const;
/**
* @brief Compute the square of the shortest distance from a point
* on the line segment to a point in 2-D.
* @param point The point to compute the squared of the distance to.
* @return The square of the shortest distance from points
* on the line segment to the input point.
*/
double DistanceSquareTo(const Vec2d &point) const;
/**
* @brief Compute the square of the shortest distance from a point
* on the line segment to a point in 2-D,
* and get the nearest point on the line segment.
* @param point The point to compute the squared of the distance to.
* @param nearest_pt The nearest point on the line segment
* to the input point.
* @return The shortest distance from points on the line segment
* to the input point.
*/
double DistanceSquareTo(const Vec2d &point, Vec2d *const nearest_pt) const;
/**
* @brief Check if a point is within the line segment.
* @param point The point to check if it is within the line segment.
* @return Whether the input point is within the line segment or not.
*/
bool IsPointIn(const Vec2d &point) const;
/**
* @brief Check if the line segment has an intersect
* with another line segment in 2-D.
* @param other_segment The line segment to check if it has an intersect.
* @return Whether the line segment has an intersect
* with the input other_segment.
*/
bool HasIntersect(const LineSegment2d &other_segment) const;
/**
* @brief Compute the intersect with another line segment in 2-D if any.
* @param other_segment The line segment to compute the intersect.
* @param point the computed intersect between the line segment and
* the input other_segment.
* @return Whether the line segment has an intersect
* with the input other_segment.
*/
bool GetIntersect(const LineSegment2d &other_segment,
Vec2d *const point) const;
/**
* @brief Compute the projection of a vector onto the line segment.
* @param point The end of the vector (starting from the start point of the
* line segment) to compute the projection onto the line segment.
* @return The projection of the vector, which is from the start point of
* the line segment to the input point, onto the unit direction.
*/
double ProjectOntoUnit(const Vec2d &point) const;
/**
* @brief Compute the cross product of a vector onto the line segment.
* @param point The end of the vector (starting from the start point of the
* line segment) to compute the cross product onto the line segment.
* @return The cross product of the unit direction and
* the vector, which is from the start point of
* the line segment to the input point.
*/
double ProductOntoUnit(const Vec2d &point) const;
/**
* @brief Compute perpendicular foot of a point in 2-D on the straight line
* expanded from the line segment.
* @param point The point to compute the perpendicular foot from.
* @param foot_point The computed perpendicular foot from the input point to
* the straight line expanded from the line segment.
* @return The distance from the input point to the perpendicular foot.
*/
double GetPerpendicularFoot(const Vec2d &point,
Vec2d *const foot_point) const;
/**
* @brief Get the debug string including the essential information.
* @return Information of the line segment for debugging.
*/
std::string DebugString() const;
private:
Vec2d start_;
Vec2d end_;
Vec2d unit_direction_;
double heading_ = 0.0;
double length_ = 0.0;
};
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common/math | apollo_public_repos/apollo/modules/common/math/qp_solver/qp_solver.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file: qp_solver.h
* @brief: quadratic programming base class
*
* min_x : q(x) = 0.5 * x^T * Q * x + x^T c
* with respect to: A * x = b (equality constraint)
* C * x >= d (inequality constraint)
**/
#pragma once
#include "Eigen/Core"
#include "Eigen/LU"
namespace apollo {
namespace common {
namespace math {
class QpSolver {
public:
QpSolver(const Eigen::MatrixXd& kernel_matrix, const Eigen::MatrixXd& offset,
const Eigen::MatrixXd& affine_inequality_matrix,
const Eigen::MatrixXd& affine_inequality_boundary,
const Eigen::MatrixXd& affine_equality_matrix,
const Eigen::MatrixXd& affine_equality_boundary);
virtual ~QpSolver() = default;
virtual void set_pos_semi_definite_hessian() {}
virtual void set_pos_definite_hessian() {}
virtual void EnableCholeskyRefactorisation(const int) {}
virtual void SetTerminationTolerance(const double) {}
virtual bool Solve() = 0;
const Eigen::MatrixXd& params() const;
const Eigen::MatrixXd& kernel_matrix() const;
const Eigen::MatrixXd& offset() const;
const Eigen::MatrixXd& affine_equality_matrix() const;
const Eigen::MatrixXd& affine_equality_boundary() const;
const Eigen::MatrixXd& affine_inequality_matrix() const;
const Eigen::MatrixXd& affine_inequality_boundary() const;
protected:
virtual bool sanity_check() = 0;
Eigen::MatrixXd params_;
Eigen::MatrixXd kernel_matrix_;
Eigen::MatrixXd offset_;
Eigen::MatrixXd affine_inequality_matrix_;
Eigen::MatrixXd affine_inequality_boundary_;
Eigen::MatrixXd affine_equality_matrix_;
Eigen::MatrixXd affine_equality_boundary_;
};
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common/math | apollo_public_repos/apollo/modules/common/math/qp_solver/qp_solver.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file: qp_solver.cc
**/
#include "modules/common/math/qp_solver/qp_solver.h"
namespace apollo {
namespace common {
namespace math {
QpSolver::QpSolver(const Eigen::MatrixXd& kernel_matrix,
const Eigen::MatrixXd& offset,
const Eigen::MatrixXd& affine_inequality_matrix,
const Eigen::MatrixXd& affine_inequality_boundary,
const Eigen::MatrixXd& affine_equality_matrix,
const Eigen::MatrixXd& affine_equality_boundary)
: kernel_matrix_(kernel_matrix),
offset_(offset),
affine_inequality_matrix_(affine_inequality_matrix),
affine_inequality_boundary_(affine_inequality_boundary),
affine_equality_matrix_(affine_equality_matrix),
affine_equality_boundary_(affine_equality_boundary) {}
const Eigen::MatrixXd& QpSolver::params() const { return params_; }
const Eigen::MatrixXd& QpSolver::kernel_matrix() const {
return kernel_matrix_;
}
const Eigen::MatrixXd& QpSolver::offset() const { return offset_; }
const Eigen::MatrixXd& QpSolver::affine_equality_matrix() const {
return affine_equality_matrix_;
}
const Eigen::MatrixXd& QpSolver::affine_equality_boundary() const {
return affine_equality_boundary_;
}
const Eigen::MatrixXd& QpSolver::affine_inequality_matrix() const {
return affine_inequality_matrix_;
}
const Eigen::MatrixXd& QpSolver::affine_inequality_boundary() const {
return affine_inequality_boundary_;
}
} // namespace math
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common/math | apollo_public_repos/apollo/modules/common/math/qp_solver/BUILD | load("@rules_cc//cc:defs.bzl", "cc_library", "cc_test")
load("//tools:cpplint.bzl", "cpplint")
package(default_visibility = ["//visibility:public"])
cc_library(
name = "qp_solver",
srcs = ["qp_solver.cc"],
hdrs = ["qp_solver.h"],
alwayslink = True,
deps = [
"@eigen",
],
)
cpplint()
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/adapters/adapter_gflags.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/adapters/adapter_gflags.h"
DEFINE_bool(enable_adapter_dump, false,
"Whether enable dumping the messages to "
"/tmp/adapters/<topic_name>/<seq_num>.txt for debugging purposes.");
DEFINE_string(gps_topic, "/apollo/sensor/gnss/odometry", "GPS topic name");
DEFINE_string(imu_topic, "/apollo/sensor/gnss/corrected_imu", "IMU topic name");
DEFINE_string(raw_imu_topic, "/apollo/sensor/gnss/imu", "Raw IMU topic name");
DEFINE_string(audio_detection_topic, "/apollo/audio_detection",
"audio detection topic name");
DEFINE_string(chassis_topic, "/apollo/canbus/chassis", "chassis topic name");
DEFINE_string(chassis_detail_topic, "/apollo/canbus/chassis_detail",
"chassis detail topic name");
DEFINE_string(localization_topic, "/apollo/localization/pose",
"localization topic name");
DEFINE_string(planning_learning_data_topic, "/apollo/planning/learning_data",
"planning learning data");
DEFINE_string(planning_trajectory_topic, "/apollo/planning",
"planning trajectory topic name");
DEFINE_string(planning_pad_topic, "/apollo/planning/pad",
"planning pad topic name");
DEFINE_string(monitor_topic, "/apollo/monitor", "Monitor");
DEFINE_string(pad_topic, "/apollo/control/pad",
"control pad message topic name");
DEFINE_string(control_command_topic, "/apollo/control",
"control command topic name");
DEFINE_string(control_preprocessor_topic, "/apollo/control/preprocessor",
"control preprocessor topic name");
DEFINE_string(control_local_view_topic, "/apollo/control/localview",
"control local view topic name");
DEFINE_string(control_core_command_topic, "/apollo/control/controlcore",
"control command core algorithm topic name");
DEFINE_string(pointcloud_topic,
"/apollo/sensor/lidar128/compensator/PointCloud2",
"pointcloud topic name");
DEFINE_string(pointcloud_16_topic,
"/apollo/sensor/lidar16/compensator/PointCloud2",
"16 beam Lidar pointcloud topic name");
DEFINE_string(pointcloud_16_raw_topic,
"/apollo/sensor/lidar16/PointCloud2",
"16 beam Lidar raw pointcloud topic name");
DEFINE_string(pointcloud_16_front_left_raw_topic,
"/apollo/sensor/lidar16/left/PointCloud2",
"16 left beam Lidar raw pointcloud topic name");
DEFINE_string(pointcloud_16_front_right_raw_topic,
"/apollo/sensor/lidar16/right/PointCloud2",
"16 left beam Lidar raw pointcloud topic name");
DEFINE_string(pointcloud_16_front_up_topic,
"/apollo/sensor/lidar16/front/up/compensator/PointCloud2",
"Front up 16 beam Lidar pointcloud topic name");
DEFINE_string(pointcloud_64_topic,
"/apollo/sensor/velodyne64/compensator/PointCloud2",
"pointcloud topic name");
DEFINE_string(pointcloud_128_topic,
"/apollo/sensor/lidar128/compensator/PointCloud2",
"pointcloud topic name for 128 beam lidar");
DEFINE_string(pointcloud_hesai_40p_topic,
"/apollo/sensor/hesai40/compensator/PointCloud2",
"pointcloud topic name for hesai40p lidar");
DEFINE_string(pointcloud_raw_topic, "/apollo/sensor/velodyne64/PointCloud2",
"pointcloud raw topic name");
DEFINE_string(velodyne_raw_topic,
"/apollo/sensor/velodyne64/VelodyneScanUnified",
"velodyne64 raw data topic name");
DEFINE_string(pointcloud_fusion_topic,
"/apollo/sensor/velodyne64/fusion/PointCloud2",
"pointcloud fusion topic name");
DEFINE_string(vlp16_pointcloud_topic,
"/apollo/sensor/velodyne16/compensator/PointCloud2",
"16 beam Lidar pointcloud topic name");
DEFINE_string(lidar_16_front_center_topic,
"/apollo/sensor/lidar16/front/center/PointCloud2",
"front center 16 beam lidar topic name");
DEFINE_string(lidar_16_front_up_topic,
"/apollo/sensor/lidar16/front/up/PointCloud2",
"front up 16 beam lidar topic name");
DEFINE_string(lidar_16_rear_left_topic,
"/apollo/sensor/lidar16/rear/left/PointCloud2",
"rear left 16 beam lidar topic name");
DEFINE_string(lidar_16_rear_right_topic,
"/apollo/sensor/lidar16/rear/right/PointCloud2",
"rear right 16 beam lidar topic name");
DEFINE_string(lidar_16_fusion_topic,
"/apollo/sensor/lidar16/fusion/PointCloud2",
"16 beam lidar fusion topic name");
DEFINE_string(lidar_16_fusion_compensator_topic,
"/apollo/sensor/lidar16/fusion/compensator/PointCloud2",
"16 beam lidar fusion compensator topic name");
DEFINE_string(lidar_128_topic, "/apollo/sensor/lidar128/PointCloud2",
"128 beam lidar topic name");
DEFINE_string(prediction_topic, "/apollo/prediction", "prediction topic name");
DEFINE_string(prediction_container_topic, "/apollo/prediction_container",
"prediction container submodule topic name");
DEFINE_string(perception_obstacle_topic, "/apollo/perception/obstacles",
"perception obstacle topic name");
DEFINE_string(drive_event_topic, "/apollo/drive_event",
"drive event topic name");
DEFINE_string(traffic_light_detection_topic, "/apollo/perception/traffic_light",
"traffic light detection topic name");
DEFINE_string(perception_lane_mask_segmentation_topic,
"/apollo/perception/lane_mask",
"lane mask segmentation topic name");
DEFINE_string(routing_request_topic, "/apollo/routing_request",
"routing request topic name");
DEFINE_string(routing_response_topic, "/apollo/routing_response",
"routing response topic name");
DEFINE_string(routing_response_history_topic,
"/apollo/routing_response_history",
"routing response history topic name");
DEFINE_string(relative_odometry_topic, "/apollo/calibration/relative_odometry",
"relative odometry topic name");
DEFINE_string(ins_stat_topic, "/apollo/sensor/gnss/ins_stat",
"ins stat topic name");
DEFINE_string(ins_status_topic, "/apollo/sensor/gnss/ins_status",
"ins status topic name");
DEFINE_string(gnss_status_topic, "/apollo/sensor/gnss/gnss_status",
"gnss status topic name");
DEFINE_string(system_status_topic, "/apollo/monitor/system_status",
"System status topic name");
DEFINE_string(static_info_topic, "/apollo/monitor/static_info",
"Static info topic name");
DEFINE_string(mobileye_topic, "/apollo/sensor/mobileye", "mobileye topic name");
DEFINE_string(smartereye_obstacles_topic, "/apollo/sensor/smartereye/obstacles",
"smartereye obstacles topic name");
DEFINE_string(smartereye_lanemark_topic, "/apollo/sensor/smartereye/lanemark",
"smartereye lanemark topic name");
DEFINE_string(smartereye_image_topic, "/apollo/sensor/smartereye/image",
"smartereye image topic name");
DEFINE_string(delphi_esr_topic, "/apollo/sensor/delphi_esr",
"delphi esr radar topic name");
DEFINE_string(conti_radar_topic, "/apollo/sensor/conti_radar",
"continental radar topic name");
DEFINE_string(racobit_radar_topic, "/apollo/sensor/racobit_radar",
"racobit radar topic name");
DEFINE_string(ultrasonic_radar_topic, "/apollo/sensor/ultrasonic_radar",
"ultrasonic esr radar topic name");
DEFINE_string(front_radar_topic, "/apollo/sensor/radar/front",
"front radar topic name");
DEFINE_string(rear_radar_topic, "/apollo/sensor/radar/rear",
"rear radar topic name");
// TODO(Authors): Change the topic name
DEFINE_string(compressed_image_topic, "camera/image_raw",
"CompressedImage topic name");
DEFINE_string(image_front_topic, "/apollo/sensor/camera/front_6mm/image",
"front camera image topic name for obstacles from camera");
DEFINE_string(image_short_topic,
"/apollo/sensor/camera/front_6mm/image/compressed",
"short camera image topic name");
DEFINE_string(image_long_topic, "/apollo/sensor/camera/traffic/image_long",
"long camera image topic name");
DEFINE_string(image_usb_cam_topic, "/apollo/sensor/camera/image_usb_cam",
"USB camera image topic name");
DEFINE_string(camera_image_long_topic, "/apollo/sensor/camera/image_long",
"long camera image topic name");
DEFINE_string(camera_image_short_topic, "/apollo/sensor/camera/image_short",
"short camera image topic name");
DEFINE_string(camera_front_6mm_topic, "/apollo/sensor/camera/front_6mm/image",
"front 6mm camera topic name");
DEFINE_string(camera_front_6mm_2_topic,
"/apollo/sensor/camera/front_6mm_2/image",
"front 6mm camera topic name 2");
DEFINE_string(camera_front_12mm_topic, "/apollo/sensor/camera/front_12mm/image",
"front 12mm camera topic name");
DEFINE_string(camera_front_6mm_compressed_topic,
"/apollo/sensor/camera/front_6mm/image/compressed",
"front 6mm camera compressed topic name");
DEFINE_string(camera_front_12mm_compressed_topic,
"/apollo/sensor/camera/front_12mm/image/compressed",
"front 12mm camera compressed topic name");
DEFINE_string(camera_left_fisheye_compressed_topic,
"/apollo/sensor/camera/left_fisheye/image/compressed",
"left fisheye camera compressed topic name");
DEFINE_string(camera_right_fisheye_compressed_topic,
"/apollo/sensor/camera/right_fisheye/image/compressed",
"right fisheye camera compressed topic name");
DEFINE_string(camera_rear_6mm_compressed_topic,
"/apollo/sensor/camera/rear_6mm/image/compressed",
"front 6mm camera compressed topic name");
DEFINE_string(camera_front_6mm_video_compressed_topic,
"/apollo/sensor/camera/front_6mm/video/compressed",
"front 6mm camera video compressed topic name");
DEFINE_string(camera_front_12mm_video_compressed_topic,
"/apollo/sensor/camera/front_12mm/video/compressed",
"front 12mm camera video compressed topic name");
DEFINE_string(camera_left_fisheye_video_compressed_topic,
"/apollo/sensor/camera/left_fisheye/video/compressed",
"left fisheye camera video compressed topic name");
DEFINE_string(camera_right_fisheye_video_compressed_topic,
"/apollo/sensor/camera/right_fisheye/video/compressed",
"right fisheye camera video compressed topic name");
DEFINE_string(camera_rear_6mm_video_compressed_topic,
"/apollo/sensor/camera/rear_6mm/video/compressed",
"front 6mm camera video compressed topic name");
DEFINE_string(gnss_rtk_obs_topic, "/apollo/sensor/gnss/rtk_obs",
"Gnss rtk observation topic name");
DEFINE_string(gnss_rtk_eph_topic, "/apollo/sensor/gnss/rtk_eph",
"Gnss rtk ephemeris topic name");
DEFINE_string(gnss_best_pose_topic, "/apollo/sensor/gnss/best_pose",
"Gnss rtk best gnss pose");
DEFINE_string(localization_gnss_topic, "/apollo/localization/msf_gnss",
"Gnss localization measurement topic name");
DEFINE_string(localization_lidar_topic, "/apollo/localization/msf_lidar",
"Lidar localization measurement topic name");
DEFINE_string(localization_ndt_topic, "/apollo/localization/ndt_lidar",
"NDT localization lidar measurement topic name");
DEFINE_string(localization_sins_pva_topic, "/apollo/localization/msf_sins_pva",
"Localization sins pva topic name");
DEFINE_string(localization_msf_status, "/apollo/localization/msf_status",
"msf localization status");
DEFINE_string(relative_map_topic, "/apollo/relative_map", "relative map");
DEFINE_string(navigation_topic, "/apollo/navigation", "navigation");
DEFINE_string(hmi_status_topic, "/apollo/hmi/status", "HMI status topic name.");
DEFINE_string(audio_capture_topic, "/apollo/hmi/audio_capture",
"HMI audio capture topic name.");
DEFINE_string(v2x_obu_traffic_light_topic,
"/apollo/v2x/obu/internal/traffic_light",
"v2x obu traffic_light topic name");
DEFINE_string(v2x_internal_obstacle_topic, "/apollo/v2x/obu/internal/obstacles",
"v2x internal obstacles topic name");
DEFINE_string(v2x_obstacle_topic, "/apollo/v2x/obstacles",
"v2x obstacles topic name");
DEFINE_string(v2x_traffic_light_topic, "/apollo/v2x/traffic_light",
"v2x traffic light topic name");
DEFINE_string(v2x_traffic_light_for_hmi_topic,
"/apollo/v2x/traffic_light/for_hmi",
"v2x traffic light topic name for hmi");
DEFINE_string(v2x_rsi_topic, "/apollo/v2x/rsi", "v2x rsi topic name");
DEFINE_string(storytelling_topic, "/apollo/storytelling",
"Storytelling topic.");
DEFINE_string(audio_event_topic, "/apollo/audio_event", "Audio event topic.");
DEFINE_string(guardian_topic, "/apollo/guardian", "Guardian topic.");
DEFINE_string(gnss_raw_data_topic, "/apollo/sensor/gnss/raw_data",
"gnss raw data topic name");
DEFINE_string(stream_status_topic, "/apollo/sensor/gnss/stream_status",
"gnss stream status topic name");
DEFINE_string(heading_topic, "/apollo/sensor/gnss/heading",
"gnss heading topic name");
DEFINE_string(rtcm_data_topic, "/apollo/sensor/gnss/rtcm_data",
"gnss rtcm data topic name");
DEFINE_string(tf_topic, "/tf", "Transform topic.");
DEFINE_string(tf_static_topic, "/tf_static", "Transform static topic.");
DEFINE_string(recorder_status_topic, "/apollo/data/recorder/status",
"Recorder status topic.");
DEFINE_string(latency_recording_topic, "/apollo/common/latency_records",
"Latency recording topic.");
DEFINE_string(latency_reporting_topic, "/apollo/common/latency_reports",
"Latency reporting topic.");
DEFINE_string(task_topic, "/apollo/task_manager", "task manager topic name");
// value: velodyne128, velodyne64, velodyne16
DEFINE_string(lidar_model_version, "",
"It determins which lidar model(16 ,64 or 128) to load, "
"if not to set, the model will be loaded by the sensor name.");
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/adapters/adapter_gflags.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#pragma once
#include "gflags/gflags.h"
DECLARE_bool(enable_adapter_dump);
DECLARE_string(gps_topic);
DECLARE_string(imu_topic);
DECLARE_string(raw_imu_topic);
DECLARE_string(audio_detection_topic);
DECLARE_string(chassis_topic);
DECLARE_string(chassis_detail_topic);
DECLARE_string(localization_topic);
DECLARE_string(planning_learning_data_topic);
DECLARE_string(planning_trajectory_topic);
DECLARE_string(planning_pad_topic);
DECLARE_string(monitor_topic);
DECLARE_string(pad_topic);
DECLARE_string(control_command_topic);
DECLARE_string(control_preprocessor_topic);
DECLARE_string(control_local_view_topic);
DECLARE_string(control_core_command_topic);
DECLARE_string(pointcloud_topic);
DECLARE_string(pointcloud_16_topic);
DECLARE_string(pointcloud_16_raw_topic);
DECLARE_string(pointcloud_16_front_left_raw_topic);
DECLARE_string(pointcloud_16_front_right_raw_topic);
DECLARE_string(pointcloud_16_front_up_topic);
DECLARE_string(pointcloud_64_topic);
DECLARE_string(pointcloud_128_topic);
DECLARE_string(pointcloud_hesai_40p_topic);
DECLARE_string(pointcloud_raw_topic);
DECLARE_string(velodyne_raw_topic);
DECLARE_string(pointcloud_fusion_topic);
DECLARE_string(vlp16_pointcloud_topic);
DECLARE_string(lidar_16_front_center_topic);
DECLARE_string(lidar_16_front_up_topic);
DECLARE_string(lidar_16_rear_left_topic);
DECLARE_string(lidar_16_rear_right_topic);
DECLARE_string(lidar_16_fusion_topic);
DECLARE_string(lidar_16_fusion_compensator_topic);
DECLARE_string(lidar_128_topic);
DECLARE_string(prediction_topic);
DECLARE_string(prediction_container_topic);
DECLARE_string(perception_obstacle_topic);
DECLARE_string(drive_event_topic);
DECLARE_string(traffic_light_detection_topic);
DECLARE_string(perception_lane_mask_segmentation_topic);
DECLARE_string(routing_request_topic);
DECLARE_string(routing_response_topic);
DECLARE_string(routing_response_history_topic);
DECLARE_string(relative_odometry_topic);
DECLARE_string(ins_stat_topic);
DECLARE_string(ins_status_topic);
DECLARE_string(gnss_status_topic);
DECLARE_string(system_status_topic);
DECLARE_string(static_info_topic);
DECLARE_string(mobileye_topic);
DECLARE_string(smartereye_obstacles_topic);
DECLARE_string(smartereye_lanemark_topic);
DECLARE_string(smartereye_image_topic);
DECLARE_string(delphi_esr_topic);
DECLARE_string(conti_radar_topic);
DECLARE_string(racobit_radar_topic);
DECLARE_string(ultrasonic_radar_topic);
DECLARE_string(front_radar_topic);
DECLARE_string(rear_radar_topic);
DECLARE_string(compressed_image_topic);
DECLARE_string(image_front_topic);
DECLARE_string(image_short_topic);
DECLARE_string(image_long_topic);
DECLARE_string(camera_image_long_topic);
DECLARE_string(camera_image_short_topic);
DECLARE_string(camera_front_6mm_topic);
DECLARE_string(camera_front_6mm_2_topic);
DECLARE_string(camera_front_12mm_topic);
DECLARE_string(camera_front_6mm_compressed_topic);
DECLARE_string(camera_front_12mm_compressed_topic);
DECLARE_string(camera_left_fisheye_compressed_topic);
DECLARE_string(camera_right_fisheye_compressed_topic);
DECLARE_string(camera_rear_6mm_compressed_topic);
DECLARE_string(camera_front_6mm_video_compressed_topic);
DECLARE_string(camera_front_12mm_video_compressed_topic);
DECLARE_string(camera_left_fisheye_video_compressed_topic);
DECLARE_string(camera_right_fisheye_video_compressed_topic);
DECLARE_string(camera_rear_6mm_video_compressed_topic);
DECLARE_string(gnss_rtk_obs_topic);
DECLARE_string(gnss_rtk_eph_topic);
DECLARE_string(gnss_best_pose_topic);
DECLARE_string(localization_gnss_topic);
DECLARE_string(localization_lidar_topic);
DECLARE_string(localization_ndt_topic);
DECLARE_string(localization_sins_pva_topic);
DECLARE_string(localization_msf_status);
DECLARE_string(relative_map_topic);
DECLARE_string(navigation_topic);
DECLARE_string(hmi_status_topic);
DECLARE_string(audio_capture_topic);
DECLARE_string(v2x_obu_traffic_light_topic);
DECLARE_string(v2x_internal_obstacle_topic);
DECLARE_string(v2x_obstacle_topic);
DECLARE_string(v2x_traffic_light_topic);
DECLARE_string(v2x_traffic_light_for_hmi_topic);
DECLARE_string(v2x_rsi_topic);
DECLARE_string(storytelling_topic);
DECLARE_string(gnss_raw_data_topic);
DECLARE_string(stream_status_topic);
DECLARE_string(heading_topic);
DECLARE_string(rtcm_data_topic);
DECLARE_string(audio_event_topic);
DECLARE_string(task_topic);
// Guardian topic
DECLARE_string(guardian_topic);
// Transform topic
DECLARE_string(tf_topic);
DECLARE_string(tf_static_topic);
// Recorder status topic
DECLARE_string(recorder_status_topic);
// Latency recording topic
DECLARE_string(latency_recording_topic);
// Latency reporting topic
DECLARE_string(latency_reporting_topic);
// It determins which lidar model(16 or 128) to load, if not to set,
// the model will be loaded by the sensor name. Mainly for D-kit.
DECLARE_string(lidar_model_version);
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/adapters/BUILD | load("@rules_cc//cc:defs.bzl", "cc_binary", "cc_library")
load("//tools:cpplint.bzl", "cpplint")
load("//tools/install:install.bzl", "install")
install(
name = "install",
library_dest = "common/lib",
data_dest = "common",
targets = [
":libadapter_gflags.so",
],
deps = ["//modules/common/adapters/proto:install"],
visibility = ["//visibility:public"],
)
cc_binary(
name = "libadapter_gflags.so",
srcs = [
"adapter_gflags.cc",
"adapter_gflags.h",
],
linkshared = True,
linkstatic = True,
deps = [
"@com_github_gflags_gflags//:gflags",
],
)
cc_library(
name = "adapter_gflags",
srcs = ["libadapter_gflags.so"],
hdrs = ["adapter_gflags.h"],
deps = [
"@com_github_gflags_gflags//:gflags",
],
alwayslink = True,
visibility = ["//visibility:public"],
)
cpplint()
| 0 |
apollo_public_repos/apollo/modules/common/adapters | apollo_public_repos/apollo/modules/common/adapters/proto/adapter_config.proto | syntax = "proto2";
package apollo.common.adapter;
// Property of a certain Input/Output that will be used by a module.
message AdapterConfig {
enum MessageType {
POINT_CLOUD = 1;
VLP16_POINT_CLOUD = 58;
GPS = 2;
IMU = 3;
CHASSIS = 4;
LOCALIZATION = 5;
PLANNING_TRAJECTORY = 6;
MONITOR = 7;
PAD = 8;
CONTROL_COMMAND = 9;
PREDICTION = 10;
PERCEPTION_OBSTACLES = 11;
TRAFFIC_LIGHT_DETECTION = 12;
CHASSIS_DETAIL = 13;
DECISION = 14 [deprecated = true];
CANBUS = 15;
ROUTING_REQUEST = 16;
ROUTING_RESPONSE = 17;
RELATIVE_ODOMETRY = 18;
INS_STAT = 19;
HMI_COMMAND = 20 [deprecated = true];
MOBILEYE = 21;
DELPHIESR = 22;
COMPRESSED_IMAGE = 23;
SYSTEM_STATUS = 24;
INS_STATUS = 25;
GNSS_STATUS = 26;
CONTI_RADAR = 27;
IMAGE_SHORT = 28;
IMAGE_LONG = 29;
DRIVE_EVENT = 30;
GNSS_RTK_OBS = 31;
GNSS_RTK_EPH = 32;
GNSS_BEST_POSE = 33;
LOCALIZATION_MSF_GNSS = 34;
LOCALIZATION_MSF_LIDAR = 35;
LOCALIZATION_MSF_SINS_PVA = 36;
RAW_IMU = 37;
LOCALIZATION_MSF_STATUS = 38;
STATIC_INFO = 39;
RELATIVE_MAP = 40;
NAVIGATION = 41;
ULTRASONIC_RADAR = 42;
AUDIO_CAPTURE = 43;
IMAGE_FRONT = 45;
PANDORA_POINT_CLOUD = 46;
PANDORA_CAMERA_FRONT_COLOR = 47;
PANDORA_CAMERA_RIGHT_GRAY = 48;
PANDORA_CAMERA_LEFT_GRAY = 49;
PANDORA_CAMERA_FRONT_GRAY = 50;
PANDORA_CAMERA_BACK_GRAY = 51;
PERCEPTION_LANE_MASK = 52;
GUARDIAN = 53;
GNSS_RAW_DATA = 54;
STREAM_STATUS = 55;
GNSS_HEADING = 56;
RTCM_DATA = 57;
RACOBIT_RADAR = 59;
// velodyne fusion configs
POINT_CLOUD_DENSE = 60;
POINT_CLOUD_DENSE_RAW = 61;
VELODYNE_SCAN_DENSE = 62;
POINT_CLOUD_SPARSE_1 = 63;
POINT_CLOUD_SPARSE_RAW_1 = 64;
VELODYNE_SCAN_SPARSE_1 = 65;
POINT_CLOUD_SPARSE_2 = 66;
POINT_CLOUD_SPARSE_RAW_2 = 67;
VELODYNE_SCAN_SPARSE_2 = 68;
POINT_CLOUD_SPARSE_3 = 69;
POINT_CLOUD_SPARSE_RAW_3 = 70;
VELODYNE_SCAN_SPARSE_3 = 71;
CAMERA_IMAGE_LONG = 72;
CAMERA_IMAGE_SHORT = 73;
PLANNING_PAD = 74;
STORYTELLING = 75;
}
enum Mode {
RECEIVE_ONLY = 0;
PUBLISH_ONLY = 1;
DUPLEX = 2;
}
optional MessageType type = 1;
optional Mode mode = 2;
// The max number of received messages to keep in the adapter, this field
// is not useful for PUBLISH_ONLY mode messages.
optional int32 message_history_limit = 3 [default = 10];
optional bool latch = 4 [default = false];
optional string topic = 5;
}
// A config to specify which messages a certain module would consume and
// produce.
message AdapterManagerConfig {
repeated AdapterConfig config = 1;
// TODO
optional bool is_ros = 2; // Whether the message comes from ROS
}
| 0 |
apollo_public_repos/apollo/modules/common/adapters | apollo_public_repos/apollo/modules/common/adapters/proto/BUILD | ## Auto generated by `proto_build_generator.py`
load("@rules_proto//proto:defs.bzl", "proto_library")
load("@rules_cc//cc:defs.bzl", "cc_proto_library")
load("//tools:python_rules.bzl", "py_proto_library")
load("//tools/install:install.bzl", "install", "install_files")
package(default_visibility = ["//visibility:public"])
cc_proto_library(
name = "adapter_config_cc_proto",
deps = [
":adapter_config_proto",
],
)
proto_library(
name = "adapter_config_proto",
srcs = ["adapter_config.proto"],
)
py_proto_library(
name = "adapter_config_py_pb2",
deps = [
":adapter_config_proto",
],
)
install_files(
name = "py_pb_common_adapter",
dest = "common/python/modules/common/adapter/proto",
files = [
"adapter_config_py_pb2",
]
)
install(
name = "install",
library_dest = "common/lib",
targets = [
":adapter_config_cc_proto",
],
visibility = ["//visibility:public"],
)
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/configs/config_gflags.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/configs/config_gflags.h"
DEFINE_string(map_dir, "/apollo/modules/map/data/sunnyvale_loop",
"Directory which contains a group of related maps.");
DEFINE_int32(local_utm_zone_id, 10, "UTM zone id.");
DEFINE_string(test_base_map_filename, "",
"If not empty, use this test base map files.");
DEFINE_string(base_map_filename, "base_map.bin|base_map.xml|base_map.txt",
"Base map files in the map_dir, search in order.");
DEFINE_string(sim_map_filename, "sim_map.bin|sim_map.txt",
"Simulation map files in the map_dir, search in order.");
DEFINE_string(routing_map_filename, "routing_map.bin|routing_map.txt",
"Routing map files in the map_dir, search in order.");
DEFINE_string(end_way_point_filename, "default_end_way_point.txt",
"End way point of the map, will be sent in RoutingRequest.");
DEFINE_string(default_routing_filename, "default_cycle_routing.txt",
"Default cycle routing of the map, will be sent in Task to Task "
"Manager Module.");
DEFINE_string(park_go_routing_filename, "park_go_routing.txt",
"Park go routing of the map, support for dreamview contest.");
DEFINE_string(speed_control_filename, "speed_control.pb.txt",
"The speed control region in a map.");
DEFINE_string(vehicle_config_path,
"/apollo/modules/common/data/vehicle_param.pb.txt",
"the file path of vehicle config file");
DEFINE_string(
vehicle_model_config_filename,
"/apollo/modules/common/vehicle_model/conf/vehicle_model_config.pb.txt",
"the file path of vehicle model config file");
DEFINE_bool(use_cyber_time, false,
"Whether Clock::Now() gets time from system_clock::now() or from "
"Cyber.");
DEFINE_string(localization_tf2_frame_id, "world", "the tf2 transform frame id");
DEFINE_string(localization_tf2_child_frame_id, "localization",
"the tf2 transform child frame id");
DEFINE_bool(use_navigation_mode, false,
"Use relative position in navigation mode");
DEFINE_string(
navigation_mode_end_way_point_file,
"modules/dreamview/conf/navigation_mode_default_end_way_point.txt",
"end_way_point file used if navigation mode is set.");
DEFINE_double(half_vehicle_width, 1.05, "half vehicle width");
DEFINE_double(look_forward_time_sec, 8.0,
"look forward time times adc speed to calculate this distance "
"when creating reference line from routing");
DEFINE_bool(use_sim_time, false, "Use bag time in mock time mode.");
DEFINE_bool(reverse_heading_vehicle_state, false,
"test flag for reverse driving.");
DEFINE_bool(state_transform_to_com_reverse, false,
"Enable vehicle states coordinate transformation from center of "
"rear-axis to center of mass, during reverse driving");
DEFINE_bool(state_transform_to_com_drive, true,
"Enable vehicle states coordinate transformation from center of "
"rear-axis to center of mass, during forward driving");
DEFINE_bool(multithread_run, false,
"multi-thread run flag mainly used by simulation");
// localization
DEFINE_bool(enable_map_reference_unify, true,
"enable IMU data convert to map reference");
// planning
DEFINE_double(replan_lateral_distance_threshold, 0.5,
"The lateral distance threshold of replan");
DEFINE_double(replan_longitudinal_distance_threshold, 2.5,
"The longitudinal distance threshold of replan");
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/configs/vehicle_config_helper.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/configs/vehicle_config_helper.h"
#include <algorithm>
#include <cmath>
#include "cyber/common/file.h"
#include "modules/common/configs/config_gflags.h"
namespace apollo {
namespace common {
VehicleConfig VehicleConfigHelper::vehicle_config_;
bool VehicleConfigHelper::is_init_ = false;
VehicleConfigHelper::VehicleConfigHelper() {}
void VehicleConfigHelper::Init() { Init(FLAGS_vehicle_config_path); }
void VehicleConfigHelper::Init(const std::string &config_file) {
VehicleConfig params;
ACHECK(cyber::common::GetProtoFromFile(config_file, ¶ms))
<< "Unable to parse vehicle config file " << config_file;
Init(params);
}
void VehicleConfigHelper::Init(const VehicleConfig &vehicle_params) {
vehicle_config_ = vehicle_params;
is_init_ = true;
}
const VehicleConfig &VehicleConfigHelper::GetConfig() {
if (!is_init_) {
Init();
}
return vehicle_config_;
}
double VehicleConfigHelper::MinSafeTurnRadius() {
const auto ¶m = vehicle_config_.vehicle_param();
double lat_edge_to_center =
std::max(param.left_edge_to_center(), param.right_edge_to_center());
double lon_edge_to_center =
std::max(param.front_edge_to_center(), param.back_edge_to_center());
return std::sqrt((lat_edge_to_center + param.min_turn_radius()) *
(lat_edge_to_center + param.min_turn_radius()) +
lon_edge_to_center * lon_edge_to_center);
}
common::math::Box2d VehicleConfigHelper::GetBoundingBox(
const common::PathPoint &path_point) {
const auto &vehicle_param = vehicle_config_.vehicle_param();
double diff_truecenter_and_pointX = (vehicle_param.front_edge_to_center() -
vehicle_param.back_edge_to_center()) /
2.0;
common::math::Vec2d true_center(
path_point.x() +
diff_truecenter_and_pointX * std::cos(path_point.theta()),
path_point.y() +
diff_truecenter_and_pointX * std::sin(path_point.theta()));
return common::math::Box2d(true_center, path_point.theta(),
vehicle_param.length(), vehicle_param.width());
}
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/configs/vehicle_config_helper_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/configs/vehicle_config_helper.h"
#include <cmath>
#include <string>
#include "gmock/gmock.h"
#include "gtest/gtest.h"
namespace apollo {
namespace common {
class VehicleConfigHelperTest : public ::testing::Test {
public:
void SetUp() {
config_.mutable_vehicle_param()->set_front_edge_to_center(2.0);
config_.mutable_vehicle_param()->set_back_edge_to_center(1.0);
config_.mutable_vehicle_param()->set_left_edge_to_center(1.0);
config_.mutable_vehicle_param()->set_right_edge_to_center(1.0);
config_.mutable_vehicle_param()->set_min_turn_radius(5.0);
}
VehicleConfig config_;
};
TEST_F(VehicleConfigHelperTest, MinSafeTurnRadius) {
config_.mutable_vehicle_param()->set_right_edge_to_center(0.5);
config_.mutable_vehicle_param()->set_front_edge_to_center(3.0);
VehicleConfigHelper::Init(config_);
auto min_radius = VehicleConfigHelper::MinSafeTurnRadius();
EXPECT_DOUBLE_EQ(min_radius, sqrt(36.0 + 9.0));
}
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/configs/vehicle_config_helper.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
*/
#pragma once
#include <string>
#include "modules/common_msgs/config_msgs/vehicle_config.pb.h"
#include "modules/common_msgs/basic_msgs/pnc_point.pb.h"
#include "cyber/common/macros.h"
#include "modules/common/math/box2d.h"
/**
* @namespace apollo::common
* @brief apollo::common
*/
namespace apollo {
namespace common {
/**
* @class VehicleConfigHelper
*
* @Brief This is a helper class that can load vehicle configurations. The
* vehicle configurations are
* defined modules/common/configs/proto/vehicle_config.proto
*/
class VehicleConfigHelper {
public:
/**
* @brief Initialize vehicle configurations with default configuration file
* pointed by gflags FLAGS_vehicle_config_path. The code will crash if
* FLAGS_vehicle_config_path does not exist or it points to a file with
* invalid format.
*/
static void Init();
/**
* @brief Initialize vehicle configurations with \p config
* @param config A VehicleConfig class instance. The VehicleConfig class is
* defined by modules/common/configs/proto/vehicle_config.proto.
*/
static void Init(const VehicleConfig &config);
/**
* @brief Initialize vehicle configurations with \p config_file.
* The code will crash if \p config_file does not exist or \p config_file has
* invalid format.
* @param config_file The configuration file path. The format of the file is
* defined by protobuf file
* modules/common/configs/proto/vehicle_config.proto.
*/
static void Init(const std::string &config_file);
/**
* @brief Get the current vehicle configuration.
* @return the current VehicleConfig instance reference.
*/
static const VehicleConfig &GetConfig();
/**
* @brief Get the safe turning radius when the vehicle is turning with
* maximum steering angle.
*
* The calculation is described by the following figure.
* <pre>
*
*
* front of car
* A +----------+ B
* | |
* / / turn with maximum steering angle
* | |
* | |
* | |
* | X | O
* |<-->.<----|-------------------------------------->* (turn center)
* | | VehicleParam.min_turn_radius()
* | |
* D +----------+ C
* back of car
*
* </pre>
*
* In the above figure, The four corner points of the vehicle is A, B, C, and
* D. XO is VehicleParam.min_turn_radius(), X to AD is left_edge_to_center,
* X to AB is VehicleParam.front_edge_to_center(). Then
* AO = sqrt((XO + left_edge_to_center) ^2 + front_edge_to_center^2).
* @return AO in the above figure, which is the minimum turn radius when the
* vehicle turns with maximum steering angle
*/
static double MinSafeTurnRadius();
/**
* @brief Get the box (four corners: ABCD) of the vehicle.
* @param path_point of a vehicle (which contains point X and heading).
* @return a box2d which contains the ABCD points info.
*/
static common::math::Box2d GetBoundingBox(
const common::PathPoint &path_point);
private:
static VehicleConfig vehicle_config_;
static bool is_init_;
DECLARE_SINGLETON(VehicleConfigHelper)
};
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/configs/config_gflags.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#pragma once
#include "gflags/gflags.h"
// The directory which contains a group of related maps, such as base_map,
// sim_map, routing_topo_grapth, etc.
DECLARE_string(map_dir);
DECLARE_int32(local_utm_zone_id);
DECLARE_string(test_base_map_filename);
DECLARE_string(base_map_filename);
DECLARE_string(sim_map_filename);
DECLARE_string(routing_map_filename);
DECLARE_string(end_way_point_filename);
DECLARE_string(default_routing_filename);
DECLARE_string(park_go_routing_filename);
DECLARE_string(speed_control_filename);
DECLARE_double(look_forward_time_sec);
DECLARE_string(vehicle_config_path);
DECLARE_string(vehicle_model_config_filename);
DECLARE_bool(use_cyber_time);
DECLARE_string(localization_tf2_frame_id);
DECLARE_string(localization_tf2_child_frame_id);
DECLARE_bool(use_navigation_mode);
DECLARE_string(navigation_mode_end_way_point_file);
DECLARE_double(half_vehicle_width);
DECLARE_bool(use_sim_time);
DECLARE_bool(reverse_heading_vehicle_state);
DECLARE_bool(state_transform_to_com_reverse);
DECLARE_bool(state_transform_to_com_drive);
DECLARE_bool(multithread_run);
// localizaiton
DECLARE_bool(enable_map_reference_unify);
// planning
// parameters for trajectory stitching and reinit planning starting point.
DECLARE_double(replan_lateral_distance_threshold);
DECLARE_double(replan_longitudinal_distance_threshold);
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/configs/BUILD | load("@rules_cc//cc:defs.bzl", "cc_binary", "cc_library", "cc_test")
load("//tools:cpplint.bzl", "cpplint")
load("//tools/install:install.bzl", "install")
install(
name = "install",
library_dest = "common/lib",
data_dest = "common",
targets = [
":libconfig_gflags.so",
":libvehicle_config_helper.so",
],
visibility = ["//visibility:public"],
)
cc_binary(
name = "libconfig_gflags.so",
srcs = [
"config_gflags.cc",
"config_gflags.h",
],
linkshared = True,
linkstatic = True,
data = [
"//modules/common/data:global_flagfile",
],
deps = [
"@com_github_gflags_gflags//:gflags",
],
)
cc_library(
name = "config_gflags",
srcs = ["libconfig_gflags.so"],
hdrs = ["config_gflags.h"],
data = [
"//modules/common/data:global_flagfile",
],
deps = [
"@com_github_gflags_gflags//:gflags",
],
visibility = ["//visibility:public"],
)
cc_binary(
name = "libvehicle_config_helper.so",
srcs = [
"vehicle_config_helper.cc",
"vehicle_config_helper.h",
],
linkshared = True,
linkstatic = True,
data = [
"//modules/common/data:vehicle_config_data",
],
deps = [
":config_gflags",
"//cyber",
"//modules/common_msgs/basic_msgs:pnc_point_cc_proto",
"//modules/common_msgs/config_msgs:vehicle_config_cc_proto",
"//modules/common/math",
],
)
cc_library(
name = "vehicle_config_helper",
srcs = ["libvehicle_config_helper.so"],
hdrs = ["vehicle_config_helper.h"],
data = [
"//modules/common/data:vehicle_config_data",
],
deps = [
":config_gflags",
"//cyber",
"//modules/common_msgs/config_msgs:vehicle_config_cc_proto",
"//modules/common/math",
"//modules/common_msgs/basic_msgs:pnc_point_cc_proto",
],
visibility = ["//visibility:public"],
)
cc_test(
name = "vehicle_config_helper_test",
size = "small",
srcs = ["vehicle_config_helper_test.cc"],
deps = [
":vehicle_config_helper",
"@com_google_googletest//:gtest_main",
],
)
cpplint()
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/monitor_log/monitor_log_buffer.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/monitor_log/monitor_log_buffer.h"
#include "cyber/common/log.h"
namespace apollo {
namespace common {
namespace monitor {
MonitorLogBuffer::MonitorLogBuffer(
const MonitorMessageItem::MessageSource &source)
: source_(source) {}
void MonitorLogBuffer::Publish() {
if (!monitor_msg_items_.empty()) {
logger_->Publish(source_, monitor_msg_items_);
monitor_msg_items_.clear();
level_ = MonitorMessageItem::INFO;
}
}
MonitorLogBuffer::~MonitorLogBuffer() { Publish(); }
void MonitorLogBuffer::AddMonitorMsgItem(
const MonitorMessageItem::LogLevel log_level, const std::string &msg) {
level_ = log_level;
monitor_msg_items_.push_back(std::make_pair(log_level, msg));
}
} // namespace monitor
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/monitor_log/monitor_logger.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file monitor_logger.h
* @brief The class of MonitorLogger
*/
#pragma once
#include <memory>
#include <string>
#include <utility>
#include <vector>
#include "cyber/cyber.h"
#include "modules/common_msgs/monitor_msgs/monitor_log.pb.h"
#include "modules/common/util/message_util.h"
/**
* @namespace apollo::common::monitor
* @brief apollo::common::monitor
*/
namespace apollo {
namespace common {
namespace monitor {
using MessageItem = std::pair<MonitorMessageItem::LogLevel, std::string>;
/**
* class MonitorLogger
*
* @brief This class helps collect and publish MonitorMessage pb to monitor
* topic. A module who wants to publish message can use macro
* `MONITOR(log_level, log_msg)` to record messages, and call
* Publish to broadcast the message to other modules.
*/
class MonitorLogger {
public:
virtual ~MonitorLogger() = default;
/**
* @brief Publish the messages.
* @param messages a list of messages for
*/
virtual void Publish(const MonitorMessageItem::MessageSource &source,
const std::vector<MessageItem> &messages) const;
private:
virtual void DoPublish(MonitorMessage *message) const;
MonitorMessageItem::MessageSource source_;
std::unique_ptr<cyber::Node> node_;
std::shared_ptr<cyber::Writer<MonitorMessage>> monitor_msg_writer_;
DECLARE_SINGLETON(MonitorLogger)
};
} // namespace monitor
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/monitor_log/monitor_logger.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/monitor_log/monitor_logger.h"
#include <memory>
#include "absl/strings/str_cat.h"
using ::apollo::cyber::Time;
namespace apollo {
namespace common {
namespace monitor {
MonitorLogger::MonitorLogger() {
const std::string node_name =
absl::StrCat("monitor_logger", Time::Now().ToNanosecond());
node_ = cyber::CreateNode(node_name);
if (node_ != nullptr) {
monitor_msg_writer_ =
node_->CreateWriter<MonitorMessage>("/apollo/monitor");
}
}
void MonitorLogger::Publish(const MonitorMessageItem::MessageSource &source,
const std::vector<MessageItem> &messages) const {
// compose a monitor message
if (messages.empty()) {
return;
}
MonitorMessage monitor_msg;
for (const auto &msg_item : messages) {
MonitorMessageItem *monitor_msg_item = monitor_msg.add_item();
monitor_msg_item->set_source(source);
monitor_msg_item->set_log_level(msg_item.first);
monitor_msg_item->set_msg(msg_item.second);
}
// publish monitor messages
DoPublish(&monitor_msg);
}
void MonitorLogger::DoPublish(MonitorMessage *message) const {
RETURN_IF_NULL(monitor_msg_writer_);
common::util::FillHeader("monitor", message);
monitor_msg_writer_->Write(*message);
}
} // namespace monitor
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/monitor_log/monitor_log_buffer.h | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file monitor_log_buffer.h
* @brief The class of MonitorLogBuffer
*/
#pragma once
#include <memory>
#include <sstream>
#include <string>
#include <utility>
#include <vector>
#include "gtest/gtest_prod.h"
#include "modules/common/monitor_log/monitor_logger.h"
#include "modules/common_msgs/monitor_msgs/monitor_log.pb.h"
/**
* @namespace apollo::common::monitor
* @brief apollo::common::monitor
*/
namespace apollo {
namespace common {
namespace monitor {
#define REG_MSG_TYPE(TYPE) \
MonitorLogBuffer &TYPE(const std::string &msg) { \
AddMonitorMsgItem(MonitorMessageItem::TYPE, msg); \
Publish(); \
return *this; \
} \
MonitorLogBuffer &TYPE() { \
level_ = MonitorMessageItem::TYPE; \
return *this; \
}
/**
* class MonitorLogBuffer
*
* @brief This class help collect MonitorMessage pb to monitor topic.
* The messages can be published automatically when the MonitorBuffer object's
* destructor is called, or can be published by calling function Publish().
*/
class MonitorLogBuffer {
public:
/**
* @brief The constructor of MonitorBuffer.
* @param a Monitor instance pointer;
*/
explicit MonitorLogBuffer(const MonitorMessageItem::MessageSource &source);
virtual ~MonitorLogBuffer();
/**
* @brief record an INFO type message
*/
REG_MSG_TYPE(INFO);
/**
* @brief record a WARN type message
*/
REG_MSG_TYPE(WARN);
/**
* @brief record an ERROR type message
*/
REG_MSG_TYPE(ERROR);
/**
* @brief record a FATAL type message
*/
REG_MSG_TYPE(FATAL);
/**
* @brief Add monitor message with MonitorMessageItem::LogLevel
* @param log_level defined in modules/common/monitor/proto/monitor.proto
* @param msg the string to send to monitor
*/
void AddMonitorMsgItem(const MonitorMessageItem::LogLevel log_level,
const std::string &msg);
/**
* @brief publish the monitor messages
*/
void Publish();
private:
MonitorLogger *logger_ = MonitorLogger::Instance();
MonitorMessageItem::LogLevel level_ = MonitorMessageItem::INFO;
std::vector<MessageItem> monitor_msg_items_;
MonitorMessageItem::MessageSource source_;
FRIEND_TEST(MonitorBufferTest, RegisterMacro);
FRIEND_TEST(MonitorBufferTest, AddMonitorMsgItem);
FRIEND_TEST(MonitorBufferTest, Operator);
};
} // namespace monitor
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/monitor_log/monitor_log_buffer_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include <sys/resource.h>
#include <sys/time.h>
#include "modules/common/monitor_log/monitor_log_buffer.h"
#include "gtest/gtest.h"
#include "cyber/common/log.h"
#include "cyber/init.h"
namespace apollo {
namespace common {
namespace monitor {
class MonitorBufferTest : public ::testing::Test {
protected:
void SetUp() override { cyber::Init("monitor_log_buffer_test"); }
void TearDown() override {}
MonitorLogBuffer buffer_{MonitorMessageItem::CONTROL};
};
TEST_F(MonitorBufferTest, RegisterMacro) {
{
buffer_.INFO("Info");
EXPECT_EQ(MonitorMessageItem::INFO, buffer_.level_);
ASSERT_EQ(0, buffer_.monitor_msg_items_.size());
}
{
buffer_.ERROR("Error");
EXPECT_EQ(MonitorMessageItem::INFO, buffer_.level_);
ASSERT_EQ(0, buffer_.monitor_msg_items_.size());
}
}
TEST_F(MonitorBufferTest, AddMonitorMsgItem) {
buffer_.AddMonitorMsgItem(MonitorMessageItem::ERROR, "TestError");
EXPECT_EQ(MonitorMessageItem::ERROR, buffer_.level_);
ASSERT_EQ(1, buffer_.monitor_msg_items_.size());
const auto &item = buffer_.monitor_msg_items_.back();
EXPECT_EQ(MonitorMessageItem::ERROR, item.first);
EXPECT_EQ("TestError", item.second);
}
} // namespace monitor
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/monitor_log/BUILD | load("@rules_cc//cc:defs.bzl", "cc_binary", "cc_library", "cc_test")
load("//tools:cpplint.bzl", "cpplint")
load("//tools/install:install.bzl", "install")
install(
name = "install",
library_dest = "common/lib",
data_dest = "common",
runtime_dest = "common/bin",
targets = [
":libmonitor_log.so",
],
visibility = ["//visibility:public"],
)
cc_binary(
name = "libmonitor_log.so",
linkshared = True,
linkstatic = True,
deps = [
":monitor_log_buffer",
":monitor_logger",
"//modules/common_msgs/monitor_msgs:monitor_log_cc_proto",
],
)
cc_library(
name = "monitor_log",
srcs = ["libmonitor_log.so"],
hdrs = [
"monitor_log_buffer.h",
"monitor_logger.h",
],
deps = [
"//cyber",
"//modules/common_msgs/monitor_msgs:monitor_log_cc_proto",
"//modules/common/util:util_tool",
"@com_google_googletest//:gtest",
"@com_google_absl//:absl",
],
visibility = ["//visibility:public"],
)
cc_library(
name = "monitor_logger",
srcs = ["monitor_logger.cc"],
hdrs = ["monitor_logger.h"],
alwayslink = True,
deps = [
"//cyber",
"//modules/common_msgs/monitor_msgs:monitor_log_cc_proto",
"//modules/common/util:util_tool",
"@com_google_absl//:absl",
],
)
cc_library(
name = "monitor_log_buffer",
srcs = ["monitor_log_buffer.cc"],
hdrs = ["monitor_log_buffer.h"],
alwayslink = True,
deps = [
":monitor_logger",
"//cyber",
"//modules/common_msgs/monitor_msgs:monitor_log_cc_proto",
"@com_google_googletest//:gtest",
],
)
cc_test(
name = "monitor_log_buffer_test",
size = "small",
srcs = ["monitor_log_buffer_test.cc"],
deps = [
":monitor_log",
"@com_google_googletest//:gtest_main",
],
)
# cc_test(
# name = "monitor_logger_test",
# size = "small",
# srcs = ["monitor_logger_test.cc"],
# deps = [
# ":monitor_log",
# "@com_google_googletest//:gtest_main",
# ],
# )
cpplint()
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/monitor_log/monitor_logger_test.cc | /******************************************************************************
* Copyright 2017 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/monitor_log/monitor_logger.h"
#include <string>
#include <vector>
#include "gtest/gtest.h"
namespace apollo {
namespace common {
namespace monitor {
class MonitorTest : public MonitorLogger {
public:
explicit MonitorTest(const MonitorMessageItem::MessageSource &source)
: MonitorLogger(source) {}
private:
void DoPublish(MonitorMessage *) const override {}
};
TEST(MonitorTest, Publish) {
MonitorTest monitor(MonitorMessageItem::CONTROL);
// std::vector<std::pair<MonitorMessageItem::LogLevel, std::string>> items{
// {MonitorMessageItem::INFO, "info message"},
// {MonitorMessageItem::WARN, "warn message"},
// {MonitorMessageItem::ERROR, "error message"},
// };
// monitor.Publish(items);
}
} // namespace monitor
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/data/vehicle_param.pb.txt | vehicle_param {
brand: LINCOLN_MKZ
vehicle_id {
other_unique_id: "mkz7"
}
front_edge_to_center: 3.89
back_edge_to_center: 1.043
left_edge_to_center: 1.055
right_edge_to_center: 1.055
length: 4.933
width: 2.11
height: 1.48
min_turn_radius: 5.05386147161
max_acceleration: 2.0
max_deceleration: -6.0
max_steer_angle: 8.20304748437
max_steer_angle_rate: 8.55211
steer_ratio: 16
wheel_base: 2.8448
wheel_rolling_radius: 0.335
max_abs_speed_when_stopped: 0.2
brake_deadzone: 14.5
throttle_deadzone: 15.4
steering_latency_param
{
dead_time: 0.1
rise_time: 0.17
peak_time: 0.0
settling_time: 0.0
}
throttle_latency_param
{
dead_time: 0.03
rise_time: 0.0
peak_time: 0.0
settling_time: 0.0
}
brake_latency_param
{
dead_time: 0.0
rise_time: 0.0
peak_time: 0.0
settling_time: 0.0
}
}
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/data/global_flagfile.txt | # 1. Flags in this file should be defined in common/configs/config_gflags.h
# 2. To use it, add the following line into your command line arguments or
# already-in-use flagfile:
# --flagfile=modules/common/data/global_flagfile.txt
# 3. To override the flag values, you must set it after this file, as all Flags
# are evaluated strictly in order.
--vehicle_config_path=/apollo/modules/common/data/vehicle_param.pb.txt
--log_dir=/apollo/data/log
--use_navigation_mode=false
--map_dir=/apollo/modules/map/data/sunnyvale_loop
--use_sim_time=false
--use_cyber_time=true
--map_dir=/apollo/modules/map/data/sunnyvale
--map_dir=/apollo/modules/map/data/sunnyvale_big_loop
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/data/BUILD | load("//tools/install:install.bzl", "install")
package(default_visibility = ["//visibility:public"])
filegroup(
name = "vehicle_config_data",
srcs = ["vehicle_param.pb.txt"],
)
filegroup(
name = "global_flagfile",
srcs = ["global_flagfile.txt"],
)
install(
name = "install",
data_dest = "common/data",
data = [
":global_flagfile",
":vehicle_config_data",
],
)
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/data/gem_config.pb.txt | vehicle_param {
brand: GEM
front_edge_to_center: 3.12
back_edge_to_center: 0.49
left_edge_to_center: 0.7
right_edge_to_center: 0.7
length: 3.43
width: 1.41
height: 1.48
min_turn_radius: 5.26
max_acceleration: 1.18
max_deceleration: -4.5
max_steer_angle: 10.935
max_steer_angle_rate: 4
min_steer_angle_rate: 0
steer_ratio: 23
wheel_base: 2.565
wheel_rolling_radius: 0.275
max_abs_speed_when_stopped: 0.15
brake_deadzone: 0.0
throttle_deadzone: 0.0
}
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/vehicle_model/vehicle_model_test.cc | /******************************************************************************
* Copyright 2019 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/vehicle_model/vehicle_model.h"
#include "gtest/gtest.h"
#include "cyber/common/file.h"
#include "modules/common/vehicle_state/proto/vehicle_state.pb.h"
#include "modules/common/vehicle_state/vehicle_state_provider.h"
namespace apollo {
namespace common {
using apollo::canbus::Chassis;
using apollo::localization::LocalizationEstimate;
class VehicleModelTest : public ::testing::Test {
public:
virtual void SetUp() {
std::string localization_pre_file =
"modules/common/vehicle_model/testdata/localization_pre.pb.txt";
ACHECK(cyber::common::GetProtoFromFile(localization_pre_file,
&localization_pre_));
std::string localization_post_file =
"modules/common/vehicle_model/testdata/localization_post.pb.txt";
ACHECK(cyber::common::GetProtoFromFile(localization_post_file,
&localization_post_));
const std::string chassis_pre_file =
"modules/common/vehicle_model/testdata/chassis_pre.pb.txt";
ACHECK(cyber::common::GetProtoFromFile(chassis_pre_file, &chassis_pre_));
const std::string chassis_post_file =
"modules/common/vehicle_model/testdata/chassis_post.pb.txt";
ACHECK(cyber::common::GetProtoFromFile(chassis_post_file, &chassis_post_));
}
protected:
LocalizationEstimate localization_pre_;
LocalizationEstimate localization_post_;
Chassis chassis_pre_;
Chassis chassis_post_;
VehicleState cur_vehicle_state_;
VehicleState predicted_vehicle_state_;
VehicleState expected_vehicle_state_;
};
TEST_F(VehicleModelTest, RearCenteredKinematicBicycleModel) {
double predicted_time_horizon = localization_post_.measurement_time() -
localization_pre_.measurement_time();
auto vehicle_state_provider =
std::make_shared<common::VehicleStateProvider>();
vehicle_state_provider->Update(localization_pre_, chassis_pre_);
cur_vehicle_state_ = vehicle_state_provider->vehicle_state();
vehicle_state_provider->Update(localization_post_, chassis_post_);
expected_vehicle_state_ = vehicle_state_provider->vehicle_state();
VehicleState predicted_vehicle_state_ =
VehicleModel::Predict(predicted_time_horizon, cur_vehicle_state_);
EXPECT_NEAR(expected_vehicle_state_.x(), predicted_vehicle_state_.x(), 2e-2);
EXPECT_NEAR(expected_vehicle_state_.y(), predicted_vehicle_state_.y(), 2e-2);
EXPECT_NEAR(expected_vehicle_state_.heading(),
predicted_vehicle_state_.heading(), 1e-3);
EXPECT_NEAR(expected_vehicle_state_.linear_velocity(),
predicted_vehicle_state_.linear_velocity(), 2e-2);
}
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/vehicle_model/vehicle_model.h | /******************************************************************************
* Copyright 2019 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#pragma once
#include "modules/common/configs/vehicle_config_helper.h"
#include "modules/common/vehicle_model/proto/vehicle_model_config.pb.h"
#include "modules/common/vehicle_state/proto/vehicle_state.pb.h"
namespace apollo {
namespace common {
class VehicleModel {
public:
VehicleModel() = delete;
static VehicleState Predict(const double predicted_time_horizon,
const VehicleState& cur_vehicle_state);
private:
static void RearCenteredKinematicBicycleModel(
const VehicleModelConfig& vehicle_model_config,
const double predicted_time_horizon,
const VehicleState& cur_vehicle_state,
VehicleState* predicted_vehicle_state);
};
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/vehicle_model/vehicle_model.cc | /******************************************************************************
* Copyright 2019 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/common/vehicle_model/vehicle_model.h"
#include "cyber/common/file.h"
#include "modules/common/configs/config_gflags.h"
namespace apollo {
namespace common {
void VehicleModel::RearCenteredKinematicBicycleModel(
const VehicleModelConfig& vehicle_model_config,
const double predicted_time_horizon, const VehicleState& cur_vehicle_state,
VehicleState* predicted_vehicle_state) {
// Kinematic bicycle model centered at rear axis center by Euler forward
// discretization
// Assume constant control command and constant z axis position
CHECK_GT(predicted_time_horizon, 0.0);
double dt = vehicle_model_config.rc_kinematic_bicycle_model().dt();
double cur_x = cur_vehicle_state.x();
double cur_y = cur_vehicle_state.y();
double cur_z = cur_vehicle_state.z();
double cur_phi = cur_vehicle_state.heading();
double cur_v = cur_vehicle_state.linear_velocity();
double cur_a = cur_vehicle_state.linear_acceleration();
double next_x = cur_x;
double next_y = cur_y;
double next_phi = cur_phi;
double next_v = cur_v;
if (dt >= predicted_time_horizon) {
dt = predicted_time_horizon;
}
double countdown_time = predicted_time_horizon;
bool finish_flag = false;
static constexpr double kepsilon = 1e-8;
while (countdown_time > kepsilon && !finish_flag) {
countdown_time -= dt;
if (countdown_time < kepsilon) {
dt = countdown_time + dt;
finish_flag = true;
}
double intermidiate_phi =
cur_phi + 0.5 * dt * cur_v * cur_vehicle_state.kappa();
next_phi =
cur_phi + dt * (cur_v + 0.5 * dt * cur_a) * cur_vehicle_state.kappa();
next_x =
cur_x + dt * (cur_v + 0.5 * dt * cur_a) * std::cos(intermidiate_phi);
next_y =
cur_y + dt * (cur_v + 0.5 * dt * cur_a) * std::sin(intermidiate_phi);
next_v = cur_v + dt * cur_a;
cur_x = next_x;
cur_y = next_y;
cur_phi = next_phi;
cur_v = next_v;
}
predicted_vehicle_state->set_x(next_x);
predicted_vehicle_state->set_y(next_y);
predicted_vehicle_state->set_z(cur_z);
predicted_vehicle_state->set_heading(next_phi);
predicted_vehicle_state->set_kappa(cur_vehicle_state.kappa());
predicted_vehicle_state->set_linear_velocity(next_v);
predicted_vehicle_state->set_linear_acceleration(
cur_vehicle_state.linear_acceleration());
}
VehicleState VehicleModel::Predict(const double predicted_time_horizon,
const VehicleState& cur_vehicle_state) {
VehicleModelConfig vehicle_model_config;
ACHECK(cyber::common::GetProtoFromFile(FLAGS_vehicle_model_config_filename,
&vehicle_model_config))
<< "Failed to load vehicle model config file "
<< FLAGS_vehicle_model_config_filename;
// Some models not supported for now
ACHECK(vehicle_model_config.model_type() !=
VehicleModelConfig::COM_CENTERED_DYNAMIC_BICYCLE_MODEL);
ACHECK(vehicle_model_config.model_type() != VehicleModelConfig::MLP_MODEL);
VehicleState predicted_vehicle_state;
if (vehicle_model_config.model_type() ==
VehicleModelConfig::REAR_CENTERED_KINEMATIC_BICYCLE_MODEL) {
RearCenteredKinematicBicycleModel(vehicle_model_config,
predicted_time_horizon, cur_vehicle_state,
&predicted_vehicle_state);
}
return predicted_vehicle_state;
}
} // namespace common
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules/common | apollo_public_repos/apollo/modules/common/vehicle_model/BUILD | load("@rules_cc//cc:defs.bzl", "cc_binary", "cc_library", "cc_test")
load("//tools/install:install.bzl", "install")
load("//tools:cpplint.bzl", "cpplint")
install(
name = "install",
library_dest = "common/lib",
runtime_dest = "common/bin",
targets = [
":libvehicle_model.so",
],
deps = ["vehicle_model_data"],
visibility = ["//visibility:public"],
)
install(
name = "vehicle_model_data",
data_dest = "common/addition_data/vehicle_model",
data = [
":vehicle_model_config_data",
":vehicle_model_test_data"
],
)
filegroup(
name = "vehicle_model_test_data",
srcs = glob([
"testdata/*",
]),
)
cc_binary(
name = "libvehicle_model.so",
srcs = [
"vehicle_model.cc",
"vehicle_model.h",
],
linkshared = True,
linkstatic = True,
deps = [
"//cyber",
"//modules/common/configs:config_gflags",
"//modules/common/configs:vehicle_config_helper",
"//modules/common/vehicle_model/proto:vehicle_model_config_cc_proto",
"//modules/common/vehicle_state/proto:vehicle_state_cc_proto",
],
)
cc_library(
name = "vehicle_model",
srcs = ["libvehicle_model.so"],
hdrs = ["vehicle_model.h"],
deps = [
"//cyber",
"//modules/common/configs:config_gflags",
"//modules/common/configs:vehicle_config_helper",
"//modules/common/vehicle_model/proto:vehicle_model_config_cc_proto",
"//modules/common/vehicle_state/proto:vehicle_state_cc_proto",
],
visibility = ["//visibility:public"],
)
cc_test(
name = "vehicle_model_test",
size = "small",
srcs = ["vehicle_model_test.cc"],
data = [
":test_data",
],
deps = [
":vehicle_model",
"//cyber",
"//modules/common/vehicle_state:vehicle_state_provider",
"@com_google_googletest//:gtest_main",
],
)
filegroup(
name = "test_data",
srcs = glob([
"testdata/*.txt",
]),
)
filegroup(
name = "vehicle_model_config_data",
srcs = ["conf/vehicle_model_config.pb.txt"],
)
cpplint()
| 0 |
apollo_public_repos/apollo/modules/common/vehicle_model | apollo_public_repos/apollo/modules/common/vehicle_model/testdata/localization_post.pb.txt | header {
timestamp_sec: 1548201255.9602075
module_name: "localization"
sequence_num: 390294
}
pose {
position {
x: 587202.25707657228
y: 4141420.7357829413
z: -31.197880225256085
}
orientation {
qx: 0.0022022418960756622
qy: 0.018860632468381357
qz: -0.83722499241519033
qw: 0.546528808709027
}
linear_velocity {
x: 1.4242965011761419
y: -0.51813658692423181
z: -0.0043025008111585161
}
linear_acceleration {
x: -0.15753569084869434
y: -0.18552716552299428
z: -0.19864443619776617
}
angular_velocity {
x: -0.0062736171332540879
y: 0.020054009699215589
z: -0.17424936560120291
}
heading: -0.41377894029307871
linear_acceleration_vrf {
x: 0.23801904899440435
y: -0.063820713797840087
z: -0.19486221767349834
}
angular_velocity_vrf {
x: -0.011589852465283034
y: -0.0087179043482407473
z: -0.17491151035017813
}
euler_angles {
x: 0.024316047206598291
y: -0.029178148500337175
z: -1.9845752670879755
}
}
measurement_time: 1548201255.95
| 0 |
apollo_public_repos/apollo/modules/common/vehicle_model | apollo_public_repos/apollo/modules/common/vehicle_model/testdata/chassis_post.pb.txt | engine_started: true
engine_rpm: 0
speed_mps: 1.6111112
odometer_m: 0
fuel_range_m: 0
throttle_percentage: 15.165942
brake_percentage: 18.248264
steering_percentage: -57.361702
steering_torque_nm: -0.4375
parking_brake: false
driving_mode: COMPLETE_AUTO_DRIVE
error_code: NO_ERROR
gear_location: GEAR_DRIVE
header {
timestamp_sec: 1548201255.9566879
module_name: "canbus"
sequence_num: 391612
}
signal {
turn_signal: TURN_NONE
high_beam: false
horn: false
}
chassis_gps {
latitude: 37.415476666666663
longitude: -122.01455333333332
gps_valid: true
year: 19
month: 1
day: 22
hours: 23
minutes: 54
seconds: 15
compass_direction: 135
pdop: 0
is_gps_fault: false
is_inferred: false
altitude: -42.5
heading: 116.31
hdop: 0.8
vdop: 1.4000000000000001
quality: FIX_3D
num_satellites: 10
gps_speed: 1.78816
}
engage_advice {
advice: READY_TO_ENGAGE
}
wheel_speed {
is_wheel_spd_rr_valid: true
wheel_direction_rr: FORWARD
wheel_spd_rr: 4.24
is_wheel_spd_rl_valid: true
wheel_direction_rl: FORWARD
wheel_spd_rl: 5.08
is_wheel_spd_fr_valid: true
wheel_direction_fr: FORWARD
wheel_spd_fr: 4.49
is_wheel_spd_fl_valid: true
wheel_direction_fl: FORWARD
wheel_spd_fl: 5.2700000000000005
}
surround {
cross_traffic_alert_left: false
cross_traffic_alert_left_enabled: false
blind_spot_left_alert: false
blind_spot_left_alert_enabled: false
cross_traffic_alert_right: false
blind_spot_right_alert: false
blind_spot_right_alert_enabled: false
sonar00: 100
sonar01: 100
sonar02: 100
sonar03: 100
sonar04: 100
sonar05: 100
sonar06: 100
sonar07: 100
sonar08: 100
sonar09: 100
sonar10: 100
sonar11: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
}
license {
vin: "3LN6L2LU5GR607996"
}
| 0 |
apollo_public_repos/apollo/modules/common/vehicle_model | apollo_public_repos/apollo/modules/common/vehicle_model/testdata/localization_pre.pb.txt | header {
timestamp_sec: 1548201255.8647678
module_name: "localization"
sequence_num: 390284
}
pose {
position {
x: 587202.10519798519
y: 4141420.7868995117
z: -31.197345808148384
}
orientation {
qx: 0.002908930204631145
qy: 0.018604564716388539
qz: -0.832502363329099
qw: 0.55370138463637875
}
linear_velocity {
x: 1.4304187503960097
y: -0.50054861209113288
z: 0.0023225288097407648
}
linear_acceleration {
x: -0.18167072165570336
y: -0.030965788190627622
z: -0.026221832899938732
}
angular_velocity {
x: -0.005429706094745565
y: 0.018219428482472381
z: -0.16396134774234433
}
heading: -0.39660175801844888
linear_acceleration_vrf {
x: 0.099484259706533615
y: -0.15481986264419831
z: -0.028007282397221604
}
angular_velocity_vrf {
x: -0.010522339557656574
y: -0.007490716850216809
z: -0.16455370663492347
}
euler_angles {
x: 0.025458686077230334
y: -0.027758895653893077
z: -1.9673980848133454
}
}
measurement_time: 1548201255.85
| 0 |
apollo_public_repos/apollo/modules/common/vehicle_model | apollo_public_repos/apollo/modules/common/vehicle_model/testdata/chassis_pre.pb.txt | engine_started: true
engine_rpm: 0
speed_mps: 1.6138889
odometer_m: 0
fuel_range_m: 0
throttle_percentage: 15.178149
brake_percentage: 20.117495
steering_percentage: -54.957447
steering_torque_nm: -0.5
parking_brake: false
driving_mode: COMPLETE_AUTO_DRIVE
error_code: NO_ERROR
gear_location: GEAR_DRIVE
header {
timestamp_sec: 1548201255.8666761
module_name: "canbus"
sequence_num: 391603
}
signal {
turn_signal: TURN_NONE
high_beam: false
horn: false
}
chassis_gps {
latitude: 37.415476666666663
longitude: -122.01455333333332
gps_valid: true
year: 19
month: 1
day: 22
hours: 23
minutes: 54
seconds: 15
compass_direction: 135
pdop: 0
is_gps_fault: false
is_inferred: false
altitude: -42.5
heading: 116.31
hdop: 0.8
vdop: 1.4000000000000001
quality: FIX_3D
num_satellites: 10
gps_speed: 1.78816
}
engage_advice {
advice: READY_TO_ENGAGE
}
wheel_speed {
is_wheel_spd_rr_valid: true
wheel_direction_rr: FORWARD
wheel_spd_rr: 4.2700000000000005
is_wheel_spd_rl_valid: true
wheel_direction_rl: FORWARD
wheel_spd_rl: 5.04
is_wheel_spd_fr_valid: true
wheel_direction_fr: FORWARD
wheel_spd_fr: 4.5
is_wheel_spd_fl_valid: true
wheel_direction_fl: FORWARD
wheel_spd_fl: 5.24
}
surround {
cross_traffic_alert_left: false
cross_traffic_alert_left_enabled: false
blind_spot_left_alert: false
blind_spot_left_alert_enabled: false
cross_traffic_alert_right: false
blind_spot_right_alert: false
blind_spot_right_alert_enabled: false
sonar00: 100
sonar01: 100
sonar02: 100
sonar03: 100
sonar04: 100
sonar05: 100
sonar06: 100
sonar07: 100
sonar08: 100
sonar09: 100
sonar10: 100
sonar11: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
sonar_range: 100
}
license {
vin: "3LN6L2LU5GR607996"
}
| 0 |
apollo_public_repos/apollo/modules/common/vehicle_model | apollo_public_repos/apollo/modules/common/vehicle_model/proto/BUILD | ## Auto generated by `proto_build_generator.py`
load("@rules_proto//proto:defs.bzl", "proto_library")
load("@rules_cc//cc:defs.bzl", "cc_proto_library")
load("//tools:python_rules.bzl", "py_proto_library")
load("//tools/install:install.bzl", "install", "install_files")
package(default_visibility = ["//visibility:public"])
cc_proto_library(
name = "vehicle_model_config_cc_proto",
deps = [
":vehicle_model_config_proto",
],
)
proto_library(
name = "vehicle_model_config_proto",
srcs = ["vehicle_model_config.proto"],
)
py_proto_library(
name = "vehicle_model_config_py_pb2",
deps = [
":vehicle_model_config_proto",
],
)
install_files(
name = "py_pb_common_vehicle_model",
dest = "common/python/modules/common/vehicle_model/proto",
files = [
"vehicle_model_config_py_pb2",
]
) | 0 |
apollo_public_repos/apollo/modules/common/vehicle_model | apollo_public_repos/apollo/modules/common/vehicle_model/proto/vehicle_model_config.proto | syntax = "proto2";
package apollo.common;
message VehicleModelConfig {
enum ModelType {
REAR_CENTERED_KINEMATIC_BICYCLE_MODEL = 0;
COM_CENTERED_DYNAMIC_BICYCLE_MODEL = 1;
MLP_MODEL = 2;
}
optional ModelType model_type = 1;
optional RearCenteredKinematicBicycleModelConfig rc_kinematic_bicycle_model =
2;
optional ComCenteredDynamicBicycleModelConfig comc_dynamic_bicycle_model = 3;
optional MlpModelConfig mlp_model = 4;
}
message RearCenteredKinematicBicycleModelConfig {
optional double dt = 1;
}
message ComCenteredDynamicBicycleModelConfig {
optional double dt = 1;
}
message MlpModelConfig {
optional double dt = 1;
}
| 0 |
apollo_public_repos/apollo/modules/common/vehicle_model | apollo_public_repos/apollo/modules/common/vehicle_model/conf/vehicle_model_config.pb.txt | model_type: REAR_CENTERED_KINEMATIC_BICYCLE_MODEL
rc_kinematic_bicycle_model: {
dt: 0.06
}
| 0 |
apollo_public_repos/apollo/modules | apollo_public_repos/apollo/modules/third_party_perception/third_party_perception_smartereye.cc | /******************************************************************************
* Copyright 2020 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/third_party_perception/third_party_perception_smartereye.h"
#include <memory>
#include "modules/common/adapters/adapter_gflags.h"
#include "modules/common/util/message_util.h"
#include "modules/third_party_perception/common/third_party_perception_gflags.h"
#include "modules/third_party_perception/tools/conversion_smartereye.h"
namespace apollo {
namespace third_party_perception {
using apollo::perception::PerceptionObstacles;
ThirdPartyPerceptionSmartereye::ThirdPartyPerceptionSmartereye(
apollo::cyber::Node* const node) :ThirdPartyPerception(node) {
smartereye_obstacles_reader_ =
node_->CreateReader<apollo::drivers::SmartereyeObstacles>(
FLAGS_smartereye_obstacles_topic,
[this](const std::shared_ptr<
apollo::drivers::SmartereyeObstacles> &message) {
OnSmartereye(*message.get());
});
smartereye_lanemark_reader_ =
node_->CreateReader<apollo::drivers::SmartereyeLanemark>(
FLAGS_smartereye_lanemark_topic,
[this](const std::shared_ptr<
apollo::drivers::SmartereyeLanemark> &message) {
OnSmartereyeLanemark(*message.get());
});
}
void ThirdPartyPerceptionSmartereye::OnSmartereye(
const apollo::drivers::SmartereyeObstacles& message) {
ADEBUG << "Received smartereye data: run smartereye callback.";
std::lock_guard<std::mutex> lock(third_party_perception_mutex_);
eye_obstacles_ = conversion_smartereye::SmartereyeToPerceptionObstacles(
message, smartereye_lanemark_, localization_, chassis_);
}
void ThirdPartyPerceptionSmartereye::OnSmartereyeLanemark(
const apollo::drivers::SmartereyeLanemark& message) {
ADEBUG << "Received smartereye data: run smartereye callback.";
std::lock_guard<std::mutex> lock(third_party_perception_mutex_);
smartereye_lanemark_.CopyFrom(message);
}
bool ThirdPartyPerceptionSmartereye::Process(
PerceptionObstacles* const response) {
ADEBUG << "Timer is triggered: publish PerceptionObstacles";
CHECK_NOTNULL(response);
std::lock_guard<std::mutex> lock(third_party_perception_mutex_);
*response = eye_obstacles_;
common::util::FillHeader(FLAGS_third_party_perception_node_name, response);
eye_obstacles_.Clear();
return true;
}
} // namespace third_party_perception
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules | apollo_public_repos/apollo/modules/third_party_perception/third_party_perception_mobileye.cc | /******************************************************************************
* Copyright 2020 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/third_party_perception/third_party_perception_mobileye.h"
#include "modules/common/adapters/adapter_gflags.h"
#include "modules/common/util/message_util.h"
#include "modules/third_party_perception/common/third_party_perception_gflags.h"
#include "modules/third_party_perception/tools/conversion_mobileye.h"
#include "modules/third_party_perception/tools/conversion_radar.h"
#include "modules/third_party_perception/tools/filter.h"
#include "modules/third_party_perception/tools/fusion.h"
namespace apollo {
namespace third_party_perception {
using apollo::drivers::ContiRadar;
using apollo::drivers::DelphiESR;
using apollo::drivers::Mobileye;
using apollo::perception::PerceptionObstacles;
ThirdPartyPerceptionMobileye::ThirdPartyPerceptionMobileye(
apollo::cyber::Node* const node)
: ThirdPartyPerception(node) {
mobileye_reader_ = node_->CreateReader<apollo::drivers::Mobileye>(
FLAGS_mobileye_topic,
[this](const std::shared_ptr<apollo::drivers::Mobileye>& message) {
OnMobileye(*message.get());
});
delphi_esr_reader_ = node_->CreateReader<apollo::drivers::DelphiESR>(
FLAGS_delphi_esr_topic,
[this](const std::shared_ptr<apollo::drivers::DelphiESR>& message) {
OnDelphiESR(*message.get());
});
conti_radar_reader_ = node_->CreateReader<apollo::drivers::ContiRadar>(
FLAGS_conti_radar_topic,
[this](const std::shared_ptr<apollo::drivers::ContiRadar>& message) {
OnContiRadar(*message.get());
});
}
void ThirdPartyPerceptionMobileye::OnMobileye(const Mobileye& message) {
ADEBUG << "Received mobileye data: run mobileye callback.";
std::lock_guard<std::mutex> lock(third_party_perception_mutex_);
eye_obstacles_ = conversion_mobileye::MobileyeToPerceptionObstacles(
message, localization_, chassis_);
}
void ThirdPartyPerceptionMobileye::OnDelphiESR(const DelphiESR& message) {
ADEBUG << "Received delphi esr data: run delphi esr callback.";
std::lock_guard<std::mutex> lock(third_party_perception_mutex_);
last_radar_obstacles_.CopyFrom(current_radar_obstacles_);
current_radar_obstacles_ = conversion_radar::DelphiToRadarObstacles(
message, localization_, last_radar_obstacles_);
RadarObstacles filtered_radar_obstacles =
filter::FilterRadarObstacles(current_radar_obstacles_);
if (FLAGS_enable_radar) {
radar_obstacles_ = conversion_radar::RadarObstaclesToPerceptionObstacles(
filtered_radar_obstacles);
}
}
void ThirdPartyPerceptionMobileye::OnContiRadar(const ContiRadar& message) {
ADEBUG << "Received delphi esr data: run continental radar callback.";
std::lock_guard<std::mutex> lock(third_party_perception_mutex_);
last_radar_obstacles_.CopyFrom(current_radar_obstacles_);
current_radar_obstacles_ = conversion_radar::ContiToRadarObstacles(
message, localization_, last_radar_obstacles_, chassis_);
RadarObstacles filtered_radar_obstacles =
filter::FilterRadarObstacles(current_radar_obstacles_);
if (FLAGS_enable_radar) {
radar_obstacles_ = conversion_radar::RadarObstaclesToPerceptionObstacles(
filtered_radar_obstacles);
}
}
bool ThirdPartyPerceptionMobileye::Process(
PerceptionObstacles* const response) {
ADEBUG << "Timer is triggered: publish PerceptionObstacles";
CHECK_NOTNULL(response);
std::lock_guard<std::mutex> lock(third_party_perception_mutex_);
*response = fusion::EyeRadarFusion(eye_obstacles_, radar_obstacles_);
common::util::FillHeader(FLAGS_third_party_perception_node_name, response);
eye_obstacles_.Clear();
radar_obstacles_.Clear();
return true;
}
} // namespace third_party_perception
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules | apollo_public_repos/apollo/modules/third_party_perception/third_party_perception_mobileye.h | /******************************************************************************
* Copyright 2020 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
*/
#pragma once
#include <memory>
#include "modules/third_party_perception/third_party_perception_base.h"
#include "modules/common_msgs/sensor_msgs/conti_radar.pb.h"
#include "modules/common_msgs/sensor_msgs/delphi_esr.pb.h"
#include "modules/common_msgs/sensor_msgs/mobileye.pb.h"
/**
* @namespace apollo::third_party_perception
* @brief apollo::third_party_perception
*/
namespace apollo {
namespace third_party_perception {
class ThirdPartyPerceptionMobileye : public ThirdPartyPerception {
public:
explicit ThirdPartyPerceptionMobileye(apollo::cyber::Node* const node);
ThirdPartyPerceptionMobileye() = default;
~ThirdPartyPerceptionMobileye() = default;
// Upon receiving mobileye data
void OnMobileye(const apollo::drivers::Mobileye& message);
// Upon receiving conti radar data
void OnContiRadar(const apollo::drivers::ContiRadar& message);
// Upon receiving esr radar data
void OnDelphiESR(const apollo::drivers::DelphiESR& message);
bool Process(
apollo::perception::PerceptionObstacles* const response) override;
private:
std::shared_ptr<apollo::cyber::Reader<apollo::drivers::Mobileye>>
mobileye_reader_ = nullptr;
std::shared_ptr<apollo::cyber::Reader<apollo::drivers::DelphiESR>>
delphi_esr_reader_ = nullptr;
std::shared_ptr<apollo::cyber::Reader<apollo::drivers::ContiRadar>>
conti_radar_reader_ = nullptr;
apollo::perception::PerceptionObstacles radar_obstacles_;
apollo::perception::PerceptionObstacles eye_obstacles_;
};
} // namespace third_party_perception
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules | apollo_public_repos/apollo/modules/third_party_perception/third_party_perception_smartereye.h | /******************************************************************************
* Copyright 2020 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
/**
* @file
*/
#pragma once
#include <memory>
#include "modules/common_msgs/sensor_msgs/smartereye.pb.h"
#include "modules/third_party_perception/third_party_perception_base.h"
/**
* @namespace apollo::third_party_perception
* @brief apollo::third_party_perception
*/
namespace apollo {
namespace third_party_perception {
class ThirdPartyPerceptionSmartereye : public ThirdPartyPerception {
public:
explicit ThirdPartyPerceptionSmartereye(apollo::cyber::Node* const node);
ThirdPartyPerceptionSmartereye() = default;
~ThirdPartyPerceptionSmartereye() = default;
// Upon receiving smartereye data
void OnSmartereye(const apollo::drivers::SmartereyeObstacles& message);
void OnSmartereyeLanemark(const apollo::drivers::SmartereyeLanemark&);
bool Process(
apollo::perception::PerceptionObstacles* const response) override;
private:
apollo::perception::PerceptionObstacles eye_obstacles_;
apollo::drivers::SmartereyeLanemark smartereye_lanemark_;
std::shared_ptr<apollo::cyber::Reader<apollo::drivers::SmartereyeObstacles>>
smartereye_obstacles_reader_ = nullptr;
std::shared_ptr<apollo::cyber::Reader<apollo::drivers::SmartereyeLanemark>>
smartereye_lanemark_reader_ = nullptr;
};
} // namespace third_party_perception
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules | apollo_public_repos/apollo/modules/third_party_perception/third_party_perception_base.cc | /******************************************************************************
* Copyright 2020 The Apollo Authors. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*****************************************************************************/
#include "modules/third_party_perception/third_party_perception_base.h"
#include "modules/common/adapters/adapter_gflags.h"
#include "modules/common/util/message_util.h"
namespace apollo {
namespace third_party_perception {
using apollo::canbus::Chassis;
using apollo::common::Status;
using apollo::localization::LocalizationEstimate;
using apollo::perception::PerceptionObstacles;
ThirdPartyPerception::ThirdPartyPerception(
apollo::cyber::Node* const node) : node_(node) {
localization_reader_ =
node_->CreateReader<apollo::localization::LocalizationEstimate>(
FLAGS_localization_topic,
[this](
const std::shared_ptr<apollo::localization::LocalizationEstimate>
&localization) {
OnLocalization(*localization.get());
});
chassis_reader_ = node_->CreateReader<apollo::canbus::Chassis>(
FLAGS_chassis_topic,
[this](const std::shared_ptr<apollo::canbus::Chassis> &chassis) {
OnChassis(*chassis.get());
});
}
std::string ThirdPartyPerception::Name() const {
return FLAGS_third_party_perception_node_name;
}
Status ThirdPartyPerception::Init() {
return Status::OK();
}
Status ThirdPartyPerception::Start() { return Status::OK(); }
void ThirdPartyPerception::Stop() {}
void ThirdPartyPerception::OnChassis(const Chassis& message) {
ADEBUG << "Received chassis data: run chassis callback.";
std::lock_guard<std::mutex> lock(third_party_perception_mutex_);
chassis_.CopyFrom(message);
}
void ThirdPartyPerception::OnLocalization(const LocalizationEstimate& message) {
ADEBUG << "Received localization data: run localization callback.";
std::lock_guard<std::mutex> lock(third_party_perception_mutex_);
localization_.CopyFrom(message);
}
bool ThirdPartyPerception::Process(PerceptionObstacles* const response) {
return true;
}
} // namespace third_party_perception
} // namespace apollo
| 0 |
apollo_public_repos/apollo/modules | apollo_public_repos/apollo/modules/third_party_perception/cyberfile.xml | <package format="2">
<name>third-party-perception</name>
<version>local</version>
<description>
In Apollo 2.5, the third_party_perception module incorporates third-party sensors like Mobileye and Conti/Delphi Radar
output with simple fusion and creates a similar perception output produced as obstacle/lane detection information as defined in
[Perception Obstacles Interface](https://github.com/ApolloAuto/apollo/blob/master/modules/perception/proto/perception_obstacle.proto).
This module was only intend to serve for the Prediction/Planning/Control algorithm in real vehicle before perception modules fully ready before 2.5. We recommend using 'modules/perception' instead for your own test purpose after Apollo 2.5 officially released.
</description>
<maintainer email="apollo-support@baidu.com">Apollo</maintainer>
<license>Apache License 2.0</license>
<url type="website">https://www.apollo.auto/</url>
<url type="repository">https://github.com/ApolloAuto/apollo</url>
<url type="bugtracker">https://github.com/ApolloAuto/apollo/issues</url>
<type>module</type>
<src_path url="https://github.com/ApolloAuto/apollo">//modules/third_party_perception</src_path>
<depend type="binary" repo_name="cyber">cyber-dev</depend>
<depend type="binary" repo_name="common" lib_names="common">common-dev</depend>
<depend repo_name="common-msgs" lib_names="common-msgs">common-msgs-dev</depend>
<depend>bazel-extend-tools-dev</depend>
<depend type="binary" repo_name="map" lib_names="map">map-dev</depend>
<depend repo_name="com_github_gflags_gflags" lib_names="gflags">3rd-gflags-dev</depend>
<depend repo_name="com_google_googletest" lib_names="gtest,gtest_main">3rd-gtest-dev</depend>
</package>
| 0 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.