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FreeCAD / src /Mod /Sketcher /App /planegcs /Constraints.cpp
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 // SPDX-License-Identifier: LGPL-2.1-or-later
/***************************************************************************
* Copyright (c) 2011 Konstantinos Poulios <logari81@gmail.com> *
* *
* This file is part of the FreeCAD CAx development system. *
* *
* This library is free software; you can redistribute it and/or *
* modify it under the terms of the GNU Library General Public *
* License as published by the Free Software Foundation; either *
* version 2 of the License, or (at your option) any later version. *
* *
* This library is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU Library General Public License for more details. *
* *
* You should have received a copy of the GNU Library General Public *
* License along with this library; see the file COPYING.LIB. If not, *
* write to the Free Software Foundation, Inc., 59 Temple Place, *
* Suite 330, Boston, MA 02111-1307, USA *
* *
***************************************************************************/
#ifdef _MSC_VER
# pragma warning(disable : 4251)
#endif
#include <cmath>
#include <numbers>
#include <algorithm>
#define DEBUG_DERIVS 0
#if DEBUG_DERIVS
# include <cassert>
#endif
#include <boost/graph/graph_concepts.hpp>
#include "Constraints.h"
namespace GCS
{
///////////////////////////////////////
// Constraints
///////////////////////////////////////
Constraint::Constraint()
: origpvec(0)
, pvec(0)
, scale(1.)
, tag(0)
, pvecChangedFlag(true)
, driving(true)
, internalAlignment(Alignment::NoInternalAlignment)
{}
void Constraint::redirectParams(const MAP_pD_pD& redirectionmap)
{
int i = 0;
for (VEC_pD::iterator param = origpvec.begin(); param != origpvec.end(); ++param, i++) {
MAP_pD_pD::const_iterator it = redirectionmap.find(*param);
if (it != redirectionmap.end()) {
pvec[i] = it->second;
}
}
pvecChangedFlag = true;
}
void Constraint::revertParams()
{
pvec = origpvec;
pvecChangedFlag = true;
}
ConstraintType Constraint::getTypeId()
{
return None;
}
void Constraint::rescale(double coef)
{
scale = coef * 1.0;
}
double Constraint::maxStep(MAP_pD_D& /*dir*/, double lim)
{
return lim;
}
int Constraint::findParamInPvec(double* param)
{
int ret = -1;
for (std::size_t i = 0; i < pvec.size(); i++) {
if (param == pvec[i]) {
ret = static_cast<int>(i);
break;
}
}
return ret;
}
// --------------------------------------------------------
// Equal
ConstraintEqual::ConstraintEqual(double* p1, double* p2, double p1p2ratio)
: ratio(p1p2ratio)
{
pvec.push_back(p1);
pvec.push_back(p2);
origpvec = pvec;
rescale();
}
ConstraintType ConstraintEqual::getTypeId()
{
return Equal;
}
double ConstraintEqual::error()
{
return scale * (*param1() - ratio * (*param2()));
}
double ConstraintEqual::grad(double* param)
{
double deriv = 0.;
if (param == param1()) {
deriv += 1;
}
if (param == param2()) {
deriv += -1;
}
return scale * deriv;
}
// --------------------------------------------------------
// Weighted Linear Combination
ConstraintWeightedLinearCombination::ConstraintWeightedLinearCombination(
size_t givennumpoles,
const std::vector<double*>& givenpvec,
const std::vector<double>& givenfactors
)
: factors(givenfactors)
, numpoles(givennumpoles)
{
pvec = givenpvec;
assert(pvec.size() == 2 * numpoles + 1);
assert(factors.size() == numpoles);
origpvec = pvec;
rescale();
}
ConstraintType ConstraintWeightedLinearCombination::getTypeId()
{
return WeightedLinearCombination;
}
double ConstraintWeightedLinearCombination::error()
{
// Explanation of the math here:
// https://forum.freecad.org/viewtopic.php?f=9&t=71130&start=120#p635538
double sum = 0;
double wsum = 0;
for (size_t i = 0; i < numpoles; ++i) {
double wcontrib = *weightat(i) * factors[i];
wsum += wcontrib;
sum += *poleat(i) * wcontrib;
}
return scale * ((*thepoint()) * wsum - sum);
}
double ConstraintWeightedLinearCombination::grad(double* param)
{
// Equations are from here:
// https://forum.freecad.org/viewtopic.php?f=9&t=71130&start=120#p635538
double deriv = 0.;
if (param == thepoint()) {
// Eq. (11)
double wsum = 0;
for (size_t i = 0; i < numpoles; ++i) {
wsum += *weightat(i) * factors[i];
}
deriv = wsum;
return scale * deriv;
}
for (size_t i = 0; i < numpoles; ++i) {
if (param == poleat(i)) {
// Eq. (12)
deriv = -(*weightat(i) * factors[i]);
return scale * deriv;
}
if (param == weightat(i)) {
// Eq. (13)
deriv = (*thepoint() - *poleat(i)) * factors[i];
return scale * deriv;
}
}
return scale * deriv;
}
// --------------------------------------------------------
// Center of Gravity
ConstraintCenterOfGravity::ConstraintCenterOfGravity(
const std::vector<double*>& givenpvec,
const std::vector<double>& givenweights
)
: weights(givenweights)
, numpoints(givenpvec.size() - 1)
{
pvec = givenpvec;
assert(pvec.size() > 1);
assert(weights.size() == numpoints);
origpvec = pvec;
rescale();
}
ConstraintType ConstraintCenterOfGravity::getTypeId()
{
return CenterOfGravity;
}
double ConstraintCenterOfGravity::error()
{
double sum = 0;
for (size_t i = 0; i < numpoints; ++i) {
sum += *pointat(i) * weights[i];
}
return scale * (*thecenter() - sum);
}
double ConstraintCenterOfGravity::grad(double* param)
{
double deriv = 0.;
if (param == thecenter()) {
deriv = 1;
}
for (size_t i = 0; i < numpoints; ++i) {
if (param == pointat(i)) {
deriv = -weights[i];
}
}
return scale * deriv;
}
// --------------------------------------------------------
// Slope at B-spline knot
ConstraintSlopeAtBSplineKnot::ConstraintSlopeAtBSplineKnot(BSpline& b, Line& l, size_t knotindex)
{
// set up pvec: pole x-coords, pole y-coords, pole weights,
// line point 1 coords, line point 2 coords
numpoles = b.degree - b.mult[knotindex] + 1;
// slope at knot doesn't make sense if there's only C0 continuity
assert(numpoles >= 2);
pvec.reserve(3 * numpoles + 4);
// `startpole` is the first pole affecting the knot with `knotindex`
size_t startpole = 0;
// See `System::addConstraintInternalAlignmentKnotPoint()` for some elaboration
for (size_t j = 1; j <= knotindex; ++j) {
startpole += b.mult[j];
}
if (!b.periodic && startpole >= b.poles.size()) {
startpole = b.poles.size() - 1;
}
for (size_t i = 0; i < numpoles; ++i) {
pvec.push_back(b.poles[(startpole + i) % b.poles.size()].x);
}
for (size_t i = 0; i < numpoles; ++i) {
pvec.push_back(b.poles[(startpole + i) % b.poles.size()].y);
}
for (size_t i = 0; i < numpoles; ++i) {
pvec.push_back(b.weights[(startpole + i) % b.weights.size()]);
}
pvec.push_back(l.p1.x);
pvec.push_back(l.p1.y);
pvec.push_back(l.p2.x);
pvec.push_back(l.p2.y);
// Set up factors to get slope at knot point
std::vector<double> tempfactors((numpoles + 1), 1.0 / (numpoles + 1));
factors.resize(numpoles);
slopefactors.resize(numpoles);
for (size_t i = 0; i < numpoles + 1; ++i) {
tempfactors[i] = b.getLinCombFactor(
*(b.knots[knotindex]),
startpole + b.degree,
startpole + i,
b.degree - 1
)
/ (b.flattenedknots[startpole + b.degree + i] - b.flattenedknots[startpole + i]);
}
for (size_t i = 0; i < numpoles; ++i) {
factors[i] = b.getLinCombFactor(*(b.knots[knotindex]), startpole + b.degree, startpole + i);
slopefactors[i] = b.degree * (tempfactors[i] - tempfactors[i + 1]);
}
origpvec = pvec;
ConstraintSlopeAtBSplineKnot::rescale();
}
ConstraintType ConstraintSlopeAtBSplineKnot::getTypeId()
{
return SlopeAtBSplineKnot;
}
void ConstraintSlopeAtBSplineKnot::rescale(double coef)
{
double slopex = 0., slopey = 0.;
for (size_t i = 0; i < numpoles; ++i) {
slopex += *polexat(i) * slopefactors[i];
slopey += *poleyat(i) * slopefactors[i];
}
scale = coef / sqrt((slopex * slopex + slopey * slopey));
}
double ConstraintSlopeAtBSplineKnot::error()
{
double xsum = 0., xslopesum = 0.;
double ysum = 0., yslopesum = 0.;
double wsum = 0., wslopesum = 0.;
for (size_t i = 0; i < numpoles; ++i) {
double wcontrib = *weightat(i) * factors[i];
double wslopecontrib = *weightat(i) * slopefactors[i];
wsum += wcontrib;
xsum += *polexat(i) * wcontrib;
ysum += *poleyat(i) * wcontrib;
wslopesum += wslopecontrib;
xslopesum += *polexat(i) * wslopecontrib;
yslopesum += *poleyat(i) * wslopecontrib;
}
// This is actually wsum^2 * the respective slopes
// See Eq (19) from:
// https://forum.freecad.org/viewtopic.php?f=9&t=71130&start=120#p635538
double slopex = wsum * xslopesum - wslopesum * xsum;
double slopey = wsum * yslopesum - wslopesum * ysum;
// Normalizing it ensures that the cross product is not zero just because
// one vector is zero.
double linex = *linep2x() - *linep1x();
double liney = *linep2y() - *linep1y();
double dirx = linex / sqrt(linex * linex + liney * liney);
double diry = liney / sqrt(linex * linex + liney * liney);
// error is the cross product
return scale * (slopex * diry - slopey * dirx);
}
double ConstraintSlopeAtBSplineKnot::grad(double* param)
{
// Equations are from here:
// https://forum.freecad.org/viewtopic.php?f=9&t=71130&start=120#p635538
double result = 0.0;
double linex = *linep2x() - *linep1x();
double liney = *linep2y() - *linep1y();
double dirx = linex / sqrt(linex * linex + liney * liney);
double diry = liney / sqrt(linex * linex + liney * liney);
for (size_t i = 0; i < numpoles; ++i) {
if (param == polexat(i)) {
// Eq. (21)
double wsum = 0., wslopesum = 0.;
for (size_t j = 0; j < numpoles; ++j) {
double wcontrib = *weightat(j) * factors[j];
double wslopecontrib = *weightat(j) * slopefactors[j];
wsum += wcontrib;
wslopesum += wslopecontrib;
}
result = (wsum * slopefactors[i] - wslopesum * factors[i]) * diry;
return scale * result;
}
if (param == poleyat(i)) {
// Eq. (21)
double wsum = 0., wslopesum = 0.;
for (size_t i = 0; i < numpoles; ++i) {
double wcontrib = *weightat(i) * factors[i];
double wslopecontrib = *weightat(i) * slopefactors[i];
wsum += wcontrib;
wslopesum += wslopecontrib;
}
result = -(wsum * slopefactors[i] - wslopesum * factors[i]) * dirx;
return scale * result;
}
if (param == weightat(i)) {
// Eq. (22)
double xsum = 0., xslopesum = 0.;
double ysum = 0., yslopesum = 0.;
for (size_t j = 0; j < numpoles; ++j) {
double wcontrib = *weightat(j) * factors[j];
double wslopecontrib = *weightat(j) * slopefactors[j];
xsum += wcontrib * (*polexat(j) - *polexat(i));
xslopesum += wslopecontrib * (*polexat(j) - *polexat(i));
ysum += wcontrib * (*poleyat(j) - *poleyat(i));
yslopesum += wslopecontrib * (*poleyat(j) - *poleyat(i));
}
result = (factors[i] * xslopesum - slopefactors[i] * xsum) * diry
- (factors[i] * yslopesum - slopefactors[i] * ysum) * dirx;
return scale * result;
}
}
double slopex = 0., slopey = 0.;
auto getSlopes = [&]() {
double xsum = 0., xslopesum = 0.;
double ysum = 0., yslopesum = 0.;
double wsum = 0., wslopesum = 0.;
for (size_t i = 0; i < numpoles; ++i) {
double wcontrib = *weightat(i) * factors[i];
double wslopecontrib = *weightat(i) * slopefactors[i];
wsum += wcontrib;
xsum += *polexat(i) * wcontrib;
ysum += *poleyat(i) * wcontrib;
wslopesum += wslopecontrib;
xslopesum += *polexat(i) * wslopecontrib;
yslopesum += *poleyat(i) * wslopecontrib;
}
// This is actually wsum^2 * the respective slopes
slopex = wsum * xslopesum - wslopesum * xsum;
slopey = wsum * yslopesum - wslopesum * ysum;
};
if (param == linep1x()) {
getSlopes();
double dDirxDLinex = (liney * liney) / pow(linex * linex + liney * liney, 1.5);
double dDiryDLinex = -(linex * liney) / pow(linex * linex + liney * liney, 1.5);
// NOTE: d(linex)/d(x1) = -1
result = slopex * (-dDiryDLinex) - slopey * (-dDirxDLinex);
return scale * result;
}
if (param == linep2x()) {
getSlopes();
double dDirxDLinex = (liney * liney) / pow(linex * linex + liney * liney, 1.5);
double dDiryDLinex = -(linex * liney) / pow(linex * linex + liney * liney, 1.5);
// NOTE: d(linex)/d(x2) = 1
result = slopex * dDiryDLinex - slopey * dDirxDLinex;
return scale * result;
}
if (param == linep1y()) {
getSlopes();
double dDirxDLiney = -(linex * liney) / pow(linex * linex + liney * liney, 1.5);
double dDiryDLiney = (linex * linex) / pow(linex * linex + liney * liney, 1.5);
// NOTE: d(liney)/d(y1) = -1
result = slopex * (-dDiryDLiney) - slopey * (-dDirxDLiney);
return scale * result;
}
if (param == linep2y()) {
getSlopes();
double dDirxDLiney = -(linex * liney) / pow(linex * linex + liney * liney, 1.5);
double dDiryDLiney = (linex * linex) / pow(linex * linex + liney * liney, 1.5);
// NOTE: d(liney)/d(y2) = 1
result = slopex * dDiryDLiney - slopey * dDirxDLiney;
return scale * result;
}
return scale * result;
}
// --------------------------------------------------------
// Point On BSpline
ConstraintPointOnBSpline::ConstraintPointOnBSpline(
double* point,
double* initparam,
int coordidx,
BSpline& b
)
: bsp(b)
{
// This is always going to be true
numpoints = bsp.degree + 1;
pvec.reserve(2 + 2 * b.poles.size());
pvec.push_back(point);
pvec.push_back(initparam);
setStartPole(*initparam);
for (size_t i = 0; i < b.poles.size(); ++i) {
if (coordidx == 0) {
pvec.push_back(b.poles[i].x);
}
else {
pvec.push_back(b.poles[i].y);
}
}
for (size_t i = 0; i < b.weights.size(); ++i) {
pvec.push_back(b.weights[i]);
}
if (bsp.flattenedknots.empty()) {
bsp.setupFlattenedKnots();
}
origpvec = pvec;
rescale();
}
ConstraintType ConstraintPointOnBSpline::getTypeId()
{
return PointOnBSpline;
}
void ConstraintPointOnBSpline::setStartPole(double u)
{
// The startpole logic is repeated in a lot of places,
// for example in GCS and slope at knot
// find relevant poles
startpole = 0;
for (size_t j = 1; j < bsp.mult.size() && *(bsp.knots[j]) <= u; ++j) {
startpole += bsp.mult[j];
}
if (!bsp.periodic && startpole >= bsp.poles.size()) {
startpole = bsp.poles.size() - bsp.degree - 1;
}
}
double ConstraintPointOnBSpline::error()
{
if (*theparam() < bsp.flattenedknots[startpole + bsp.degree]
|| *theparam() > bsp.flattenedknots[startpole + bsp.degree + 1]) {
setStartPole(*theparam());
}
double sum = 0;
double wsum = 0;
// TODO: maybe make it global so it doesn't have to be created every time
VEC_D d(numpoints);
for (size_t i = 0; i < numpoints; ++i) {
d[i] = *poleat(i) * *weightat(i);
}
sum = BSpline::splineValue(*theparam(), startpole + bsp.degree, bsp.degree, d, bsp.flattenedknots);
for (size_t i = 0; i < numpoints; ++i) {
d[i] = *weightat(i);
}
wsum = BSpline::splineValue(*theparam(), startpole + bsp.degree, bsp.degree, d, bsp.flattenedknots);
// TODO: Change the poles as the point moves between pieces
return scale * (*thepoint() * wsum - sum);
}
double ConstraintPointOnBSpline::grad(double* gcsparam)
{
double deriv = 0.;
if (gcsparam == thepoint()) {
VEC_D d(numpoints);
for (size_t i = 0; i < numpoints; ++i) {
d[i] = *weightat(i);
}
double wsum = BSpline::splineValue(
*theparam(),
startpole + bsp.degree,
bsp.degree,
d,
bsp.flattenedknots
);
deriv += wsum;
}
if (gcsparam == theparam()) {
VEC_D d(numpoints - 1);
for (size_t i = 1; i < numpoints; ++i) {
d[i - 1] = (*poleat(i) * *weightat(i) - *poleat(i - 1) * *weightat(i - 1))
/ (bsp.flattenedknots[startpole + i + bsp.degree] - bsp.flattenedknots[startpole + i]);
}
double slopevalue = BSpline::splineValue(
*theparam(),
startpole + bsp.degree,
bsp.degree - 1,
d,
bsp.flattenedknots
);
for (size_t i = 1; i < numpoints; ++i) {
d[i - 1] = (*weightat(i) - *weightat(i - 1))
/ (bsp.flattenedknots[startpole + i + bsp.degree] - bsp.flattenedknots[startpole + i]);
}
double wslopevalue = BSpline::splineValue(
*theparam(),
startpole + bsp.degree,
bsp.degree - 1,
d,
bsp.flattenedknots
);
deriv += (*thepoint() * wslopevalue - slopevalue) * bsp.degree;
}
for (size_t i = 0; i < numpoints; ++i) {
if (gcsparam == poleat(i)) {
auto factorsI = bsp.getLinCombFactor(*theparam(), startpole + bsp.degree, startpole + i);
deriv += -(*weightat(i) * factorsI);
}
if (gcsparam == weightat(i)) {
auto factorsI = bsp.getLinCombFactor(*theparam(), startpole + bsp.degree, startpole + i);
deriv += (*thepoint() - *poleat(i)) * factorsI;
}
}
return scale * deriv;
}
// Difference
ConstraintDifference::ConstraintDifference(double* p1, double* p2, double* d)
{
pvec.push_back(p1);
pvec.push_back(p2);
pvec.push_back(d);
origpvec = pvec;
rescale();
}
ConstraintType ConstraintDifference::getTypeId()
{
return Difference;
}
double ConstraintDifference::error()
{
return scale * (*param2() - *param1() - *difference());
}
double ConstraintDifference::grad(double* param)
{
double deriv = 0.;
if (param == param1()) {
deriv += -1;
}
if (param == param2()) {
deriv += 1;
}
if (param == difference()) {
deriv += -1;
}
return scale * deriv;
}
// --------------------------------------------------------
// P2PDistance
ConstraintP2PDistance::ConstraintP2PDistance(Point& p1, Point& p2, double* d)
{
pvec.push_back(p1.x);
pvec.push_back(p1.y);
pvec.push_back(p2.x);
pvec.push_back(p2.y);
pvec.push_back(d);
origpvec = pvec;
rescale();
}
ConstraintType ConstraintP2PDistance::getTypeId()
{
return P2PDistance;
}
double ConstraintP2PDistance::error()
{
double dx = (*p1x() - *p2x());
double dy = (*p1y() - *p2y());
double d = sqrt(dx * dx + dy * dy);
double dist = *distance();
return scale * (d - dist);
}
double ConstraintP2PDistance::grad(double* param)
{
double deriv = 0.;
if (param == p1x() || param == p1y() || param == p2x() || param == p2y()) {
double dx = (*p1x() - *p2x());
double dy = (*p1y() - *p2y());
double d = sqrt(dx * dx + dy * dy);
if (param == p1x()) {
deriv += dx / d;
}
if (param == p1y()) {
deriv += dy / d;
}
if (param == p2x()) {
deriv += -dx / d;
}
if (param == p2y()) {
deriv += -dy / d;
}
}
if (param == distance()) {
deriv += -1.;
}
return scale * deriv;
}
double ConstraintP2PDistance::maxStep(MAP_pD_D& dir, double lim)
{
MAP_pD_D::iterator it;
it = dir.find(distance());
if (it != dir.end()) {
if (it->second < 0.) {
lim = std::min(lim, -(*distance()) / it->second);
}
}
// restrict actual distance change
double ddx = 0., ddy = 0.;
it = dir.find(p1x());
if (it != dir.end()) {
ddx += it->second;
}
it = dir.find(p1y());
if (it != dir.end()) {
ddy += it->second;
}
it = dir.find(p2x());
if (it != dir.end()) {
ddx -= it->second;
}
it = dir.find(p2y());
if (it != dir.end()) {
ddy -= it->second;
}
double dd = sqrt(ddx * ddx + ddy * ddy);
double dist = *distance();
if (dd > dist) {
double dx = (*p1x() - *p2x());
double dy = (*p1y() - *p2y());
double d = sqrt(dx * dx + dy * dy);
if (dd > d) {
lim = std::min(lim, std::max(d, dist) / dd);
}
}
return lim;
}
// --------------------------------------------------------
// P2PAngle
ConstraintP2PAngle::ConstraintP2PAngle(Point& p1, Point& p2, double* a, double da_)
: da(da_)
{
pvec.push_back(p1.x);
pvec.push_back(p1.y);
pvec.push_back(p2.x);
pvec.push_back(p2.y);
pvec.push_back(a);
origpvec = pvec;
rescale();
}
ConstraintType ConstraintP2PAngle::getTypeId()
{
return P2PAngle;
}
double ConstraintP2PAngle::error()
{
double dx = (*p2x() - *p1x());
double dy = (*p2y() - *p1y());
double a = *angle() + da;
double ca = cos(a);
double sa = sin(a);
double x = dx * ca + dy * sa;
double y = -dx * sa + dy * ca;
return scale * atan2(y, x);
}
double ConstraintP2PAngle::grad(double* param)
{
double deriv = 0.;
if (param == p1x() || param == p1y() || param == p2x() || param == p2y()) {
double dx = (*p2x() - *p1x());
double dy = (*p2y() - *p1y());
double a = *angle() + da;
double ca = cos(a);
double sa = sin(a);
double x = dx * ca + dy * sa;
double y = -dx * sa + dy * ca;
double r2 = dx * dx + dy * dy;
dx = -y / r2;
dy = x / r2;
if (param == p1x()) {
deriv += (-ca * dx + sa * dy);
}
if (param == p1y()) {
deriv += (-sa * dx - ca * dy);
}
if (param == p2x()) {
deriv += (ca * dx - sa * dy);
}
if (param == p2y()) {
deriv += (sa * dx + ca * dy);
}
}
if (param == angle()) {
deriv += -1;
}
return scale * deriv;
}
double ConstraintP2PAngle::maxStep(MAP_pD_D& dir, double lim)
{
constexpr double pi_18 = std::numbers::pi / 18;
MAP_pD_D::iterator it = dir.find(angle());
if (it != dir.end()) {
double step = std::abs(it->second);
if (step > pi_18) {
lim = std::min(lim, pi_18 / step);
}
}
return lim;
}
// --------------------------------------------------------
// P2LDistance
ConstraintP2LDistance::ConstraintP2LDistance(Point& p, Line& l, double* d)
{
pvec.push_back(p.x);
pvec.push_back(p.y);
pvec.push_back(l.p1.x);
pvec.push_back(l.p1.y);
pvec.push_back(l.p2.x);
pvec.push_back(l.p2.y);
pvec.push_back(d);
origpvec = pvec;
rescale();
}
ConstraintType ConstraintP2LDistance::getTypeId()
{
return P2LDistance;
}
double ConstraintP2LDistance::error()
{
double x0 = *p0x(), x1 = *p1x(), x2 = *p2x();
double y0 = *p0y(), y1 = *p1y(), y2 = *p2y();
double dist = *distance();
double dx = x2 - x1;
double dy = y2 - y1;
double d = sqrt(dx * dx + dy * dy); // line length
double area = std::abs(-x0 * dy + y0 * dx + x1 * y2 - x2 * y1);
return scale * (area / d - dist);
}
double ConstraintP2LDistance::grad(double* param)
{
double deriv = 0.;
if (param == p0x() || param == p0y() || param == p1x() || param == p1y() || param == p2x()
|| param == p2y()) {
double x0 = *p0x(), x1 = *p1x(), x2 = *p2x();
double y0 = *p0y(), y1 = *p1y(), y2 = *p2y();
double dx = x2 - x1;
double dy = y2 - y1;
double d2 = dx * dx + dy * dy;
double d = sqrt(d2);
double area = -x0 * dy + y0 * dx + x1 * y2 - x2 * y1;
if (param == p0x()) {
deriv += (y1 - y2) / d;
}
if (param == p0y()) {
deriv += (x2 - x1) / d;
}
if (param == p1x()) {
deriv += ((y2 - y0) * d + (dx / d) * area) / d2;
}
if (param == p1y()) {
deriv += ((x0 - x2) * d + (dy / d) * area) / d2;
}
if (param == p2x()) {
deriv += ((y0 - y1) * d - (dx / d) * area) / d2;
}
if (param == p2y()) {
deriv += ((x1 - x0) * d - (dy / d) * area) / d2;
}
if (area < 0) {
deriv *= -1;
}
}
if (param == distance()) {
deriv += -1;
}
return scale * deriv;
}
double ConstraintP2LDistance::maxStep(MAP_pD_D& dir, double lim)
{
MAP_pD_D::iterator it;
it = dir.find(distance());
if (it != dir.end()) {
if (it->second < 0.) {
lim = std::min(lim, -(*distance()) / it->second);
}
}
// restrict actual area change
double darea = 0.;
double x0 = *p0x(), x1 = *p1x(), x2 = *p2x();
double y0 = *p0y(), y1 = *p1y(), y2 = *p2y();
it = dir.find(p0x());
if (it != dir.end()) {
darea += (y1 - y2) * it->second;
}
it = dir.find(p0y());
if (it != dir.end()) {
darea += (x2 - x1) * it->second;
}
it = dir.find(p1x());
if (it != dir.end()) {
darea += (y2 - y0) * it->second;
}
it = dir.find(p1y());
if (it != dir.end()) {
darea += (x0 - x2) * it->second;
}
it = dir.find(p2x());
if (it != dir.end()) {
darea += (y0 - y1) * it->second;
}
it = dir.find(p2y());
if (it != dir.end()) {
darea += (x1 - x0) * it->second;
}
darea = std::abs(darea);
if (darea > 0.) {
double dx = x2 - x1;
double dy = y2 - y1;
double area = 0.3 * (*distance()) * sqrt(dx * dx + dy * dy);
if (darea > area) {
area = std::max(area, 0.3 * std::abs(-x0 * dy + y0 * dx + x1 * y2 - x2 * y1));
if (darea > area) {
lim = std::min(lim, area / darea);
}
}
}
return lim;
}
// --------------------------------------------------------
// PointOnLine
ConstraintPointOnLine::ConstraintPointOnLine(Point& p, Line& l)
{
pvec.push_back(p.x);
pvec.push_back(p.y);
pvec.push_back(l.p1.x);
pvec.push_back(l.p1.y);
pvec.push_back(l.p2.x);
pvec.push_back(l.p2.y);
origpvec = pvec;
rescale();
}
ConstraintPointOnLine::ConstraintPointOnLine(Point& p, Point& lp1, Point& lp2)
{
pvec.push_back(p.x);
pvec.push_back(p.y);
pvec.push_back(lp1.x);
pvec.push_back(lp1.y);
pvec.push_back(lp2.x);
pvec.push_back(lp2.y);
origpvec = pvec;
rescale();
}
ConstraintType ConstraintPointOnLine::getTypeId()
{
return PointOnLine;
}
double ConstraintPointOnLine::error()
{
double x0 = *p0x(), x1 = *p1x(), x2 = *p2x();
double y0 = *p0y(), y1 = *p1y(), y2 = *p2y();
double dx = x2 - x1;
double dy = y2 - y1;
double d = sqrt(dx * dx + dy * dy);
double area = -x0 * dy + y0 * dx + x1 * y2 - x2 * y1;
return scale * area / d;
}
double ConstraintPointOnLine::grad(double* param)
{
double deriv = 0.;
if (param == p0x() || param == p0y() || param == p1x() || param == p1y() || param == p2x()
|| param == p2y()) {
double x0 = *p0x(), x1 = *p1x(), x2 = *p2x();
double y0 = *p0y(), y1 = *p1y(), y2 = *p2y();
double dx = x2 - x1;
double dy = y2 - y1;
double d2 = dx * dx + dy * dy;
double d = sqrt(d2);
double area = -x0 * dy + y0 * dx + x1 * y2 - x2 * y1;
if (param == p0x()) {
deriv += (y1 - y2) / d;
}
if (param == p0y()) {
deriv += (x2 - x1) / d;
}
if (param == p1x()) {
deriv += ((y2 - y0) * d + (dx / d) * area) / d2;
}
if (param == p1y()) {
deriv += ((x0 - x2) * d + (dy / d) * area) / d2;
}
if (param == p2x()) {
deriv += ((y0 - y1) * d - (dx / d) * area) / d2;
}
if (param == p2y()) {
deriv += ((x1 - x0) * d - (dy / d) * area) / d2;
}
}
return scale * deriv;
}
// --------------------------------------------------------
// PointOnPerpBisector
ConstraintPointOnPerpBisector::ConstraintPointOnPerpBisector(Point& p, Line& l)
{
pvec.push_back(p.x);
pvec.push_back(p.y);
pvec.push_back(l.p1.x);
pvec.push_back(l.p1.y);
pvec.push_back(l.p2.x);
pvec.push_back(l.p2.y);
origpvec = pvec;
rescale();
}
ConstraintPointOnPerpBisector::ConstraintPointOnPerpBisector(Point& p, Point& lp1, Point& lp2)
{
pvec.push_back(p.x);
pvec.push_back(p.y);
pvec.push_back(lp1.x);
pvec.push_back(lp1.y);
pvec.push_back(lp2.x);
pvec.push_back(lp2.y);
origpvec = pvec;
rescale();
}
ConstraintType ConstraintPointOnPerpBisector::getTypeId()
{
return PointOnPerpBisector;
}
void ConstraintPointOnPerpBisector::errorgrad(double* err, double* grad, double* param)
{
DeriVector2 p0(Point(p0x(), p0y()), param);
DeriVector2 p1(Point(p1x(), p1y()), param);
DeriVector2 p2(Point(p2x(), p2y()), param);
DeriVector2 d1 = p0.subtr(p1);
DeriVector2 d2 = p0.subtr(p2);
DeriVector2 D = p2.subtr(p1).getNormalized();
double projd1, dprojd1;
projd1 = d1.scalarProd(D, &dprojd1);
double projd2, dprojd2;
projd2 = d2.scalarProd(D, &dprojd2);
if (err) {
*err = projd1 + projd2;
}
if (grad) {
*grad = dprojd1 + dprojd2;
}
}
// --------------------------------------------------------
// Parallel
ConstraintParallel::ConstraintParallel(Line& l1, Line& l2)
{
pvec.push_back(l1.p1.x);
pvec.push_back(l1.p1.y);
pvec.push_back(l1.p2.x);
pvec.push_back(l1.p2.y);
pvec.push_back(l2.p1.x);
pvec.push_back(l2.p1.y);
pvec.push_back(l2.p2.x);
pvec.push_back(l2.p2.y);
origpvec = pvec;
ConstraintParallel::rescale();
}
ConstraintType ConstraintParallel::getTypeId()
{
return Parallel;
}
void ConstraintParallel::rescale(double coef)
{
double dx1 = (*l1p1x() - *l1p2x());
double dy1 = (*l1p1y() - *l1p2y());
double dx2 = (*l2p1x() - *l2p2x());
double dy2 = (*l2p1y() - *l2p2y());
scale = coef / sqrt((dx1 * dx1 + dy1 * dy1) * (dx2 * dx2 + dy2 * dy2));
}
double ConstraintParallel::error()
{
double dx1 = (*l1p1x() - *l1p2x());
double dy1 = (*l1p1y() - *l1p2y());
double dx2 = (*l2p1x() - *l2p2x());
double dy2 = (*l2p1y() - *l2p2y());
return scale * (dx1 * dy2 - dy1 * dx2);
}
double ConstraintParallel::grad(double* param)
{
double deriv = 0.;
if (param == l1p1x()) {
deriv += (*l2p1y() - *l2p2y()); // = dy2
}
if (param == l1p2x()) {
deriv += -(*l2p1y() - *l2p2y()); // = -dy2
}
if (param == l1p1y()) {
deriv += -(*l2p1x() - *l2p2x()); // = -dx2
}
if (param == l1p2y()) {
deriv += (*l2p1x() - *l2p2x()); // = dx2
}
if (param == l2p1x()) {
deriv += -(*l1p1y() - *l1p2y()); // = -dy1
}
if (param == l2p2x()) {
deriv += (*l1p1y() - *l1p2y()); // = dy1
}
if (param == l2p1y()) {
deriv += (*l1p1x() - *l1p2x()); // = dx1
}
if (param == l2p2y()) {
deriv += -(*l1p1x() - *l1p2x()); // = -dx1
}
return scale * deriv;
}
// --------------------------------------------------------
// Perpendicular
ConstraintPerpendicular::ConstraintPerpendicular(Line& l1, Line& l2)
{
pvec.push_back(l1.p1.x);
pvec.push_back(l1.p1.y);
pvec.push_back(l1.p2.x);
pvec.push_back(l1.p2.y);
pvec.push_back(l2.p1.x);
pvec.push_back(l2.p1.y);
pvec.push_back(l2.p2.x);
pvec.push_back(l2.p2.y);
origpvec = pvec;
ConstraintPerpendicular::rescale();
}
ConstraintPerpendicular::ConstraintPerpendicular(Point& l1p1, Point& l1p2, Point& l2p1, Point& l2p2)
{
pvec.push_back(l1p1.x);
pvec.push_back(l1p1.y);
pvec.push_back(l1p2.x);
pvec.push_back(l1p2.y);
pvec.push_back(l2p1.x);
pvec.push_back(l2p1.y);
pvec.push_back(l2p2.x);
pvec.push_back(l2p2.y);
origpvec = pvec;
ConstraintPerpendicular::rescale();
}
ConstraintType ConstraintPerpendicular::getTypeId()
{
return Perpendicular;
}
void ConstraintPerpendicular::rescale(double coef)
{
double dx1 = (*l1p1x() - *l1p2x());
double dy1 = (*l1p1y() - *l1p2y());
double dx2 = (*l2p1x() - *l2p2x());
double dy2 = (*l2p1y() - *l2p2y());
scale = coef / sqrt((dx1 * dx1 + dy1 * dy1) * (dx2 * dx2 + dy2 * dy2));
}
double ConstraintPerpendicular::error()
{
double dx1 = (*l1p1x() - *l1p2x());
double dy1 = (*l1p1y() - *l1p2y());
double dx2 = (*l2p1x() - *l2p2x());
double dy2 = (*l2p1y() - *l2p2y());
return scale * (dx1 * dx2 + dy1 * dy2);
}
double ConstraintPerpendicular::grad(double* param)
{
double deriv = 0.;
if (param == l1p1x()) {
deriv += (*l2p1x() - *l2p2x()); // = dx2
}
if (param == l1p2x()) {
deriv += -(*l2p1x() - *l2p2x()); // = -dx2
}
if (param == l1p1y()) {
deriv += (*l2p1y() - *l2p2y()); // = dy2
}
if (param == l1p2y()) {
deriv += -(*l2p1y() - *l2p2y()); // = -dy2
}
if (param == l2p1x()) {
deriv += (*l1p1x() - *l1p2x()); // = dx1
}
if (param == l2p2x()) {
deriv += -(*l1p1x() - *l1p2x()); // = -dx1
}
if (param == l2p1y()) {
deriv += (*l1p1y() - *l1p2y()); // = dy1
}
if (param == l2p2y()) {
deriv += -(*l1p1y() - *l1p2y()); // = -dy1
}
return scale * deriv;
}
// --------------------------------------------------------
// L2LAngle
ConstraintL2LAngle::ConstraintL2LAngle(Line& l1, Line& l2, double* a)
{
pvec.push_back(l1.p1.x);
pvec.push_back(l1.p1.y);
pvec.push_back(l1.p2.x);
pvec.push_back(l1.p2.y);
pvec.push_back(l2.p1.x);
pvec.push_back(l2.p1.y);
pvec.push_back(l2.p2.x);
pvec.push_back(l2.p2.y);
pvec.push_back(a);
origpvec = pvec;
rescale();
}
ConstraintL2LAngle::ConstraintL2LAngle(Point& l1p1, Point& l1p2, Point& l2p1, Point& l2p2, double* a)
{
pvec.push_back(l1p1.x);
pvec.push_back(l1p1.y);
pvec.push_back(l1p2.x);
pvec.push_back(l1p2.y);
pvec.push_back(l2p1.x);
pvec.push_back(l2p1.y);
pvec.push_back(l2p2.x);
pvec.push_back(l2p2.y);
pvec.push_back(a);
origpvec = pvec;
rescale();
}
ConstraintType ConstraintL2LAngle::getTypeId()
{
return L2LAngle;
}
double ConstraintL2LAngle::error()
{
double dx1 = (*l1p2x() - *l1p1x());
double dy1 = (*l1p2y() - *l1p1y());
double dx2 = (*l2p2x() - *l2p1x());
double dy2 = (*l2p2y() - *l2p1y());
double a = atan2(dy1, dx1) + *angle();
double ca = cos(a);
double sa = sin(a);
double x2 = dx2 * ca + dy2 * sa;
double y2 = -dx2 * sa + dy2 * ca;
return scale * atan2(y2, x2);
}
double ConstraintL2LAngle::grad(double* param)
{
double deriv = 0.;
if (param == l1p1x() || param == l1p1y() || param == l1p2x() || param == l1p2y()) {
double dx1 = (*l1p2x() - *l1p1x());
double dy1 = (*l1p2y() - *l1p1y());
double r2 = dx1 * dx1 + dy1 * dy1;
if (param == l1p1x()) {
deriv += -dy1 / r2;
}
if (param == l1p1y()) {
deriv += dx1 / r2;
}
if (param == l1p2x()) {
deriv += dy1 / r2;
}
if (param == l1p2y()) {
deriv += -dx1 / r2;
}
}
if (param == l2p1x() || param == l2p1y() || param == l2p2x() || param == l2p2y()) {
double dx1 = (*l1p2x() - *l1p1x());
double dy1 = (*l1p2y() - *l1p1y());
double dx2 = (*l2p2x() - *l2p1x());
double dy2 = (*l2p2y() - *l2p1y());
double a = atan2(dy1, dx1) + *angle();
double ca = cos(a);
double sa = sin(a);
double x2 = dx2 * ca + dy2 * sa;
double y2 = -dx2 * sa + dy2 * ca;
double r2 = dx2 * dx2 + dy2 * dy2;
dx2 = -y2 / r2;
dy2 = x2 / r2;
if (param == l2p1x()) {
deriv += (-ca * dx2 + sa * dy2);
}
if (param == l2p1y()) {
deriv += (-sa * dx2 - ca * dy2);
}
if (param == l2p2x()) {
deriv += (ca * dx2 - sa * dy2);
}
if (param == l2p2y()) {
deriv += (sa * dx2 + ca * dy2);
}
}
if (param == angle()) {
deriv += -1;
}
return scale * deriv;
}
double ConstraintL2LAngle::maxStep(MAP_pD_D& dir, double lim)
{
constexpr double pi_18 = std::numbers::pi / 18;
MAP_pD_D::iterator it = dir.find(angle());
if (it != dir.end()) {
double step = std::abs(it->second);
if (step > pi_18) {
lim = std::min(lim, pi_18 / step);
}
}
return lim;
}
// --------------------------------------------------------
// MidpointOnLine
ConstraintMidpointOnLine::ConstraintMidpointOnLine(Line& l1, Line& l2)
{
pvec.push_back(l1.p1.x);
pvec.push_back(l1.p1.y);
pvec.push_back(l1.p2.x);
pvec.push_back(l1.p2.y);
pvec.push_back(l2.p1.x);
pvec.push_back(l2.p1.y);
pvec.push_back(l2.p2.x);
pvec.push_back(l2.p2.y);
origpvec = pvec;
rescale();
}
ConstraintMidpointOnLine::ConstraintMidpointOnLine(Point& l1p1, Point& l1p2, Point& l2p1, Point& l2p2)
{
pvec.push_back(l1p1.x);
pvec.push_back(l1p1.y);
pvec.push_back(l1p2.x);
pvec.push_back(l1p2.y);
pvec.push_back(l2p1.x);
pvec.push_back(l2p1.y);
pvec.push_back(l2p2.x);
pvec.push_back(l2p2.y);
origpvec = pvec;
rescale();
}
ConstraintType ConstraintMidpointOnLine::getTypeId()
{
return MidpointOnLine;
}
double ConstraintMidpointOnLine::error()
{
double x0 = ((*l1p1x()) + (*l1p2x())) / 2;
double y0 = ((*l1p1y()) + (*l1p2y())) / 2;
double x1 = *l2p1x(), x2 = *l2p2x();
double y1 = *l2p1y(), y2 = *l2p2y();
double dx = x2 - x1;
double dy = y2 - y1;
double d = sqrt(dx * dx + dy * dy);
double area = -x0 * dy + y0 * dx + x1 * y2 - x2 * y1; // = 2*(triangle area)
return scale * area / d;
}
double ConstraintMidpointOnLine::grad(double* param)
{
double deriv = 0.;
if (param == l1p1x() || param == l1p1y() || param == l1p2x() || param == l1p2y()
|| param == l2p1x() || param == l2p1y() || param == l2p2x() || param == l2p2y()) {
double x0 = ((*l1p1x()) + (*l1p2x())) / 2;
double y0 = ((*l1p1y()) + (*l1p2y())) / 2;
double x1 = *l2p1x(), x2 = *l2p2x();
double y1 = *l2p1y(), y2 = *l2p2y();
double dx = x2 - x1;
double dy = y2 - y1;
double d2 = dx * dx + dy * dy;
double d = sqrt(d2);
double area = -x0 * dy + y0 * dx + x1 * y2 - x2 * y1;
if (param == l1p1x()) {
deriv += (y1 - y2) / (2 * d);
}
if (param == l1p1y()) {
deriv += (x2 - x1) / (2 * d);
}
if (param == l1p2x()) {
deriv += (y1 - y2) / (2 * d);
}
if (param == l1p2y()) {
deriv += (x2 - x1) / (2 * d);
}
if (param == l2p1x()) {
deriv += ((y2 - y0) * d + (dx / d) * area) / d2;
}
if (param == l2p1y()) {
deriv += ((x0 - x2) * d + (dy / d) * area) / d2;
}
if (param == l2p2x()) {
deriv += ((y0 - y1) * d - (dx / d) * area) / d2;
}
if (param == l2p2y()) {
deriv += ((x1 - x0) * d - (dy / d) * area) / d2;
}
}
return scale * deriv;
}
// --------------------------------------------------------
// TangentCircumf
ConstraintTangentCircumf::ConstraintTangentCircumf(
Point& p1,
Point& p2,
double* rad1,
double* rad2,
bool internal_
)
: internal(internal_)
{
pvec.push_back(p1.x);
pvec.push_back(p1.y);
pvec.push_back(p2.x);
pvec.push_back(p2.y);
pvec.push_back(rad1);
pvec.push_back(rad2);
origpvec = pvec;
rescale();
}
ConstraintType ConstraintTangentCircumf::getTypeId()
{
return TangentCircumf;
}
double ConstraintTangentCircumf::error()
{
double dx = (*c1x() - *c2x());
double dy = (*c1y() - *c2y());
double d_sq = dx * dx + dy * dy;
// Handle the singularity for near-concentric circles.
// When concentric, tangency is equivalent to equal radii.
// We switch to the robust 'r1 - r2 = 0' formulation, which has a
// constant non-zero gradient, avoiding the singularity.
if (d_sq < 1e-14) {
return scale * (*r1() - *r2());
}
if (internal) {
return scale * (d_sq - (*r1() - *r2()) * (*r1() - *r2()));
}
else {
return scale * (d_sq - (*r1() + *r2()) * (*r1() + *r2()));
}
}
double ConstraintTangentCircumf::grad(double* param)
{
double deriv = 0.;
if (param == c1x() || param == c1y() || param == c2x() || param == c2y() || param == r1()
|| param == r2()) {
double dx = (*c1x() - *c2x());
double dy = (*c1y() - *c2y());
double d_sq = dx * dx + dy * dy;
// Provide the gradient corresponding to the robust 'r1 - r2 = 0' error function.
// This gradient is constant and non-zero, preventing the false redundancy report.
if (d_sq < 1e-14) {
if (param == r1()) {
deriv = 1.0;
}
else if (param == r2()) {
deriv = -1.0;
}
// The gradient is 0 for all other parameters (center coordinates).
return scale * deriv;
}
if (param == c1x()) {
deriv += 2 * dx;
}
if (param == c1y()) {
deriv += 2 * dy;
}
if (param == c2x()) {
deriv += 2 * -dx;
}
if (param == c2y()) {
deriv += 2 * -dy;
}
if (internal) {
if (param == r1()) {
deriv += 2 * (*r2() - *r1());
}
if (param == r2()) {
deriv += 2 * (*r1() - *r2());
}
}
else {
if (param == r1()) {
deriv += -2 * (*r1() + *r2());
}
if (param == r2()) {
deriv += -2 * (*r1() + *r2());
}
}
}
return scale * deriv;
}
// --------------------------------------------------------
// ConstraintPointOnEllipse
ConstraintPointOnEllipse::ConstraintPointOnEllipse(Point& p, Ellipse& e)
{
pvec.push_back(p.x);
pvec.push_back(p.y);
pvec.push_back(e.center.x);
pvec.push_back(e.center.y);
pvec.push_back(e.focus1.x);
pvec.push_back(e.focus1.y);
pvec.push_back(e.radmin);
origpvec = pvec;
rescale();
}
ConstraintType ConstraintPointOnEllipse::getTypeId()
{
return PointOnEllipse;
}
double ConstraintPointOnEllipse::error()
{
double X_0 = *p1x();
double Y_0 = *p1y();
double X_c = *cx();
double Y_c = *cy();
double X_F1 = *f1x();
double Y_F1 = *f1y();
double b = *rmin();
double err = sqrt(pow(X_0 - X_F1, 2) + pow(Y_0 - Y_F1, 2))
+ sqrt(pow(X_0 + X_F1 - 2 * X_c, 2) + pow(Y_0 + Y_F1 - 2 * Y_c, 2))
- 2 * sqrt(pow(b, 2) + pow(X_F1 - X_c, 2) + pow(Y_F1 - Y_c, 2));
return scale * err;
}
double ConstraintPointOnEllipse::grad(double* param)
{
double deriv = 0.;
if (param == p1x() || param == p1y() || param == f1x() || param == f1y() || param == cx()
|| param == cy() || param == rmin()) {
double X_0 = *p1x();
double Y_0 = *p1y();
double X_c = *cx();
double Y_c = *cy();
double X_F1 = *f1x();
double Y_F1 = *f1y();
double b = *rmin();
if (param == p1x()) {
deriv += (X_0 - X_F1) / sqrt(pow(X_0 - X_F1, 2) + pow(Y_0 - Y_F1, 2))
+ (X_0 + X_F1 - 2 * X_c)
/ sqrt(pow(X_0 + X_F1 - 2 * X_c, 2) + pow(Y_0 + Y_F1 - 2 * Y_c, 2));
}
if (param == p1y()) {
deriv += (Y_0 - Y_F1) / sqrt(pow(X_0 - X_F1, 2) + pow(Y_0 - Y_F1, 2))
+ (Y_0 + Y_F1 - 2 * Y_c)
/ sqrt(pow(X_0 + X_F1 - 2 * X_c, 2) + pow(Y_0 + Y_F1 - 2 * Y_c, 2));
}
if (param == f1x()) {
deriv += -(X_0 - X_F1) / sqrt(pow(X_0 - X_F1, 2) + pow(Y_0 - Y_F1, 2))
- 2 * (X_F1 - X_c) / sqrt(pow(b, 2) + pow(X_F1 - X_c, 2) + pow(Y_F1 - Y_c, 2))
+ (X_0 + X_F1 - 2 * X_c)
/ sqrt(pow(X_0 + X_F1 - 2 * X_c, 2) + pow(Y_0 + Y_F1 - 2 * Y_c, 2));
}
if (param == f1y()) {
deriv += -(Y_0 - Y_F1) / sqrt(pow(X_0 - X_F1, 2) + pow(Y_0 - Y_F1, 2))
- 2 * (Y_F1 - Y_c) / sqrt(pow(b, 2) + pow(X_F1 - X_c, 2) + pow(Y_F1 - Y_c, 2))
+ (Y_0 + Y_F1 - 2 * Y_c)
/ sqrt(pow(X_0 + X_F1 - 2 * X_c, 2) + pow(Y_0 + Y_F1 - 2 * Y_c, 2));
}
if (param == cx()) {
deriv += 2 * (X_F1 - X_c) / sqrt(pow(b, 2) + pow(X_F1 - X_c, 2) + pow(Y_F1 - Y_c, 2))
- 2 * (X_0 + X_F1 - 2 * X_c)
/ sqrt(pow(X_0 + X_F1 - 2 * X_c, 2) + pow(Y_0 + Y_F1 - 2 * Y_c, 2));
}
if (param == cy()) {
deriv += 2 * (Y_F1 - Y_c) / sqrt(pow(b, 2) + pow(X_F1 - X_c, 2) + pow(Y_F1 - Y_c, 2))
- 2 * (Y_0 + Y_F1 - 2 * Y_c)
/ sqrt(pow(X_0 + X_F1 - 2 * X_c, 2) + pow(Y_0 + Y_F1 - 2 * Y_c, 2));
}
if (param == rmin()) {
deriv += -2 * b / sqrt(pow(b, 2) + pow(X_F1 - X_c, 2) + pow(Y_F1 - Y_c, 2));
}
}
return scale * deriv;
}
// --------------------------------------------------------
// ConstraintEllipseTangentLine
ConstraintEllipseTangentLine::ConstraintEllipseTangentLine(Line& l, Ellipse& e)
: l(l)
, e(e)
{
this->l.PushOwnParams(pvec);
this->e.PushOwnParams(pvec); // DeepSOIC: hopefully, this won't push arc's parameters
origpvec = pvec;
pvecChangedFlag = true;
rescale();
}
void ConstraintEllipseTangentLine::ReconstructGeomPointers()
{
int i = 0;
l.ReconstructOnNewPvec(pvec, i);
e.ReconstructOnNewPvec(pvec, i);
pvecChangedFlag = false;
}
ConstraintType ConstraintEllipseTangentLine::getTypeId()
{
return TangentEllipseLine;
}
void ConstraintEllipseTangentLine::errorgrad(double* err, double* grad, double* param)
{
// DeepSOIC equation
// https://forum.freecad.org/viewtopic.php?f=10&t=7520&start=140
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
DeriVector2 p1(l.p1, param);
DeriVector2 p2(l.p2, param);
DeriVector2 f1(e.focus1, param);
DeriVector2 c(e.center, param);
DeriVector2 f2 = c.linCombi(2.0, f1, -1.0); // 2*cv - f1v
// mirror F1 against the line
DeriVector2 nl = l.CalculateNormal(l.p1, param).getNormalized();
double distF1L = 0, ddistF1L = 0; // distance F1 to line
distF1L = f1.subtr(p1).scalarProd(nl, &ddistF1L);
DeriVector2 f1m = f1.sum(nl.multD(-2 * distF1L, -2 * ddistF1L)); // f1m = f1 mirrored
// calculate distance form f1m to f2
double distF1mF2, ddistF1mF2;
distF1mF2 = f2.subtr(f1m).length(ddistF1mF2);
// calculate major radius (to compare the distance to)
double dradmin = (param == e.radmin) ? 1.0 : 0.0;
double radmaj, dradmaj;
radmaj = e.getRadMaj(c, f1, *e.radmin, dradmin, dradmaj);
if (err) {
*err = distF1mF2 - 2 * radmaj;
}
if (grad) {
*grad = ddistF1mF2 - 2 * dradmaj;
}
}
// --------------------------------------------------------
// ConstraintInternalAlignmentPoint2Ellipse
ConstraintInternalAlignmentPoint2Ellipse::ConstraintInternalAlignmentPoint2Ellipse(
Ellipse& e,
Point& p1,
InternalAlignmentType alignmentType
)
: e(e)
, p(p1)
, AlignmentType(alignmentType)
{
pvec.push_back(p.x);
pvec.push_back(p.y);
this->e.PushOwnParams(pvec);
origpvec = pvec;
rescale();
}
void ConstraintInternalAlignmentPoint2Ellipse::ReconstructGeomPointers()
{
int i = 0;
p.x = pvec[i];
i++;
p.y = pvec[i];
i++;
e.ReconstructOnNewPvec(pvec, i);
pvecChangedFlag = false;
}
ConstraintType ConstraintInternalAlignmentPoint2Ellipse::getTypeId()
{
return InternalAlignmentPoint2Ellipse;
}
void ConstraintInternalAlignmentPoint2Ellipse::errorgrad(double* err, double* grad, double* param)
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
// todo: prefill only what's needed, not everything
DeriVector2 c(e.center, param);
DeriVector2 f1(e.focus1, param);
DeriVector2 emaj = f1.subtr(c).getNormalized();
DeriVector2 emin = emaj.rotate90ccw();
DeriVector2 pv(p, param);
double b, db; // minor radius
b = *e.radmin;
db = (e.radmin == param) ? 1.0 : 0.0;
// major radius
double a, da;
a = e.getRadMaj(c, f1, b, db, da);
DeriVector2 poa; // point to align to
bool by_y_not_by_x = false; // a flag to indicate if the alignment error function is for y
// (false - x, true - y)
switch (AlignmentType) {
case EllipsePositiveMajorX:
case EllipsePositiveMajorY:
poa = c.sum(emaj.multD(a, da));
by_y_not_by_x = AlignmentType == EllipsePositiveMajorY;
break;
case EllipseNegativeMajorX:
case EllipseNegativeMajorY:
poa = c.sum(emaj.multD(-a, -da));
by_y_not_by_x = AlignmentType == EllipseNegativeMajorY;
break;
case EllipsePositiveMinorX:
case EllipsePositiveMinorY:
poa = c.sum(emin.multD(b, db));
by_y_not_by_x = AlignmentType == EllipsePositiveMinorY;
break;
case EllipseNegativeMinorX:
case EllipseNegativeMinorY:
poa = c.sum(emin.multD(-b, -db));
by_y_not_by_x = AlignmentType == EllipseNegativeMinorY;
break;
case EllipseFocus2X:
case EllipseFocus2Y:
poa = c.linCombi(2.0, f1, -1.0);
by_y_not_by_x = AlignmentType == EllipseFocus2Y;
break;
default:
// shouldn't happen
poa = pv; // align to the point itself, doing nothing essentially
}
if (err) {
*err = by_y_not_by_x ? pv.y - poa.y : pv.x - poa.x;
}
if (grad) {
*grad = by_y_not_by_x ? pv.dy - poa.dy : pv.dx - poa.dx;
}
}
// --------------------------------------------------------
// ConstraintInternalAlignmentPoint2Hyperbola
ConstraintInternalAlignmentPoint2Hyperbola::ConstraintInternalAlignmentPoint2Hyperbola(
Hyperbola& e,
Point& p1,
InternalAlignmentType alignmentType
)
: e(e)
, p(p1)
, AlignmentType(alignmentType)
{
pvec.push_back(p.x);
pvec.push_back(p.y);
this->e.PushOwnParams(pvec);
origpvec = pvec;
rescale();
}
void ConstraintInternalAlignmentPoint2Hyperbola::ReconstructGeomPointers()
{
int i = 0;
p.x = pvec[i];
i++;
p.y = pvec[i];
i++;
e.ReconstructOnNewPvec(pvec, i);
pvecChangedFlag = false;
}
ConstraintType ConstraintInternalAlignmentPoint2Hyperbola::getTypeId()
{
return InternalAlignmentPoint2Hyperbola;
}
void ConstraintInternalAlignmentPoint2Hyperbola::errorgrad(double* err, double* grad, double* param)
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
// todo: prefill only what's needed, not everything
DeriVector2 c(e.center, param);
DeriVector2 f1(e.focus1, param);
DeriVector2 emaj = f1.subtr(c).getNormalized();
DeriVector2 emin = emaj.rotate90ccw();
DeriVector2 pv(p, param);
double b, db; // minor radius
b = *e.radmin;
db = (e.radmin == param) ? 1.0 : 0.0;
// major radius
double a, da;
a = e.getRadMaj(c, f1, b, db, da);
DeriVector2 poa; // point to align to
bool by_y_not_by_x = false; // a flag to indicate if the alignment error function is for y
// (false - x, true - y)
switch (AlignmentType) {
case HyperbolaPositiveMajorX:
case HyperbolaPositiveMajorY:
poa = c.sum(emaj.multD(a, da));
by_y_not_by_x = AlignmentType == HyperbolaPositiveMajorY;
break;
case HyperbolaNegativeMajorX:
case HyperbolaNegativeMajorY:
poa = c.sum(emaj.multD(-a, -da));
by_y_not_by_x = AlignmentType == HyperbolaNegativeMajorY;
break;
case HyperbolaPositiveMinorX:
case HyperbolaPositiveMinorY: {
DeriVector2 pa = c.sum(emaj.multD(a, da));
// DeriVector2 A(pa.x,pa.y);
// poa = A.sum(emin.multD(b, db));
poa = pa.sum(emin.multD(b, db));
by_y_not_by_x = AlignmentType == HyperbolaPositiveMinorY;
break;
}
case HyperbolaNegativeMinorX:
case HyperbolaNegativeMinorY: {
DeriVector2 pa = c.sum(emaj.multD(a, da));
// DeriVector2 A(pa.x,pa.y);
// poa = A.sum(emin.multD(-b, -db));
poa = pa.sum(emin.multD(-b, -db));
by_y_not_by_x = AlignmentType == HyperbolaNegativeMinorY;
break;
}
default:
// shouldn't happen
poa = pv; // align to the point itself, doing nothing essentially
}
if (err) {
*err = by_y_not_by_x ? pv.y - poa.y : pv.x - poa.x;
}
if (grad) {
*grad = by_y_not_by_x ? pv.dy - poa.dy : pv.dx - poa.dx;
}
}
// --------------------------------------------------------
// ConstraintEqualMajorAxesEllipse
ConstraintEqualMajorAxesConic::ConstraintEqualMajorAxesConic(MajorRadiusConic* a1, MajorRadiusConic* a2)
: e1(a1)
, e2(a2)
{
this->e1->PushOwnParams(pvec);
this->e2->PushOwnParams(pvec);
origpvec = pvec;
pvecChangedFlag = true;
rescale();
}
void ConstraintEqualMajorAxesConic::ReconstructGeomPointers()
{
int i = 0;
e1->ReconstructOnNewPvec(pvec, i);
e2->ReconstructOnNewPvec(pvec, i);
pvecChangedFlag = false;
}
ConstraintType ConstraintEqualMajorAxesConic::getTypeId()
{
return EqualMajorAxesConic;
}
void ConstraintEqualMajorAxesConic::errorgrad(double* err, double* grad, double* param)
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
double a1, da1;
a1 = e1->getRadMaj(param, da1);
double a2, da2;
a2 = e2->getRadMaj(param, da2);
if (err) {
*err = a2 - a1;
}
if (grad) {
*grad = da2 - da1;
}
}
// ConstraintEqualFocalDistance
ConstraintEqualFocalDistance::ConstraintEqualFocalDistance(ArcOfParabola* a1, ArcOfParabola* a2)
{
this->e1 = a1;
this->e1->PushOwnParams(pvec);
this->e2 = a2;
this->e2->PushOwnParams(pvec);
origpvec = pvec;
pvecChangedFlag = true;
rescale();
}
void ConstraintEqualFocalDistance::ReconstructGeomPointers()
{
int i = 0;
e1->ReconstructOnNewPvec(pvec, i);
e2->ReconstructOnNewPvec(pvec, i);
pvecChangedFlag = false;
}
ConstraintType ConstraintEqualFocalDistance::getTypeId()
{
return EqualFocalDistance;
}
void ConstraintEqualFocalDistance::errorgrad(double* err, double* grad, double* param)
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
DeriVector2 focus1(this->e1->focus1, param);
DeriVector2 vertex1(this->e1->vertex, param);
DeriVector2 focalvect1 = vertex1.subtr(focus1);
double focal1, dfocal1;
focal1 = focalvect1.length(dfocal1);
DeriVector2 focus2(this->e2->focus1, param);
DeriVector2 vertex2(this->e2->vertex, param);
DeriVector2 focalvect2 = vertex2.subtr(focus2);
double focal2, dfocal2;
focal2 = focalvect2.length(dfocal2);
if (err) {
*err = focal2 - focal1;
}
if (grad) {
*grad = dfocal2 - dfocal1;
}
}
// --------------------------------------------------------
// ConstraintCurveValue
ConstraintCurveValue::ConstraintCurveValue(Point& p, double* pcoord, Curve& c, double* u)
: crv(c.Copy())
{
pvec.push_back(p.x);
pvec.push_back(p.y);
pvec.push_back(pcoord);
pvec.push_back(u);
crv->PushOwnParams(pvec);
pvecChangedFlag = true;
origpvec = pvec;
rescale();
}
ConstraintCurveValue::~ConstraintCurveValue()
{
delete this->crv;
this->crv = nullptr;
}
void ConstraintCurveValue::ReconstructGeomPointers()
{
int i = 0;
p.x = pvec[i];
i++;
p.y = pvec[i];
i++;
i++; // we have an inline function for point coordinate
i++; // we have an inline function for the parameterU
this->crv->ReconstructOnNewPvec(pvec, i);
pvecChangedFlag = false;
}
ConstraintType ConstraintCurveValue::getTypeId()
{
return CurveValue;
}
void ConstraintCurveValue::errorgrad(double* err, double* grad, double* param)
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
double u, du;
u = *(this->u());
du = (param == this->u()) ? 1.0 : 0.0;
DeriVector2 P_to; // point of curve at parameter value of u, in global coordinates
P_to = this->crv->Value(u, du, param);
DeriVector2 P_from(this->p, param); // point to be constrained
DeriVector2 err_vec = P_from.subtr(P_to);
if (this->pcoord() == this->p.x) { // this constraint is for X projection
if (err) {
*err = err_vec.x;
}
if (grad) {
*grad = err_vec.dx;
}
}
else if (this->pcoord() == this->p.y) { // this constraint is for Y projection
if (err) {
*err = err_vec.y;
}
if (grad) {
*grad = err_vec.dy;
}
}
else {
assert(false /*this constraint is neither X nor Y. Nothing to do..*/);
}
}
double ConstraintCurveValue::maxStep(MAP_pD_D& /*dir*/, double lim)
{
return lim;
}
// --------------------------------------------------------
// ConstraintPointOnHyperbola
ConstraintPointOnHyperbola::ConstraintPointOnHyperbola(Point& p, Hyperbola& e)
{
pvec.push_back(p.x);
pvec.push_back(p.y);
pvec.push_back(e.center.x);
pvec.push_back(e.center.y);
pvec.push_back(e.focus1.x);
pvec.push_back(e.focus1.y);
pvec.push_back(e.radmin);
origpvec = pvec;
rescale();
}
ConstraintPointOnHyperbola::ConstraintPointOnHyperbola(Point& p, ArcOfHyperbola& e)
{
pvec.push_back(p.x);
pvec.push_back(p.y);
pvec.push_back(e.center.x);
pvec.push_back(e.center.y);
pvec.push_back(e.focus1.x);
pvec.push_back(e.focus1.y);
pvec.push_back(e.radmin);
origpvec = pvec;
rescale();
}
ConstraintType ConstraintPointOnHyperbola::getTypeId()
{
return PointOnHyperbola;
}
double ConstraintPointOnHyperbola::error()
{
double X_0 = *p1x();
double Y_0 = *p1y();
double X_c = *cx();
double Y_c = *cy();
double X_F1 = *f1x();
double Y_F1 = *f1y();
double b = *rmin();
// Full sage worksheet at:
// https://forum.freecad.org/viewtopic.php?f=10&t=8038&p=110447#p110447
//
// Err = |PF2| - |PF1| - 2*a
// sage code:
// C = vector([X_c,Y_c])
// F2 = C+(C-F1)
// X_F2 = F2[0]
// Y_F2 = F2[1]
// a = sqrt((F1-C)*(F1-C)-b*b);
// show(a)
// DM=sqrt((P-F2)*(P-F2))-sqrt((P-F1)*(P-F1))-2*a
// show(DM.simplify_radical())
double err = -sqrt(pow(X_0 - X_F1, 2) + pow(Y_0 - Y_F1, 2))
+ sqrt(pow(X_0 + X_F1 - 2 * X_c, 2) + pow(Y_0 + Y_F1 - 2 * Y_c, 2))
- 2 * sqrt(-pow(b, 2) + pow(X_F1 - X_c, 2) + pow(Y_F1 - Y_c, 2));
return scale * err;
}
double ConstraintPointOnHyperbola::grad(double* param)
{
double deriv = 0.;
if (param == p1x() || param == p1y() || param == f1x() || param == f1y() || param == cx()
|| param == cy() || param == rmin()) {
double X_0 = *p1x();
double Y_0 = *p1y();
double X_c = *cx();
double Y_c = *cy();
double X_F1 = *f1x();
double Y_F1 = *f1y();
double b = *rmin();
if (param == p1x()) {
deriv += -(X_0 - X_F1) / sqrt(pow(X_0 - X_F1, 2) + pow(Y_0 - Y_F1, 2))
+ (X_0 + X_F1 - 2 * X_c)
/ sqrt(pow(X_0 + X_F1 - 2 * X_c, 2) + pow(Y_0 + Y_F1 - 2 * Y_c, 2));
}
if (param == p1y()) {
deriv += -(Y_0 - Y_F1) / sqrt(pow(X_0 - X_F1, 2) + pow(Y_0 - Y_F1, 2))
+ (Y_0 + Y_F1 - 2 * Y_c)
/ sqrt(pow(X_0 + X_F1 - 2 * X_c, 2) + pow(Y_0 + Y_F1 - 2 * Y_c, 2));
}
if (param == f1x()) {
deriv += (X_0 - X_F1) / sqrt(pow(X_0 - X_F1, 2) + pow(Y_0 - Y_F1, 2))
- 2 * (X_F1 - X_c) / sqrt(-pow(b, 2) + pow(X_F1 - X_c, 2) + pow(Y_F1 - Y_c, 2))
+ (X_0 + X_F1 - 2 * X_c)
/ sqrt(pow(X_0 + X_F1 - 2 * X_c, 2) + pow(Y_0 + Y_F1 - 2 * Y_c, 2));
}
if (param == f1y()) {
deriv += (Y_0 - Y_F1) / sqrt(pow(X_0 - X_F1, 2) + pow(Y_0 - Y_F1, 2))
- 2 * (Y_F1 - Y_c) / sqrt(-pow(b, 2) + pow(X_F1 - X_c, 2) + pow(Y_F1 - Y_c, 2))
+ (Y_0 + Y_F1 - 2 * Y_c)
/ sqrt(pow(X_0 + X_F1 - 2 * X_c, 2) + pow(Y_0 + Y_F1 - 2 * Y_c, 2));
}
if (param == cx()) {
deriv += 2 * (X_F1 - X_c) / sqrt(-pow(b, 2) + pow(X_F1 - X_c, 2) + pow(Y_F1 - Y_c, 2))
- 2 * (X_0 + X_F1 - 2 * X_c)
/ sqrt(pow(X_0 + X_F1 - 2 * X_c, 2) + pow(Y_0 + Y_F1 - 2 * Y_c, 2));
}
if (param == cy()) {
deriv += 2 * (Y_F1 - Y_c) / sqrt(-pow(b, 2) + pow(X_F1 - X_c, 2) + pow(Y_F1 - Y_c, 2))
- 2 * (Y_0 + Y_F1 - 2 * Y_c)
/ sqrt(pow(X_0 + X_F1 - 2 * X_c, 2) + pow(Y_0 + Y_F1 - 2 * Y_c, 2));
}
if (param == rmin()) {
deriv += 2 * b / sqrt(-pow(b, 2) + pow(X_F1 - X_c, 2) + pow(Y_F1 - Y_c, 2));
}
}
return scale * deriv;
}
// --------------------------------------------------------
// ConstraintPointOnParabola
ConstraintPointOnParabola::ConstraintPointOnParabola(Point& p, Parabola& e)
: parab(e.Copy())
{
pvec.push_back(p.x);
pvec.push_back(p.y);
parab->PushOwnParams(pvec);
pvecChangedFlag = true;
origpvec = pvec;
rescale();
}
ConstraintPointOnParabola::ConstraintPointOnParabola(Point& p, ArcOfParabola& e)
: parab(e.Copy())
{
pvec.push_back(p.x);
pvec.push_back(p.y);
parab->PushOwnParams(pvec);
pvecChangedFlag = true;
origpvec = pvec;
rescale();
}
ConstraintPointOnParabola::~ConstraintPointOnParabola()
{
delete this->parab;
this->parab = nullptr;
}
void ConstraintPointOnParabola::ReconstructGeomPointers()
{
int i = 0;
p.x = pvec[i];
i++;
p.y = pvec[i];
i++;
this->parab->ReconstructOnNewPvec(pvec, i);
pvecChangedFlag = false;
}
ConstraintType ConstraintPointOnParabola::getTypeId()
{
return PointOnParabola;
}
void ConstraintPointOnParabola::errorgrad(double* err, double* grad, double* param)
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
DeriVector2 focus(this->parab->focus1, param);
DeriVector2 vertex(this->parab->vertex, param);
DeriVector2 point(this->p, param); // point to be constrained to parabola
DeriVector2 focalvect = focus.subtr(vertex);
DeriVector2 xdir = focalvect.getNormalized();
DeriVector2 point_to_focus = point.subtr(focus);
double focal, dfocal;
focal = focalvect.length(dfocal);
double pf, dpf;
pf = point_to_focus.length(dpf);
double proj, dproj;
proj = point_to_focus.scalarProd(xdir, &dproj);
if (err) {
*err = pf - 2 * focal - proj;
}
if (grad) {
*grad = dpf - 2 * dfocal - dproj;
}
}
// --------------------------------------------------------
// ConstraintAngleViaPoint
ConstraintAngleViaPoint::ConstraintAngleViaPoint(Curve& acrv1, Curve& acrv2, Point p, double* angle)
: crv1(acrv1.Copy())
, crv2(acrv2.Copy())
{
pvec.push_back(angle);
pvec.push_back(p.x);
pvec.push_back(p.y);
crv1->PushOwnParams(pvec);
crv2->PushOwnParams(pvec);
origpvec = pvec;
pvecChangedFlag = true;
rescale();
}
ConstraintAngleViaPoint::~ConstraintAngleViaPoint()
{
delete crv1;
crv1 = nullptr;
delete crv2;
crv2 = nullptr;
}
void ConstraintAngleViaPoint::ReconstructGeomPointers()
{
int cnt = 0;
cnt++; // skip angle - we have an inline function for that
poa.x = pvec[cnt];
cnt++;
poa.y = pvec[cnt];
cnt++;
crv1->ReconstructOnNewPvec(pvec, cnt);
crv2->ReconstructOnNewPvec(pvec, cnt);
pvecChangedFlag = false;
}
ConstraintType ConstraintAngleViaPoint::getTypeId()
{
return AngleViaPoint;
}
double ConstraintAngleViaPoint::error()
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
double ang = *angle();
DeriVector2 n1 = crv1->CalculateNormal(poa);
DeriVector2 n2 = crv2->CalculateNormal(poa);
// rotate n1 by angle
DeriVector2 n1r(n1.x * cos(ang) - n1.y * sin(ang), n1.x * sin(ang) + n1.y * cos(ang));
// calculate angle between n1r and n2. Since we have rotated the n1, the angle is the error
// function. for our atan2, y is a dot product (n2) * (n1r rotated ccw by 90 degrees).
// x is a dot product (n2) * (n1r)
double err = atan2(-n2.x * n1r.y + n2.y * n1r.x, n2.x * n1r.x + n2.y * n1r.y);
// essentially, the function is equivalent to atan2(n2)-(atan2(n1)+angle). The only difference
// is behavior when normals are zero (the intended result is also zero in this case).
return scale * err;
}
double ConstraintAngleViaPoint::grad(double* param)
{
// first of all, check that we need to compute anything.
if (findParamInPvec(param) == -1) {
return 0.0;
}
double deriv = 0.;
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
if (param == angle()) {
deriv += -1.0;
}
DeriVector2 n1 = crv1->CalculateNormal(poa, param);
DeriVector2 n2 = crv2->CalculateNormal(poa, param);
deriv -= ((-n1.dx) * n1.y / pow(n1.length(), 2) + n1.dy * n1.x / pow(n1.length(), 2));
deriv += ((-n2.dx) * n2.y / pow(n2.length(), 2) + n2.dy * n2.x / pow(n2.length(), 2));
return scale * deriv;
}
// --------------------------------------------------------
// ConstraintAngleViaTwoPoints
ConstraintAngleViaTwoPoints::ConstraintAngleViaTwoPoints(
Curve& acrv1,
Curve& acrv2,
Point p1,
Point p2,
double* angle
)
: crv1(acrv1.Copy())
, crv2(acrv2.Copy())
{
pvec.push_back(angle);
pvec.push_back(p1.x);
pvec.push_back(p1.y);
pvec.push_back(p2.x);
pvec.push_back(p2.y);
crv1->PushOwnParams(pvec);
crv2->PushOwnParams(pvec);
origpvec = pvec;
pvecChangedFlag = true;
rescale();
}
ConstraintAngleViaTwoPoints::~ConstraintAngleViaTwoPoints()
{
delete crv1;
crv1 = nullptr;
delete crv2;
crv2 = nullptr;
}
void ConstraintAngleViaTwoPoints::ReconstructGeomPointers()
{
int cnt = 0;
cnt++; // skip angle - we have an inline function for that
poa1.x = pvec[cnt];
cnt++;
poa1.y = pvec[cnt];
cnt++;
poa2.x = pvec[cnt];
cnt++;
poa2.y = pvec[cnt];
cnt++;
crv1->ReconstructOnNewPvec(pvec, cnt);
crv2->ReconstructOnNewPvec(pvec, cnt);
pvecChangedFlag = false;
}
ConstraintType ConstraintAngleViaTwoPoints::getTypeId()
{
return AngleViaTwoPoints;
}
double ConstraintAngleViaTwoPoints::error()
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
double ang = *angle();
DeriVector2 n1 = crv1->CalculateNormal(poa1);
DeriVector2 n2 = crv2->CalculateNormal(poa2);
// rotate n1 by angle
DeriVector2 n1r(n1.x * cos(ang) - n1.y * sin(ang), n1.x * sin(ang) + n1.y * cos(ang));
// calculate angle between n1r and n2. Since we have rotated the n1, the angle is the error
// function. for our atan2, y is a dot product (n2) * (n1r rotated ccw by 90 degrees).
// x is a dot product (n2) * (n1r)
double err = atan2(-n2.x * n1r.y + n2.y * n1r.x, n2.x * n1r.x + n2.y * n1r.y);
// essentially, the function is equivalent to atan2(n2)-(atan2(n1)+angle). The only difference
// is behavior when normals are zero (the intended result is also zero in this case).
return scale * err;
}
double ConstraintAngleViaTwoPoints::grad(double* param)
{
// first of all, check that we need to compute anything.
if (findParamInPvec(param) == -1) {
return 0.0;
}
double deriv = 0.;
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
if (param == angle()) {
deriv += -1.0;
}
DeriVector2 n1 = crv1->CalculateNormal(poa1, param);
DeriVector2 n2 = crv2->CalculateNormal(poa2, param);
deriv -= ((-n1.dx) * n1.y / pow(n1.length(), 2) + n1.dy * n1.x / pow(n1.length(), 2));
deriv += ((-n2.dx) * n2.y / pow(n2.length(), 2) + n2.dy * n2.x / pow(n2.length(), 2));
return scale * deriv;
}
// --------------------------------------------------------
// ConstraintAngleViaPointAndParam
ConstraintAngleViaPointAndParam::ConstraintAngleViaPointAndParam(
Curve& acrv1,
Curve& acrv2,
Point p,
double* cparam,
double* angle
)
: crv1(acrv1.Copy())
, crv2(acrv2.Copy())
{
pvec.push_back(angle);
pvec.push_back(p.x);
pvec.push_back(p.y);
pvec.push_back(cparam);
crv1->PushOwnParams(pvec);
crv2->PushOwnParams(pvec);
origpvec = pvec;
pvecChangedFlag = true;
rescale();
}
ConstraintAngleViaPointAndParam::~ConstraintAngleViaPointAndParam()
{
delete crv1;
crv1 = nullptr;
delete crv2;
crv2 = nullptr;
}
void ConstraintAngleViaPointAndParam::ReconstructGeomPointers()
{
int cnt = 0;
cnt++; // skip angle - we have an inline function for that
poa.x = pvec[cnt];
cnt++;
poa.y = pvec[cnt];
cnt++;
cnt++; // skip cparam
crv1->ReconstructOnNewPvec(pvec, cnt);
crv2->ReconstructOnNewPvec(pvec, cnt);
pvecChangedFlag = false;
}
ConstraintType ConstraintAngleViaPointAndParam::getTypeId()
{
return AngleViaPointAndParam;
}
double ConstraintAngleViaPointAndParam::error()
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
double ang = *angle();
DeriVector2 n1 = crv1->CalculateNormal(cparam());
DeriVector2 n2 = crv2->CalculateNormal(poa);
// rotate n1 by angle
DeriVector2 n1r(n1.x * cos(ang) - n1.y * sin(ang), n1.x * sin(ang) + n1.y * cos(ang));
// calculate angle between n1r and n2. Since we have rotated the n1, the angle is the error
// function. for our atan2, y is a dot product (n2) * (n1r rotated ccw by 90 degrees).
// x is a dot product (n2) * (n1r)
double err = atan2(-n2.x * n1r.y + n2.y * n1r.x, n2.x * n1r.x + n2.y * n1r.y);
// essentially, the function is equivalent to atan2(n2)-(atan2(n1)+angle). The only difference
// is behavior when normals are zero (the intended result is also zero in this case).
return scale * err;
}
double ConstraintAngleViaPointAndParam::grad(double* param)
{
// first of all, check that we need to compute anything.
if (findParamInPvec(param) == -1) {
return 0.0;
}
double deriv = 0.;
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
if (param == angle()) {
deriv += -1.0;
}
DeriVector2 n1 = crv1->CalculateNormal(cparam(), param);
DeriVector2 n2 = crv2->CalculateNormal(poa, param);
deriv -= ((-n1.dx) * n1.y / pow(n1.length(), 2) + n1.dy * n1.x / pow(n1.length(), 2));
deriv += ((-n2.dx) * n2.y / pow(n2.length(), 2) + n2.dy * n2.x / pow(n2.length(), 2));
return scale * deriv;
}
// --------------------------------------------------------
// ConstraintAngleViaPointAndTwoParams
ConstraintAngleViaPointAndTwoParams::ConstraintAngleViaPointAndTwoParams(
Curve& acrv1,
Curve& acrv2,
Point p,
double* cparam1,
double* cparam2,
double* angle
)
: crv1(acrv1.Copy())
, crv2(acrv2.Copy())
{
pvec.push_back(angle);
pvec.push_back(p.x);
pvec.push_back(p.y);
pvec.push_back(cparam1);
pvec.push_back(cparam2);
crv1->PushOwnParams(pvec);
crv2->PushOwnParams(pvec);
origpvec = pvec;
pvecChangedFlag = true;
rescale();
}
ConstraintAngleViaPointAndTwoParams::~ConstraintAngleViaPointAndTwoParams()
{
delete crv1;
crv1 = nullptr;
delete crv2;
crv2 = nullptr;
}
void ConstraintAngleViaPointAndTwoParams::ReconstructGeomPointers()
{
int cnt = 0;
cnt++; // skip angle - we have an inline function for that
poa.x = pvec[cnt];
cnt++;
poa.y = pvec[cnt];
cnt++;
cnt++; // skip cparam1 - we have an inline function for that
cnt++; // skip cparam2 - we have an inline function for that
crv1->ReconstructOnNewPvec(pvec, cnt);
crv2->ReconstructOnNewPvec(pvec, cnt);
pvecChangedFlag = false;
}
ConstraintType ConstraintAngleViaPointAndTwoParams::getTypeId()
{
return AngleViaPointAndTwoParams;
}
double ConstraintAngleViaPointAndTwoParams::error()
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
double ang = *angle();
DeriVector2 n1 = crv1->CalculateNormal(cparam1());
DeriVector2 n2 = crv2->CalculateNormal(cparam2());
// rotate n1 by angle
DeriVector2 n1r(n1.x * cos(ang) - n1.y * sin(ang), n1.x * sin(ang) + n1.y * cos(ang));
// calculate angle between n1r and n2. Since we have rotated the n1, the angle is the error
// function. for our atan2, y is a dot product (n2) * (n1r rotated ccw by 90 degrees).
// x is a dot product (n2) * (n1r)
double err = atan2(-n2.x * n1r.y + n2.y * n1r.x, n2.x * n1r.x + n2.y * n1r.y);
// essentially, the function is equivalent to atan2(n2)-(atan2(n1)+angle). The only difference
// is behavior when normals are zero (the intended result is also zero in this case).
return scale * err;
}
double ConstraintAngleViaPointAndTwoParams::grad(double* param)
{
// first of all, check that we need to compute anything.
if (findParamInPvec(param) == -1) {
return 0.0;
}
double deriv = 0.;
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
if (param == angle()) {
deriv += -1.0;
}
DeriVector2 n1 = crv1->CalculateNormal(cparam1(), param);
DeriVector2 n2 = crv2->CalculateNormal(cparam2(), param);
deriv -= ((-n1.dx) * n1.y / pow(n1.length(), 2) + n1.dy * n1.x / pow(n1.length(), 2));
deriv += ((-n2.dx) * n2.y / pow(n2.length(), 2) + n2.dy * n2.x / pow(n2.length(), 2));
return scale * deriv;
}
// --------------------------------------------------------
// ConstraintSnell
ConstraintSnell::ConstraintSnell(
Curve& r1,
Curve& r2,
Curve& b,
Point p,
double* n1,
double* n2,
bool flipn1,
bool flipn2
)
: ray1(r1.Copy())
, ray2(r2.Copy())
, boundary(b.Copy())
, flipn1(flipn1)
, flipn2(flipn2)
{
pvec.push_back(n1);
pvec.push_back(n2);
pvec.push_back(p.x);
pvec.push_back(p.y);
ray1->PushOwnParams(pvec);
ray2->PushOwnParams(pvec);
boundary->PushOwnParams(pvec);
origpvec = pvec;
pvecChangedFlag = true;
rescale();
}
ConstraintSnell::~ConstraintSnell()
{
delete ray1;
ray1 = nullptr;
delete ray2;
ray2 = nullptr;
delete boundary;
boundary = nullptr;
}
void ConstraintSnell::ReconstructGeomPointers()
{
int cnt = 0;
cnt++;
cnt++; // skip n1, n2 - we have an inline function for that
poa.x = pvec[cnt];
cnt++;
poa.y = pvec[cnt];
cnt++;
ray1->ReconstructOnNewPvec(pvec, cnt);
ray2->ReconstructOnNewPvec(pvec, cnt);
boundary->ReconstructOnNewPvec(pvec, cnt);
pvecChangedFlag = false;
}
ConstraintType ConstraintSnell::getTypeId()
{
return Snell;
}
// error and gradient combined. Values are returned through pointers.
void ConstraintSnell::errorgrad(double* err, double* grad, double* param)
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
DeriVector2 tang1 = ray1->CalculateNormal(poa, param).rotate90cw().getNormalized();
DeriVector2 tang2 = ray2->CalculateNormal(poa, param).rotate90cw().getNormalized();
DeriVector2 tangB = boundary->CalculateNormal(poa, param).rotate90cw().getNormalized();
double sin1, dsin1, sin2, dsin2;
sin1 = tang1.scalarProd(tangB, &dsin1); // sinus of angle of incidence
sin2 = tang2.scalarProd(tangB, &dsin2);
if (flipn1) {
sin1 = -sin1;
dsin1 = -dsin1;
}
if (flipn2) {
sin2 = -sin2;
dsin2 = -dsin2;
}
double dn1 = (param == n1()) ? 1.0 : 0.0;
double dn2 = (param == n2()) ? 1.0 : 0.0;
if (err) {
*err = *n1() * sin1 - *n2() * sin2;
}
if (grad) {
*grad = dn1 * sin1 + *n1() * dsin1 - dn2 * sin2 - *n2() * dsin2;
}
}
// --------------------------------------------------------
// ConstraintEqualLineLength
ConstraintEqualLineLength::ConstraintEqualLineLength(Line& l1, Line& l2)
: l1(l1)
, l2(l2)
{
this->l1.PushOwnParams(pvec);
this->l2.PushOwnParams(pvec);
origpvec = pvec;
pvecChangedFlag = true;
rescale();
}
void ConstraintEqualLineLength::ReconstructGeomPointers()
{
int i = 0;
l1.ReconstructOnNewPvec(pvec, i);
l2.ReconstructOnNewPvec(pvec, i);
pvecChangedFlag = false;
}
ConstraintType ConstraintEqualLineLength::getTypeId()
{
return EqualLineLength;
}
void ConstraintEqualLineLength::errorgrad(double* err, double* grad, double* param)
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
DeriVector2 p1(l1.p1, param);
DeriVector2 p2(l1.p2, param);
DeriVector2 p3(l2.p1, param);
DeriVector2 p4(l2.p2, param);
DeriVector2 v1 = p1.subtr(p2);
DeriVector2 v2 = p3.subtr(p4);
double length1, dlength1;
length1 = v1.length(dlength1);
double length2, dlength2;
length2 = v2.length(dlength2);
if (err) {
*err = length2 - length1;
}
if (grad) {
*grad = dlength2 - dlength1;
// if the one of the lines gets vertical or horizontal, the gradients will become zero. this
// will affect the diagnose function and the detection of dependent/independent parameters.
//
// So here we maintain the very small derivative of 1e-10 when the gradient is under such
// value, such that the diagnose function with pivot threshold of 1e-13 treats the value as
// non-zero and correctly detects and can tell apart when a parameter is fully constrained
// or just locked into a maximum/minimum
if (fabs(*grad) < 1e-10) {
double surrogate = 1e-10;
if (param == l1.p1.x) {
*grad = v1.x > 0 ? surrogate : -surrogate;
}
if (param == l1.p1.y) {
*grad = v1.y > 0 ? surrogate : -surrogate;
}
if (param == l1.p2.x) {
*grad = v1.x > 0 ? -surrogate : surrogate;
}
if (param == l1.p2.y) {
*grad = v1.y > 0 ? -surrogate : surrogate;
}
if (param == l2.p1.x) {
*grad = v2.x > 0 ? surrogate : -surrogate;
}
if (param == l2.p1.y) {
*grad = v2.y > 0 ? surrogate : -surrogate;
}
if (param == l2.p2.x) {
*grad = v2.x > 0 ? -surrogate : surrogate;
}
if (param == l2.p2.y) {
*grad = v2.y > 0 ? -surrogate : surrogate;
}
}
}
}
// --------------------------------------------------------
// ConstraintC2CDistance
ConstraintC2CDistance::ConstraintC2CDistance(Circle& c1, Circle& c2, double* d)
: c1(c1)
, c2(c2)
{
pvec.push_back(d);
this->c1.PushOwnParams(pvec);
this->c2.PushOwnParams(pvec);
origpvec = pvec;
pvecChangedFlag = true;
rescale();
}
void ConstraintC2CDistance::ReconstructGeomPointers()
{
int i = 0;
i++; // skip the first parameter as there is the inline function distance for it
c1.ReconstructOnNewPvec(pvec, i);
c2.ReconstructOnNewPvec(pvec, i);
pvecChangedFlag = false;
}
ConstraintType ConstraintC2CDistance::getTypeId()
{
return C2CDistance;
}
void ConstraintC2CDistance::errorgrad(double* err, double* grad, double* param)
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
DeriVector2 ct1(c1.center, param);
DeriVector2 ct2(c2.center, param);
DeriVector2 vector_ct12 = ct1.subtr(ct2);
double length_ct12, dlength_ct12;
length_ct12 = vector_ct12.length(dlength_ct12);
// outer case (defined as the centers of the circles are outside the center of the other
// circles) it may well be that the circles intersect.
if (length_ct12 >= *c1.rad && length_ct12 >= *c2.rad) {
if (err) {
*err = length_ct12 - (*c2.rad + *c1.rad + *distance());
}
else if (grad) {
double drad = (param == c2.rad || param == c1.rad || param == distance()) ? -1.0 : 0.0;
*grad = dlength_ct12 + drad;
}
}
else {
double* bigradius = (*c1.rad >= *c2.rad) ? c1.rad : c2.rad;
double* smallradius = (*c1.rad >= *c2.rad) ? c2.rad : c1.rad;
double smallspan = *smallradius + length_ct12 + *distance();
if (err) {
*err = *bigradius - smallspan;
}
else if (grad) {
double drad = 0.0;
if (param == bigradius) {
drad = 1.0;
}
else if (param == smallradius) {
drad = -1.0;
}
else if (param == distance()) {
drad = (*distance() < 0.) ? 1.0 : -1.0;
}
if (length_ct12 > 1e-13) {
*grad = -dlength_ct12 + drad;
}
else { // concentric case
*grad = drad;
}
}
}
}
// --------------------------------------------------------
// ConstraintC2LDistance
ConstraintC2LDistance::ConstraintC2LDistance(Circle& c, Line& l, double* d)
: circle(c)
, line(l)
{
pvec.push_back(d);
this->circle.PushOwnParams(pvec);
this->line.PushOwnParams(pvec);
origpvec = pvec;
pvecChangedFlag = true;
rescale();
}
ConstraintType ConstraintC2LDistance::getTypeId()
{
return C2LDistance;
}
void ConstraintC2LDistance::ReconstructGeomPointers()
{
int i = 0;
i++; // skip the first parameter as there is the inline function distance for it
circle.ReconstructOnNewPvec(pvec, i);
line.ReconstructOnNewPvec(pvec, i);
pvecChangedFlag = false;
}
void ConstraintC2LDistance::errorgrad(double* err, double* grad, double* param)
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
DeriVector2 ct(circle.center, param);
DeriVector2 p1(line.p1, param);
DeriVector2 p2(line.p2, param);
DeriVector2 v_line = p2.subtr(p1);
DeriVector2 v_p1ct = ct.subtr(p1);
// center to line distance (=h) and its derivative (=dh)
double darea = 0.0;
double area = v_line.crossProdZ(v_p1ct, darea); // parallelogram oriented area
double dlength;
double length = v_line.length(dlength);
// vector product (cross vector) has a magnitude corresponding to the area of
// the parallelogram defined by the vectors above. The area of the triangle is
// half the parallelogram area. The height of the triangle is the area divided by
// the base, which is the distance from the center of the circle to the line.
//
// However, the vector (which points in z direction), can be positive or negative.
// the area is the absolute value
double h = std::abs(area) / length;
// darea is the magnitude of a vector in the z direction, which makes the area vector
// increase or decrease. If area vector is negative a negative value makes the area increase
// and a positive value makes it decrease.
darea = std::signbit(area) ? -darea : darea;
double dh = (darea - h * dlength) / length;
if (err) {
if (h < *circle.rad) {
*err = *circle.rad - std::abs(*distance()) - h;
}
else {
*err = *circle.rad + std::abs(*distance()) - h;
}
}
else if (grad) {
if (param == distance() || param == circle.rad) {
if (h < *circle.rad) {
*grad = -1.0;
}
else {
*grad = 1.0;
}
}
else {
*grad = -dh;
}
}
}
// --------------------------------------------------------
// ConstraintP2CDistance
ConstraintP2CDistance::ConstraintP2CDistance(Point& p, Circle& c, double* d)
: circle(c)
, pt(p)
{
pvec.push_back(d);
this->circle.PushOwnParams(pvec);
this->pt.PushOwnParams(pvec);
origpvec = pvec;
pvecChangedFlag = true;
rescale();
}
ConstraintType ConstraintP2CDistance::getTypeId()
{
return P2CDistance;
}
void ConstraintP2CDistance::ReconstructGeomPointers()
{
int i = 0;
i++; // skip the first parameter as there is the inline function distance for it
circle.ReconstructOnNewPvec(pvec, i);
pt.ReconstructOnNewPvec(pvec, i);
pvecChangedFlag = false;
}
void ConstraintP2CDistance::errorgrad(double* err, double* grad, double* param)
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
DeriVector2 ct(circle.center, param);
DeriVector2 p(pt, param);
DeriVector2 v_length = ct.subtr(p);
double dlength;
double length = v_length.length(dlength);
if (err) {
*err = *circle.rad + *distance() - length;
if (length < *circle.rad) {
*err = *circle.rad - *distance() - length;
}
}
else if (grad) {
if (param == distance()) {
*grad = 1.0;
if (length < *circle.rad) {
*grad = -1.0;
}
}
else if (param == circle.rad) {
*grad = 1.0;
}
else {
*grad = -dlength;
}
}
}
// --------------------------------------------------------
// ConstraintArcLength
ConstraintArcLength::ConstraintArcLength(Arc& a, double* d)
: arc(a)
{
pvec.push_back(d);
this->arc.PushOwnParams(pvec);
origpvec = pvec;
pvecChangedFlag = true;
rescale();
}
void ConstraintArcLength::ReconstructGeomPointers()
{
int i = 0;
i++; // skip the first parameter as there is the inline function distance for it
arc.ReconstructOnNewPvec(pvec, i);
pvecChangedFlag = false;
}
ConstraintType ConstraintArcLength::getTypeId()
{
return ArcLength;
}
void ConstraintArcLength::errorgrad(double* err, double* grad, double* param)
{
if (pvecChangedFlag) {
ReconstructGeomPointers();
}
double rad = *arc.rad;
double endA = *arc.endAngle;
double startA = *arc.startAngle;
// Assume positive angles and CCW arc
while (startA < 0.) {
startA += 2. * std::numbers::pi;
}
while (endA < startA) {
endA += 2. * std::numbers::pi;
}
if (err) {
*err = rad * (endA - startA) - *distance();
}
else if (grad) {
if (param == distance()) {
// if constraint is not driving it varies on distance().
*grad = -1.;
}
else {
double dRad = param == arc.rad ? 1. : 0.;
double dStartA = param == arc.startAngle ? 1. : 0.;
double dEndA = param == arc.endAngle ? 1. : 0.;
*grad = rad * (dEndA - dStartA) + dRad * (endA - startA);
}
}
}
} // namespace GCS