File size: 4,830 Bytes
ea66a99 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 | #
# Copyright (C) 2023, Inria
# GRAPHDECO research group, https://team.inria.fr/graphdeco
# All rights reserved.
#
# This software is free for non-commercial, research and evaluation use
# under the terms of the LICENSE.md file.
#
# For inquiries contact george.drettakis@inria.fr
#
import torch
import math
import numpy as np
from typing import NamedTuple
class BasicPointCloud(NamedTuple):
points : np.array
colors : np.array
normals : np.array
def geom_transform_points(points, transf_matrix):
P, _ = points.shape
ones = torch.ones(P, 1, dtype=points.dtype, device=points.device)
points_hom = torch.cat([points, ones], dim=1)
points_out = torch.matmul(points_hom, transf_matrix.unsqueeze(0))
denom = points_out[..., 3:] + 0.0000001
return (points_out[..., :3] / denom).squeeze(dim=0)
def getWorld2View(R, t):
Rt = np.zeros((4, 4))
Rt[:3, :3] = R.transpose()
Rt[:3, 3] = t
Rt[3, 3] = 1.0
return np.float32(Rt)
def getWorld2View2(R, t, translate=np.array([.0, .0, .0]), scale=1.0):
Rt = np.zeros((4, 4))
Rt[:3, :3] = R.transpose()
Rt[:3, 3] = t
Rt[3, 3] = 1.0
C2W = np.linalg.inv(Rt)
cam_center = C2W[:3, 3]
cam_center = (cam_center + translate) * scale
C2W[:3, 3] = cam_center
Rt = np.linalg.inv(C2W)
return np.float32(Rt)
def getProjectionMatrix(znear, zfar, fovX, fovY):
tanHalfFovY = math.tan((fovY / 2))
tanHalfFovX = math.tan((fovX / 2))
top = tanHalfFovY * znear
bottom = -top
right = tanHalfFovX * znear
left = -right
P = torch.zeros(4, 4)
z_sign = 1.0
P[0, 0] = 2.0 * znear / (right - left)
P[1, 1] = 2.0 * znear / (top - bottom)
P[0, 2] = (right + left) / (right - left)
P[1, 2] = (top + bottom) / (top - bottom)
P[3, 2] = z_sign
P[2, 2] = z_sign * zfar / (zfar - znear)
P[2, 3] = -(zfar * znear) / (zfar - znear)
return P
def getProjectionMatrixCV(znear, zfar, fovX, fovY, cx=0.0, cy=0.0):
"""
Projection with off-centre principal point. cx, cy are normalised offsets
in [-0.5, 0.5] relative to image width/height.
"""
tan_half_y = math.tan(fovY / 2)
tan_half_x = math.tan(fovX / 2)
top = tan_half_y * znear
bottom = -top
right = tan_half_x * znear
left = -right
delta_x = (2 * tan_half_x * znear) * cx
delta_y = (2 * tan_half_y * znear) * cy
left += delta_x
right += delta_x
top += delta_y
bottom += delta_y
P = torch.zeros(4, 4)
z_sign = 1.0
P[0, 0] = 2.0 * znear / (right - left)
P[1, 1] = 2.0 * znear / (top - bottom)
P[0, 2] = (right + left) / (right - left)
P[1, 2] = (top + bottom) / (top - bottom)
P[3, 2] = z_sign
P[2, 2] = z_sign * (zfar + znear) / (zfar - znear)
P[2, 3] = -(zfar * znear) / (zfar - znear)
return P
def fov2focal(fov, pixels):
return pixels / (2 * math.tan(fov / 2))
def focal2fov(focal, pixels):
return 2*math.atan(pixels/(2*focal))
def apply_rotation(q1, q2):
"""
Applies a rotation to a quaternion.
Parameters:
q1 (Tensor): The original quaternion.
q2 (Tensor): The rotation quaternion to be applied.
Returns:
Tensor: The resulting quaternion after applying the rotation.
"""
# Extract components for readability
w1, x1, y1, z1 = q1
w2, x2, y2, z2 = q2
# Compute the product of the two quaternions
w3 = w1 * w2 - x1 * x2 - y1 * y2 - z1 * z2
x3 = w1 * x2 + x1 * w2 + y1 * z2 - z1 * y2
y3 = w1 * y2 - x1 * z2 + y1 * w2 + z1 * x2
z3 = w1 * z2 + x1 * y2 - y1 * x2 + z1 * w2
# Combine the components into a new quaternion tensor
q3 = torch.tensor([w3, x3, y3, z3])
# Normalize the resulting quaternion
q3_normalized = q3 / torch.norm(q3)
return q3_normalized
def batch_quaternion_multiply(q1, q2):
"""
Multiply batches of quaternions.
Args:
- q1 (torch.Tensor): A tensor of shape [N, 4] representing the first batch of quaternions.
- q2 (torch.Tensor): A tensor of shape [N, 4] representing the second batch of quaternions.
Returns:
- torch.Tensor: The resulting batch of quaternions after applying the rotation.
"""
# Calculate the product of each quaternion in the batch
w = q1[:, 0] * q2[:, 0] - q1[:, 1] * q2[:, 1] - q1[:, 2] * q2[:, 2] - q1[:, 3] * q2[:, 3]
x = q1[:, 0] * q2[:, 1] + q1[:, 1] * q2[:, 0] + q1[:, 2] * q2[:, 3] - q1[:, 3] * q2[:, 2]
y = q1[:, 0] * q2[:, 2] - q1[:, 1] * q2[:, 3] + q1[:, 2] * q2[:, 0] + q1[:, 3] * q2[:, 1]
z = q1[:, 0] * q2[:, 3] + q1[:, 1] * q2[:, 2] - q1[:, 2] * q2[:, 1] + q1[:, 3] * q2[:, 0]
# Combine into new quaternions
q3 = torch.stack((w, x, y, z), dim=1)
# Normalize the quaternions
norm_q3 = q3 / torch.norm(q3, dim=1, keepdim=True)
return norm_q3
|