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#
# 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, K = None, img_h = None, img_w = None):
if K is None:
tanHalfFovY = math.tan((fovY / 2))
tanHalfFovX = math.tan((fovX / 2))
top = tanHalfFovY * znear
bottom = -top
right = tanHalfFovX * znear
left = -right
else:
near_fx = znear / K[0, 0]
near_fy = znear / K[1, 1]
left = - (img_w - K[0, 2]) * near_fx
right = K[0, 2] * near_fx
bottom = (K[1, 2] - img_h) * near_fy
top = K[1, 2] * near_fy
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 fov2focal(fov, pixels):
return pixels / (2 * math.tan(fov / 2))
def focal2fov(focal, pixels):
return 2*math.atan(pixels/(2*focal))
def _so3_exp_map(
log_rot: torch.Tensor, eps: float = 0.0001
):
"""
A helper function that computes the so3 exponential map and,
apart from the rotation matrix, also returns intermediate variables
that can be re-used in other functions.
"""
def hat(v: torch.Tensor) -> torch.Tensor:
"""
Compute the Hat operator [1] of a batch of 3D vectors.
Args:
v: Batch of vectors of shape `(minibatch , 3)`.
Returns:
Batch of skew-symmetric matrices of shape
`(minibatch, 3 , 3)` where each matrix is of the form:
`[ 0 -v_z v_y ]
[ v_z 0 -v_x ]
[ -v_y v_x 0 ]`
Raises:
ValueError if `v` is of incorrect shape.
[1] https://en.wikipedia.org/wiki/Hat_operator
"""
N, dim = v.shape
if dim != 3:
raise ValueError("Input vectors have to be 3-dimensional.")
h = torch.zeros((N, 3, 3), dtype=v.dtype, device=v.device)
x, y, z = v.unbind(1)
h[:, 0, 1] = -z
h[:, 0, 2] = y
h[:, 1, 0] = z
h[:, 1, 2] = -x
h[:, 2, 0] = -y
h[:, 2, 1] = x
return h
_, dim = log_rot.shape
if dim != 3:
raise ValueError("Input tensor shape has to be Nx3.")
nrms = (log_rot * log_rot).sum(1)
# phis ... rotation angles
rot_angles = torch.clamp(nrms, eps).sqrt()
rot_angles_inv = 1.0 / rot_angles
fac1 = rot_angles_inv * rot_angles.sin()
fac2 = rot_angles_inv * rot_angles_inv * (1.0 - rot_angles.cos())
skews = hat(log_rot)
skews_square = torch.bmm(skews, skews)
R = (
# pyre-fixme[16]: `float` has no attribute `__getitem__`.
fac1[:, None, None] * skews
+ fac2[:, None, None] * skews_square
+ torch.eye(3, dtype=log_rot.dtype, device=log_rot.device)[None]
)
return R, rot_angles, skews, skews_square
def so3_exp_map(log_rot: torch.Tensor, eps: float = 0.0001) -> torch.Tensor:
"""
Convert a batch of logarithmic representations of rotation matrices `log_rot`
to a batch of 3x3 rotation matrices using Rodrigues formula [1].
In the logarithmic representation, each rotation matrix is represented as
a 3-dimensional vector (`log_rot`) who's l2-norm and direction correspond
to the magnitude of the rotation angle and the axis of rotation respectively.
The conversion has a singularity around `log(R) = 0`
which is handled by clamping controlled with the `eps` argument.
Args:
log_rot: Batch of vectors of shape `(minibatch, 3)`.
eps: A float constant handling the conversion singularity.
Returns:
Batch of rotation matrices of shape `(minibatch, 3, 3)`.
Raises:
ValueError if `log_rot` is of incorrect shape.
[1] https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula
"""
return _so3_exp_map(log_rot, eps=eps)[0]
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