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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
from typing import Tuple
from torch import Tensor
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):
# 用于从 w2c 中提取的 R 和 t，得到 平移和缩放后的 c2w
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 fov2focal(fov, pixels):
return pixels / (2 * math.tan(fov / 2))
def focal2fov(focal, pixels):
return 2*math.atan(pixels/(2*focal))
def get_rays(
x: Tensor, y: Tensor, c2w: Tensor, intrinsic: Tensor
) -> Tuple[Tensor, Tensor, Tensor]:
"""
Args:
x: the horizontal coordinates of the pixels, shape: (num_rays,)
y: the vertical coordinates of the pixels, shape: (num_rays,)
c2w: the camera-to-world matrices, shape: (num_cams, 4, 4)
intrinsic: the camera intrinsic matrices, shape: (num_cams, 3, 3)
Returns:
origins: the ray origins, shape: (num_rays, 3)
viewdirs: the ray directions, shape: (num_rays, 3)
direction_norm: the norm of the ray directions, shape: (num_rays, 1)
"""
if len(intrinsic.shape) == 2:
intrinsic = intrinsic[None, :, :]
if len(c2w.shape) == 2:
c2w = c2w[None, :, :]
camera_dirs = torch.nn.functional.pad(
torch.stack(
[
(x - intrinsic[:, 0, 2] + 0.5) / intrinsic[:, 0, 0],
(y - intrinsic[:, 1, 2] + 0.5) / intrinsic[:, 1, 1],
],
dim=-1,
),
(0, 1),
value=1.0,
) # [num_rays, 3]
# rotate the camera rays w.r.t. the camera pose
directions = (camera_dirs[:, None, :] * c2w[:, :3, :3]).sum(dim=-1)
origins = torch.broadcast_to(c2w[:, :3, -1], directions.shape)
# TODO: not sure if we still need direction_norm
direction_norm = torch.linalg.norm(directions, dim=-1, keepdims=True)
# normalize the ray directions
viewdirs = directions / (direction_norm + 1e-8)
return origins, viewdirs, direction_norm
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
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