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c1e2af3 | 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 | # SPDX-FileCopyrightText: Copyright (c) 2026 NVIDIA CORPORATION & AFFILIATES. All rights reserved.
# SPDX-License-Identifier: Apache-2.0
import torch
import torch.nn.functional as F
def angle_to_Y_rotation_matrix(angle):
cos, sin = torch.cos(angle), torch.sin(angle)
one, zero = torch.ones_like(angle), torch.zeros_like(angle)
mat = torch.stack((cos, zero, sin, zero, one, zero, -sin, zero, cos), -1)
mat = mat.reshape(angle.shape + (3, 3))
return mat
def matrix_to_cont6d(matrix):
cont_6d = torch.concat([matrix[..., 0], matrix[..., 1]], dim=-1)
return cont_6d
def cont6d_to_matrix(cont6d):
assert cont6d.shape[-1] == 6, "The last dimension must be 6"
x_raw = cont6d[..., 0:3]
y_raw = cont6d[..., 3:6]
x = x_raw / torch.norm(x_raw, dim=-1, keepdim=True)
z = torch.cross(x, y_raw, dim=-1)
z = z / torch.norm(z, dim=-1, keepdim=True)
y = torch.cross(z, x, dim=-1)
x = x[..., None]
y = y[..., None]
z = z[..., None]
mat = torch.cat([x, y, z], dim=-1)
return mat
def axis_angle_to_matrix(axis_angle: torch.Tensor) -> torch.Tensor:
"""
Convert axis-angle to rotation matrix.
Args:
axis_angle: (..., 3) axis-angle vectors (angle = norm, axis = normalized)
Returns:
rotmat: (..., 3, 3) rotation matrices
"""
eps = 1e-6
angle = torch.norm(axis_angle, dim=-1, keepdim=True) # (..., 1)
axis = axis_angle / (angle + eps)
x, y, z = axis.unbind(-1)
zero = torch.zeros_like(x)
K = torch.stack([zero, -z, y, z, zero, -x, -y, x, zero], dim=-1).reshape(*axis.shape[:-1], 3, 3)
eye = torch.eye(3, device=axis.device, dtype=axis.dtype)
eye = eye.expand(*axis.shape[:-1], 3, 3)
sin = torch.sin(angle)[..., None]
cos = torch.cos(angle)[..., None]
R = eye + sin * K + (1 - cos) * (K @ K)
return R
def matrix_to_axis_angle(R: torch.Tensor) -> torch.Tensor:
"""Convert rotation matrix to axis-angle.
Args:
R: (..., 3, 3) rotation matrices
Returns:
axis_angle: (..., 3)
"""
eps = 1e-6
trace = R[..., 0, 0] + R[..., 1, 1] + R[..., 2, 2]
cos_angle = (trace - 1) / 2
cos_angle = torch.clamp(cos_angle, -1 + eps, 1 - eps)
angle = torch.acos(cos_angle)
rx = R[..., 2, 1] - R[..., 1, 2]
ry = R[..., 0, 2] - R[..., 2, 0]
rz = R[..., 1, 0] - R[..., 0, 1]
axis = torch.stack([rx, ry, rz], dim=-1)
sin_angle = torch.sin(angle)
axis = axis / (2 * sin_angle[..., None] + eps)
return axis * angle[..., None]
def _sqrt_positive_part(x: torch.Tensor) -> torch.Tensor:
"""Returns torch.sqrt(torch.max(0, x)) subgradient is zero where x is 0."""
return torch.sqrt(x * (x > 0).to(x.dtype))
def matrix_to_quaternion(matrix: torch.Tensor) -> torch.Tensor:
"""Convert rotations given as rotation matrices to quaternions.
Args:
matrix: Rotation matrices as tensor of shape (..., 3, 3).
Returns:
quaternions with real part first, as tensor of shape (..., 4).
"""
if matrix.size(-1) != 3 or matrix.size(-2) != 3:
raise ValueError(f"Invalid rotation matrix shape {matrix.shape}.")
batch_dim = matrix.shape[:-2]
m00, m01, m02, m10, m11, m12, m20, m21, m22 = torch.unbind(matrix.reshape(batch_dim + (9,)), dim=-1)
q_abs = _sqrt_positive_part(
torch.stack(
[
1.0 + m00 + m11 + m22,
1.0 + m00 - m11 - m22,
1.0 - m00 + m11 - m22,
1.0 - m00 - m11 + m22,
],
dim=-1,
)
)
quat_by_rijk = torch.stack(
[
torch.stack([q_abs[..., 0] ** 2, m21 - m12, m02 - m20, m10 - m01], dim=-1),
torch.stack([m21 - m12, q_abs[..., 1] ** 2, m10 + m01, m02 + m20], dim=-1),
torch.stack([m02 - m20, m10 + m01, q_abs[..., 2] ** 2, m12 + m21], dim=-1),
torch.stack([m10 - m01, m20 + m02, m21 + m12, q_abs[..., 3] ** 2], dim=-1),
],
dim=-2,
)
flr = torch.tensor(0.1).to(dtype=q_abs.dtype, device=q_abs.device)
quat_candidates = quat_by_rijk / (2.0 * q_abs[..., None].max(flr))
return (
(F.one_hot(q_abs.argmax(dim=-1), num_classes=4)[..., None] * quat_candidates)
.sum(dim=-2)
.reshape(batch_dim + (4,))
)
def quaternion_to_matrix(quaternions: torch.Tensor) -> torch.Tensor:
"""Convert rotations given as quaternions to rotation matrices.
Args:
quaternions: quaternions with real part first,
as tensor of shape (..., 4).
Returns:
Rotation matrices as tensor of shape (..., 3, 3).
"""
r, i, j, k = torch.unbind(quaternions, -1)
two_s = 2.0 / (quaternions * quaternions).sum(-1)
o = torch.stack(
(
1 - two_s * (j * j + k * k),
two_s * (i * j - k * r),
two_s * (i * k + j * r),
two_s * (i * j + k * r),
1 - two_s * (i * i + k * k),
two_s * (j * k - i * r),
two_s * (i * k - j * r),
two_s * (j * k + i * r),
1 - two_s * (i * i + j * j),
),
-1,
)
return o.reshape(quaternions.shape[:-1] + (3, 3))
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