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# Copyright (c) OpenMMLab. All rights reserved. | |
import torch | |
from torch.nn import functional as F | |
def rot6d_to_rotmat(x): | |
"""Convert 6D rotation representation to 3x3 rotation matrix. | |
Based on Zhou et al., "On the Continuity of Rotation | |
Representations in Neural Networks", CVPR 2019 | |
Input: | |
(B,6) Batch of 6-D rotation representations | |
Output: | |
(B,3,3) Batch of corresponding rotation matrices | |
""" | |
x = x.view(-1, 3, 2) | |
a1 = x[:, :, 0] | |
a2 = x[:, :, 1] | |
b1 = F.normalize(a1) | |
b2 = F.normalize(a2 - torch.einsum('bi,bi->b', b1, a2).unsqueeze(-1) * b1) | |
b3 = torch.cross(b1, b2) | |
return torch.stack((b1, b2, b3), dim=-1) | |
def batch_rodrigues(theta): | |
"""Convert axis-angle representation to rotation matrix. | |
Args: | |
theta: size = [B, 3] | |
Returns: | |
Rotation matrix corresponding to the quaternion | |
-- size = [B, 3, 3] | |
""" | |
l2norm = torch.norm(theta + 1e-8, p=2, dim=1) | |
angle = torch.unsqueeze(l2norm, -1) | |
normalized = torch.div(theta, angle) | |
angle = angle * 0.5 | |
v_cos = torch.cos(angle) | |
v_sin = torch.sin(angle) | |
quat = torch.cat([v_cos, v_sin * normalized], dim=1) | |
return quat_to_rotmat(quat) | |
def quat_to_rotmat(quat): | |
"""Convert quaternion coefficients to rotation matrix. | |
Args: | |
quat: size = [B, 4] 4 <===>(w, x, y, z) | |
Returns: | |
Rotation matrix corresponding to the quaternion | |
-- size = [B, 3, 3] | |
""" | |
norm_quat = quat | |
norm_quat = norm_quat / norm_quat.norm(p=2, dim=1, keepdim=True) | |
w, x, y, z = norm_quat[:, 0], norm_quat[:, 1],\ | |
norm_quat[:, 2], norm_quat[:, 3] | |
B = quat.size(0) | |
w2, x2, y2, z2 = w.pow(2), x.pow(2), y.pow(2), z.pow(2) | |
wx, wy, wz = w * x, w * y, w * z | |
xy, xz, yz = x * y, x * z, y * z | |
rotMat = torch.stack([ | |
w2 + x2 - y2 - z2, 2 * xy - 2 * wz, 2 * wy + 2 * xz, 2 * wz + 2 * xy, | |
w2 - x2 + y2 - z2, 2 * yz - 2 * wx, 2 * xz - 2 * wy, 2 * wx + 2 * yz, | |
w2 - x2 - y2 + z2 | |
], | |
dim=1).view(B, 3, 3) | |
return rotMat | |