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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 | |