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