so3

SO(3) exp and log map

Log map

The log map on SO(3) is equivalent to finding the axis-angle of rotation corresponding to a rotation matrix \(\mathbf R\). This is numerically unstable near rotations \(\theta = 0\) or \(\theta = \pi\).

We port the numerically stable implementation for pytransform3d to PyTorch to enable batched computation of multiple transformations on a GPU.

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so3_log_map

 so3_log_map (R:torch.Tensor)

Find the axis of rotation for a rotation matrix R. The norm of the axis corresponds to the angle of rotation.

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cross_product_matrix

 cross_product_matrix (axis_angle)

Convert the axis-angle to the matrix log(R).

Exp map

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so3_exp_map

 so3_exp_map (log_R_vee, n=10)