pytransform3d.rotations.robust_polar_decomposition#
- pytransform3d.rotations.robust_polar_decomposition(A, n_iter=20, eps=2.220446049250313e-16)[source]#
Orthonormalize rotation matrix with robust polar decomposition.
Robust polar decomposition [1] [2] is a computationally more costly method, but it spreads the error more evenly between the basis vectors in comparison to Gram-Schmidt orthonormalization (as in
norm_matrix()).Robust polar decomposition finds an orthonormal matrix that minimizes the Frobenius norm
\[||\boldsymbol{A} - \boldsymbol{R}||^2\]between the input \(\boldsymbol{A}\) that is not orthonormal and the output \(\boldsymbol{R}\) that is orthonormal.
- Parameters:
- Aarray-like, shape (3, 3)
Matrix that contains a basis vector in each column. The basis does not have to be orthonormal.
- n_iterint, optional (default: 20)
Maximum number of iterations for which we refine the estimation of the rotation matrix.
- epsfloat, optional (default: np.finfo(float).eps)
Precision for termination criterion of iterative refinement.
- Returns:
- Rarray, shape (3, 3)
Orthonormalized rotation matrix.
See also
norm_matrixThe cheaper default orthonormalization method that uses Gram-Schmidt orthonormalization optimized for 3 dimensions.
References
[1]Selstad, J. (2019). Orthonormalization. https://zalo.github.io/blog/polar-decomposition/
[2]Müller, M., Bender, J., Chentanez, N., Macklin, M. (2016). A Robust Method to Extract the Rotational Part of Deformations. In MIG ‘16: Proceedings of the 9th International Conference on Motion in Games, pp. 55-60, doi: 10.1145/2994258.2994269.
