discretize.utils.rotation_matrix_from_normals#
- discretize.utils.rotation_matrix_from_normals(v0, v1, tol=1e-20)[source]#
Generate a 3x3 rotation matrix defining the rotation from vector v0 to v1.
This function uses Rodrigues’ rotation formula to generate the rotation matrix \(\mathbf{A}\) going from vector \(\mathbf{v_0}\) to vector \(\mathbf{v_1}\). Thus:
\[\mathbf{Av_0} = \mathbf{v_1}\]For detailed desciption of the algorithm, see https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula
- Parameters:
- v0(3)
numpy.ndarray Starting orientation direction
- v1(3)
numpy.ndarray Finishing orientation direction
- tol
float,optional Numerical tolerance. If the length of the rotation axis is below this value, it is assumed to be no rotation, and an identity matrix is returned.
- v0(3)
- Returns:
- (3, 3)
numpy.ndarray The rotation matrix from v0 to v1.
- (3, 3)