pytransform3d.rotations.norm_matrix

pytransform3d.rotations.norm_matrix(R)

Orthonormalize rotation matrix.

A rotation matrix is defined as

\[\begin{split}\boldsymbol R = \left( \begin{array}{ccc} r_{11} & r_{12} & r_{13}\\ r_{21} & r_{22} & r_{23}\\ r_{31} & r_{32} & r_{33}\\ \end{array} \right) \in SO(3)\end{split}\]

and must be orthonormal, which results in 6 constraints:

• column vectors must have unit norm (3 constraints)

• and must be orthogonal to each other (3 constraints)

A more compact representation of these constraints is \(\boldsymbol R^T \boldsymbol R = \boldsymbol I\).

Because of numerical problems, a rotation matrix might not satisfy the constraints anymore. This function will enforce them.

Parameters:

Rarray-like, shape (3, 3)

Rotation matrix with small numerical errors.

Returns:

Rarray, shape (3, 3)

Orthonormalized rotation matrix.

See also

check_matrix

Checks orthonormality of a rotation matrix.

matrix_requires_renormalization

Checks if a rotation matrix needs renormalization.