pytransform3d.transformations.dual_quaternion_requires_renormalization

pytransform3d.transformations.dual_quaternion_requires_renormalization(dq, tolerance=1e-06)

Check if dual quaternion requires renormalization.

Dual quaternions that represent transformations in 3D should have unit norm. Since the real and the dual quaternion are orthogonal, their dot product should be 0. In addition, \(\epsilon^2 = 0\). Hence,

\[||\boldsymbol{p} + \epsilon \boldsymbol{q}|| = \sqrt{(\boldsymbol{p} + \epsilon \boldsymbol{q}) \cdot (\boldsymbol{p} + \epsilon \boldsymbol{q})} = \sqrt{\boldsymbol{p}\cdot\boldsymbol{p} + 2\epsilon \boldsymbol{p}\cdot\boldsymbol{q} + \epsilon^2 \boldsymbol{q}\cdot\boldsymbol{q}} = \sqrt{\boldsymbol{p}\cdot\boldsymbol{p}},\]

i.e., the norm only depends on the real quaternion.

This function checks unit norm and orthogonality of the real and dual part.

Parameters:

dqarray-like, shape (8,)

Dual quaternion to represent transform: (pw, px, py, pz, qw, qx, qy, qz)

tolerancefloat, optional (default: 1e-6)

Tolerance for check.

Returns:

requiredbool

Indicates if renormalization is required.

See also

check_dual_quaternion

Input validation of dual quaternion representation. Has an option to normalize the dual quaternion.

norm_dual_quaternion

Normalization that enforces unit norm and orthogonality of the real and dual quaternion.

assert_unit_dual_quaternion

Checks unit norm and orthogonality of real and dual quaternion.