dual_quat_conjugateDualQuatConjugateDualQuatConjugatedual_quat_conjugateT_dual_quat_conjugate🔗

Short description🔗

dual_quat_conjugateDualQuatConjugateDualQuatConjugatedual_quat_conjugateT_dual_quat_conjugate — Conjugate a dual quaternion.

Signature🔗

dual_quat_conjugate( dual_quaternion DualQuaternion, out dual_quaternion DualQuaternionConjugate )

Description🔗

The operator dual_quat_conjugateDualQuatConjugate computes the conjugation DualQuaternionConjugatedualQuaternionConjugatedual_quaternion_conjugate of the input dual quaternion DualQuaterniondualQuaterniondual_quaternion.

For a brief introduction to dual quaternions, the used notation, and the relationship between dual quaternions and screws, see “Solution Guide III-C - 3D Vision”.

The conjugation of a dual quaternion \(\hat{q} = q_{r} + \varepsilon q_{d}\) is given by \(\bar{\hat{q}} = \bar{q}_{r} + \varepsilon \bar{q}_{d}\), where \(\bar{q}_{r}\) and \(\bar{q}_{d}\) are the conjugations of the quaternions \(q_{r}\) and \(q_{d}\).

For the conjugation of quaternions see quat_conjugateQuatConjugate.

If DualQuaterniondualQuaterniondual_quaternion is a unit dual quaternion and, hence, represents a 3D rigid transformation, its inverse is its conjugate, i.e., \(\hat{q}^{-1}=\bar{\hat{q}}\). Consequently, DualQuaternionConjugatedualQuaternionConjugatedual_quaternion_conjugate represents the inverse 3D rigid transformation of DualQuaterniondualQuaterniondual_quaternion. Therefore, dual_quat_conjugateDualQuatConjugate can be used to invert a 3D rigid transformation analogously to pose_invertPoseInvert or hom_mat3d_invertHomMat3dInvert.

Execution information🔗

Execution information

Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Processed without parallelization.

Parameters🔗

DualQuaterniondualQuaterniondual_quaternion (input_control) dual_quaternion(-array) → (real)HTuple (double)HDualQuaternion, HTuple (double)Sequence[float]Htuple (double)

Dual quaternion.

DualQuaternionConjugatedualQuaternionConjugatedual_quaternion_conjugate (output_control) dual_quaternion(-array) → (real)HTuple (double)HDualQuaternion, HTuple (double)Sequence[float]Htuple (double)

Conjugate of the dual quaternion.

Combinations with other operators🔗

Combinations

Possible predecessors

dual_quat_composeDualQuatCompose, pose_to_dual_quatPoseToDualQuat, screw_to_dual_quatScrewToDualQuat

Possible successors

dual_quat_composeDualQuatCompose, dual_quat_to_hom_mat3dDualQuatToHomMat3d, dual_quat_to_screwDualQuatToScrew, dual_quat_interpolateDualQuatInterpolate, dual_quat_to_poseDualQuatToPose

Alternatives

pose_invertPoseInvert, hom_mat3d_invertHomMat3dInvert

Module🔗

Foundation