dual_quat_composeDualQuatComposeDualQuatComposedual_quat_composeT_dual_quat_compose🔗

Short description🔗

dual_quat_composeDualQuatComposeDualQuatComposedual_quat_composeT_dual_quat_compose — Multiply two dual quaternions.

Signature🔗

dual_quat_compose( dual_quaternion DualQuaternionLeft, dual_quaternion DualQuaternionRight, out dual_quaternion DualQuaternionComposed )

Description🔗

The operator dual_quat_composeDualQuatCompose multiplies the two dual quaternions DualQuaternionLeftdualQuaternionLeftdual_quaternion_left and DualQuaternionRightdualQuaternionRightdual_quaternion_right and returns the product in DualQuaternionComposeddualQuaternionComposeddual_quaternion_composed.

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 multiplication of the dual quaternions \(\hat{p}\) and \(\hat{q}\) is \(\hat{p} \hat{q} = p_{r}q_{r}+\varepsilon (p_{r}q_{d} + p_{d}q_{r})\).

For the multiplication of quaternions see quat_composeQuatCompose.

Note that the multiplication of two dual quaternions is not commutative, i.e., \(\hat{p} \hat{q} \neq \hat{q} \hat{p}\).

If DualQuaternionLeftdualQuaternionLeftdual_quaternion_left and DualQuaternionRightdualQuaternionRightdual_quaternion_right are unit dual quaternions and, hence, represent 3D rigid transformations, their multiplication corresponds to the multiplication of their corresponding homogeneous transformation matrices. Consequently, dual_quat_composeDualQuatCompose can be used to concatenate two 3D rigid transformations analogously to pose_composePoseCompose or hom_mat3d_composeHomMat3dCompose.

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🔗

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

Left dual quaternion.

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

Right dual quaternion.

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

Product of the dual quaternions.

Combinations with other operators🔗

Combinations

Possible predecessors

screw_to_dual_quatScrewToDualQuat

Possible successors

dual_quat_to_hom_mat3dDualQuatToHomMat3d, dual_quat_to_poseDualQuatToPose, dual_quat_to_screwDualQuatToScrew

Alternatives

pose_composePoseCompose, hom_mat3d_composeHomMat3dCompose

Module🔗

Foundation