quat_to_hom_mat3dQuatToHomMat3dQuatToHomMat3dquat_to_hom_mat3dT_quat_to_hom_mat3d🔗

Short description🔗

quat_to_hom_mat3dQuatToHomMat3dQuatToHomMat3dquat_to_hom_mat3dT_quat_to_hom_mat3d — Convert a quaternion into the corresponding rotation matrix.

Signature🔗

quat_to_hom_mat3d( quaternion Quaternion, out hom_mat3d RotationMatrix )

Description🔗

The operator quat_to_hom_mat3dQuatToHomMat3d converts a unit quaternion Quaternionquaternionquaternion into its corresponding rotation matrix RotationMatrixrotationMatrixrotation_matrix.

The RotationMatrixrotationMatrixrotation_matrix for a quaternion \(x=x_{0}+x_{1}i+x_{2}j+x_{3}k\) is given by:

\[\begin{eqnarray*} \left( \begin{array}{ccc} x_{0}^2+x_{1}^2-x_{2}^2-x_{3}^2 & 2 x_{1} x_{2}-2 x_{0} x_{3} & 2 x_{0} x_{2}+2 x_{1} x_{3} \\ 2 x_{0} x_{3}+2 x_{1} x_{2} & x_{0}^2-x_{1}^2+x_{2}^2-x_{3}^2 & 2 x_{2} x_{3}-2 x_{0} x_{1} \\ 2 x_{1} x_{3}-2 x_{0} x_{2} & 2 x_{0} x_{1}+2 x_{2} x_{3} & x_{0}^2-x_{1}^2-x_{2}^2+x_{3}^2 \end{array} \right) \end{eqnarray*}\]

Attention🔗

RotationMatrixrotationMatrixrotation_matrix will only be a valid rotation matrix if Quaternionquaternionquaternion is a unit quaternion.

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🔗

Quaternionquaternionquaternion (input_control) quaternion → (real)HTuple (double)HQuaternion, HTuple (double)Sequence[float]Htuple (double)

Rotation quaternion.

RotationMatrixrotationMatrixrotation_matrix (output_control) hom_mat3d → (real)HTuple (double)HHomMat3D, HTuple (double)Sequence[float]Htuple (double)

Rotation matrix.

Combinations with other operators🔗

Combinations

Possible predecessors

axis_angle_to_quatAxisAngleToQuat, quat_composeQuatCompose

Possible successors

affine_trans_point_3dAffineTransPoint3d

Module🔗

Foundation