Rotation Matrix to VR Rotation

Convert rotation matrix to axis/angle rotation

• Library:

• Simulink 3D Animation / Utilities

• 

Description

The Rotation Matrix to VR Rotation converts Rotation Matrix (defined columnwise as 3-by-3 matrix or as a 9-element column vector) into the Axis / Angle rotation representation used for defining rotations in VR.

Ports

Input

input 1 — Rotation matrix

3-by-3 matrix

3D rotation, specified as a 3-by-3 columnwise-defined matrix, also known as a direction cosine matrix.

A representation of a three-dimensional spherical rotation as a 3-by-3 real, orthogonal matrix R: R^TR = RR^T = I, where I is the 3-by-3 identity and R^T is the transpose of R. This matrix is also known as the direction cosine matrix (DCM). The DCM is the orientation of the object in space, relative to its parent node.

$$R=\left(\begin{array}{ccc}{R}_{11}& R_{12}& R_{13}\\ R_{21}& R_{22}& R_{23}\\ R_{31}& R_{32}& R_{33}\end{array}\right)=\left(\begin{array}{ccc}{R}_{xx}& R_{xy}& R_{xz}\\ R_{yx}& R_{yy}& R_{yz}\\ R_{zx}& R_{zy}& R_{zz}\end{array}\right)$$

Data Types: single | double

Output

Port 1 — Axis/Angle Rotation

4 element vector

Output rotation, returned as a 4-element vector in axis/angle notation,. The first three elements specify the axis of rotation and the fourth element specifies the angle.

Parameters

Maximum value to treat input value as zero — Effective zero value

1e-12 (default) | scalar

Input signal value is considered to be zero if it is equal to or lower than the value set in this parameter. By default, the parameter is set to ε = 1e-12.