VR Rotation to Rotation Matrix

Convert axis/angle rotation to rotation matrix

• Library:

• Simulink 3D Animation / Utilities

• 

Description

The VR Rotation to Rotation Matrix block converts the axis / angle rotation representation used for defining rotations in virtual reality to a 3-by-3 rotation matrix

Ports

Input

Input 1 — Axis/Angle rotation

4-element vector

Input rotation, specified 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.

Data Types: single | double

Output

Output 1 — Rotation matrix

3-by-3 matrix

3D rotation, returned 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

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.