RandomRotationMatri​x

Version 1.0.2 (1.43 KB) by Seong Hun Lee
Generate a random 3 x 3 rotation matrix in SO(3).
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Updated 12 Aug 2023

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Note that each column of a 3 x 3 rotation matrix can be thought of as the x, y and z-axis of some reference frame placed with some orientation.
Using this fact, we do the following:
  1. We set the x-axis to be a random 3D unit vector.
  2. Then, we generate the y-axis by finding a unit vector that is perpendicular to the x-axis. This is done by generating another random 3D vector and then computing the cross product with the x-axis.
  3. Finally, the z-axis must be the cross product of the x-axis and the y-axis.
Puting these three axis in one matrix side by side, we get a 3 x 3 rotation matrix.

Cite As

Seong Hun Lee (2024). RandomRotationMatrix (https://www.mathworks.com/matlabcentral/fileexchange/132613-randomrotationmatrix), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2023a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
1.0.2

Fixed the way a random 3D unit vector is generated.
1.0.1

Updated the description.
1.0.0