The SO3 points clouds have been generated from the ISOI software available
at this webpage : 
https://mitchell-lab.biochem.wisc.edu/soi/index.php

This software is an implementation of the two following papers:

J. C. Mitchell. Discrete Uniform Sampling of Rotation Groups Using Orthogonal Images. SIAM Journal of Scientific Computing, 30(1):525-547, 2007. 

A. Yershova, S. Jain, S. M. LaValle, and J. C. Mitchell. Generating Uniform Incremental Grids on SO(3) Using the Hopf Fibration International Journal of Robotics Research, November 2009. 

This software copyright is GNU General Public License as published by the Free Software Foundation version 2.