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.