The Successive Orthogonal Images (SOI) and Incremental Successive Orthogonal Images (ISOI) codes generate uniform samples of spheres, ellipsoids and of rotation groups. Both the SOI and ISOI codes provide rotation samples having excellent uniformity (good covering of the 2-sphere and SO(3) are obtained, which can be formulated in terms of spherical dispersion and discrepancy). The SOI code performs a discrete uniform sample that is very uniform, while ISOI attempts to create a series of uniform samplings by adding one point at a time.

SOI is copyrighted but free for non-commercial use.

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

Please cite: 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. View Abstract

This code provides a uniform deterministic sequence of samples over
S^2. It generates an ordered sequence of points from the
multiresolution grid structure provided by HEALPix. The output is
parametrized by (x,y,z) coordinates in 3D.

This code provides a uniform multiresolution grids over SO(3). The
method uses Hopf coordinates to generate grid cells. The
base-resolution grid consists of 72 points. The output is
parametrized using unit quaternions, represented by (x1,x2,x3,x4) in
4D.

This code provides a uniform deterministic sequence over SO(3). The
base-resolution grid consists of 72 points. The method uses Hopf
coordinates to generate grid cells. The output is parametrized
using unit quaternions, represented by (x1,x2,x3,x4) in 4D.