Main web page 
http://rotations.mitchelllab.org

Publications 
Anna Yershova, Swati Jain, Steven M. LaValle, and Julie C. Mitchell, International Journal of Robotics Research, IJRR 2009 Anna Yershova, Steven M. LaValle, and Julie C. Mitchell, In Proc. Eighth International Workshop on the Algorithmic Foundations of Robotics (WAFR 2008) 
Software 
Below are the implementations of the sequences over the
2sphere and 3dimensional rotation group, SO(3), presented in
our publications. The code is written using
C++. The README file contains the
instructions on how to download and run the code. 
S2_sequence.tar.gz 
This code provides a uniform deterministic sequence of samples
over the 2sphere. 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. 
SO3_grid.tar.gz 
This code provides a uniform multiresolution grids over
SO(3). The method uses Hopf coordinates to generate grid
cells. The baseresolution grid consists of 72 points. The
output is parametrized using unit quaternions, represented by
(x,y,z,w) in 4D. 
SO3_sequence.tar.gz 
This code provides a uniform deterministic sequence over
SO(3). The baseresolution grid consists of 72 points. The
method uses Hopf coordinates to generate grid cells. The
output is parametrized using unit quaternions, represented by
(x,y,z,w) in 4D. The advantages of the deterministic sequences provided by this software are: uniformity (good covering of the 2sphere and SO(3) is obtained, this can be formulated in terms of spherical dispersion and discrepancy), incremental quality (samples are added one by one maintaining the uniformity of the resulting distribution), explicit neighborhood structure (the samples are organized in a grid fashion, allowing efficient nearest neighbor calculations). It is important to note that the resulting sequence is infinite, that is, infinitely many samples can be generated retaining all of the above properties. Deterministic sequences were tested in samplingbased motion planning algorithms and compared to the performance of random sequences. While the performance efficiency is usually comparable, deterministic sequences provide important resolution completeness guarantees to motion planning methods. 