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614190 
Journal Article 
SAMPLING ROTATION GROUPS BY SUCCESSIVE ORTHOGONAL IMAGES 
Mitchell, JC 
2008 
30 
1 
525-547 
The ability to construct uniform deterministic samples of rotation groups is useful in many contexts, but there are inherent mathematical difficulties that prevent an exact solution. Here, we present successive orthogonal images, an effective means for uniform deterministic sampling of orthogonal groups. The method is valid in any dimension, and analytical bounds are provided on the sampling uniformity. Numerical comparisons with other sampling methods are given for the special case of SO(3). We make use of non-Riemannian distance metrics that are group-invariant and locally compatible with the Haar measure. In addition, our results provide a semi-unique decomposition of any orthogonal matrix into the product of planar rotations. [ABSTRACT FROM AUTHOR] Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial and Applied Mathematics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts) 
ROTATION groups; ORTHOGONAL arrays; ORTHOGONALIZATION methods; ALGEBRAS, Linear; NUMERICAL analysis; dispersion; Haar measure; orthogonal group; SO(3); SO(n); uniform sampling