Fast Random Rotation matrices

Publisher Summary This chapter describes a method for generation of uniformly distributed random rotations of a unit sphere and illustrates an efficient procedure for creating random 3 × 3 rotation matrices. The chapter describes a complete algorithm, combining the reflection and simple rotation. The procedure of random rotation requires three uniformly distributed random numbers between 0 and 1. If the three random numbers are obtained by stratified or jittered sampling of the unit cube, the resulting rotation matrices will inherit the benefit of, less clumping. If the range of the random input variables is restricted, then uniformly distributed perturbations or wobbles within given limits can be generated. The chapter presents the result of applying 1,000 random rotations to a sphere with an arrow painted at one pole. The resulting pattern looks much the same from any vantage point, providing visual confirmation of uniformity.