Graphics Gems III (IBM Version)

III.6

UNIFORM RANDOM ROTATIONS

Ken Shoemake,     Otter Enterprises, Palo Alto, California

Publisher Summary

A planar rotation can be represented in several ways—for example, as an angle between 0 and 2π or as a unit complex number x + iy = cos θ + i sin θ. Planar rotations combine by summing their angles modulo 2π ; so one way to generate a uniform planar rotation is to generate a uniform angle. This chapter describes a uniformly distributed spatial rotation as one not having a uniformly distributed angle. For a unit quaternion, the ω component is the cosine of half the angle of rotation. When the angle is uniformly distributed between 0 and 2π, the average magnitude of ω will be 2/π 0.6366, which exceeds the correct value for a uniform rotation ...