Super-Fibonacci Spirals: Fast, Low-Discrepancy Sampling of SO(3)

Abstract

Super-Fibonacci spirals are an extension of Fibonacci spirals, enabling fast generation of an arbitrary but fixed number of 3D orientations. The algorithm is simple and fast. A comprehensive evaluation comparing to other meth-ods shows that the generated sets of orientations have low discrepancy, minimal spurious components in the power spectrum, and almost identical Voronoi volumes. This makes them useful for a variety of applications, in partic-ular Monte Carlo sampling.