Interpolating Rotations with Non-abelian Kuramoto Model on the 3-Sphere

Abstract

The paper presents a novel method for interpolating rotations based on the non-Abelian Kuramoto model on sphere S3. The algorithm, introduced in this paper, finds the shortest and most direct path between two rotations. We have discovered that it gives approximately the same results as a Spherical Linear Interpolation algorithm. Simulation results of our algorithm are visualized on S2 using Hopf fibration. In addition, in order to gain a better insight, we have provided one short video illustrating the rotation of an object between two positions.