Approximation to uniform distribution in SO(3)

Abstract

Using the theory of determinantal point processes we give upper bounds for the Green and Riesz energies for the rotation group SO(3), with Riesz parameter up to 3. The Green function is computed explicitly, and a lower bound for the Green energy is established, enabling comparison of uniform point constructions on SO(3). The variance of rotation matrices sampled by the determinantal point process is estimated, and formulas for the L2 -norm of Gegenbauer polynomials with index 2 are deduced, which might be of independent interest. Also a simple but effective algorithm to sample points in SO(3) is given.

arXiv comment24 pages, 1 figure

References in corpus (5)

• Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres
• Complex determinantal processes and H1 noise
• Expected Riesz energy of some determinantal processes on flat tori
• On the separation distance of minimal Green energy points on compact Riemannian manifolds
• Surface Spline Approximation on SO(3)

Cited by in corpus (2)

• On the Logarithmic Energy of Points on S^2
• On the $L^2$-norm of Gegenbauer polynomials