Distributing points uniformly on the unit sphere under a mirror reflection symmetry constraint
arXiv:1403.3851 · doi:10.1016/j.jocs.2014.06.008
Abstract
Uniformly distributed point sets on the unit sphere with and without symmetry constraints have been found useful in many scientific and engineering applications. Here, a novel variant of the Thomson problem is proposed and formulated as an unconstrained optimization problem. While the goal of the Thomson problem is to find the minimum energy configuration of electrons constrained on the surface of the unit sphere, this novel variant imposes a new symmetry constraint---mirror reflection symmetry with the - plane as the plane of symmetry. Qualitative features of the two-dimensional projection of the optimal configurations are briefly mentioned and compared to the ground-state configurations of the two dimensional system of charged particles laterally confined by a parabolic potential well.
14 pages, 3 figures
References in corpus (5)
- Macroscopic 2D Wigner islands
- Sparse and Optimal Acquisition Design for Diffusion MRI and Beyond
- Identifying Star Streams in the Milky Way Halo
- Equilibrium spherically curved 2D Lennard-Jones systems
- Pseudometrically Constrained Centroidal Voronoi Tessellations: Generating uniform antipodally symmetric points on the unit sphere with a novel acceleration strategy and its applications to Diffusion and 3D radial MRI