# Distributing Points on the Sphere, I

@article{Katanforoush2003DistributingPO, title={Distributing Points on the Sphere, I}, author={Ali Katanforoush and Mehrdad Shahshahani}, journal={Experimental Mathematics}, year={2003}, volume={12}, pages={199 - 209} }

We study four different methods for distributing points on the sphere and numerically analyze their relative merits with respect to certain metrics.

## 91 Citations

Energy Minimization of Point Charges on a Sphere with a Spectral Projected Gradient Method

- Physics
- 2012

Thomson problem, which is one of the problems concerning of optimal configuration on the sphere, is defined. A Nonmonotone Spectral Projected Gradient Method that has been intensively used in many…

Spherical Distribution of 5 Points with Maximal Distance Sum

- MathematicsDiscret. Comput. Geom.
- 2011

This paper studies the problem of spherical distribution of 5 points, that is, how to configure 5 points on the unit sphere such that the mutual distance sum is maximal, using interval methods and related techniques, and gives a computer-assisted proof.

On the Minimax Spherical Designs

- MathematicsRandom Structures & Algorithms
- 2022

This paper considers a novel energy function that arises naturally from statistics and combinatorial optimization, and studies its theoretical properties, and solves both the exact optimal spherical point configurations in certain cases and the minimal energy asymptotics under general assumptions.

Experimental Study of Energy-Minimizing Point Configurations on Spheres

- Computer ScienceExp. Math.
- 2009

Experimental evidence is presented for two new universal optima (consisting of 40 points in 10 dimensions and 64 points in 14 dimensions), as well as evidence that there are no others with at most 64 points.

Distributions of angles in random packing on spheres

- MathematicsJ. Mach. Learn. Res.
- 2013

The results reveal interesting differences in the two settings and provide a precise characterization of the folklore that "all high-dimensional random vectors are almost always nearly orthogonal to each other".

Generation of View Representation from View Points on Spiral Trajectory

- MathematicsIP&C
- 2010

The new method of view representation generation is proposed and the arrangement of view point is more evenly then in other known similar methods and can be formulated by only one parameter.

Energy of zeros of random sections on Riemann Surface

- Mathematics
- 2007

The purpose of this paper is to determine the asymptotic of the average energy of a configuration of N zeros of system of random polynomials of degree N as N tends to infinity and more generally the…

ENERGIES OF ZEROS OF RANDOM SECTIONS ON RIEMANN SURFACES

- Mathematics
- 2008

The purpose of this paper is to determine the asymptotic of the average energy of a configuration of N zeros of a system of random polynomials of degree N as N?8 and more generally the zeros of…

The sphere by itself: can we distribute points on it evenly?

- Mathematics
- 2010

As we shall see throughout this chapter, the geometry of the “ordinary sphere” S2 – two dimensional in a space of three dimensions – harbors many pitfalls. It’s much more subtle than we might think,…

Sphere Anchored Map: A Visualization Technique for Bipartite Graphs in 3D

- MathematicsHCI
- 2009

The results of the study revealed that more clusters of free nodes can be found using sphere anchored maps than using circular anchored maps, and the maps have high readability, particularly around anchors.

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