Some spherical coverings on S2 and their algebraic numbers
Randall L. Rathbun
TL;DR
This paper investigates spherical coverings on the S2 sphere, focusing on algebraic numbers associated with putatively optimal solutions for covering the sphere with spherical caps, and also examines some locally optimal solutions.
Contribution
It presents new putatively optimal solutions for covering the sphere with spherical caps and analyzes their algebraic numbers, including some locally optimal configurations.
Findings
Identified putatively optimal coverings with minimal radius
Analyzed algebraic numbers associated with these coverings
Examined some locally optimal solutions
Abstract
Spherical coverings on the S2 sphere and their algebraic numbers are given for the putatively optimal global solutions for some n-congruent spherical caps with minimal radius to completely cover the S2 sphere. A few locally optimal solutions are also examined.
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Taxonomy
TopicsStructural Analysis and Optimization · Elasticity and Material Modeling · Computational Geometry and Mesh Generation