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On the problem of the densest packing of spherical segments into a sphere Sobre o problema do empacotamento mais denso de segmentos esféricos em uma esfera
On the problem of the densest packing of spherical segments into a sphere Sobre o problema do empacotamento mais denso de segmentos esféricos em uma esfera
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Date
2023
Authors
Duc Thinh Vu, The Bao Phung, A.A. Lempert, Duc Minh Nguyen.
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Abstract
"The paper considers a particular variant of the classical optimal packing problem when the
container is a sphere, the packed elements are equal spherical caps, and the optimality criterion
is to maximize their geodesic radius. At the same time, we deal with a special integral metric
to determine the distance between points, which becomes Euclidean in the simplest case. We
propose a heuristic numerical algorithm based on the construction of spherical Voronoi
diagrams, which makes it possible to obtain a locally optimal solution to the problem under
consideration. Numerical calculations show the operability and effectiveness of the proposed
method and allow us to draw some conclusions about the properties of packings."
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Keywords
Optimal Coverage. Sphere. Voronoi Diagram. Optical Analogy. Chebyshev Center.