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Area preserving maps and volume preserving maps between a class of polyhedrons and a sphere

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Abstract

We construct a bijective continuous area preserving map from a class of elongated dipyramids to the sphere, together with its inverse. Then we investigate for which such solid polyhedrons the area preserving map can be used for constructing a bijective continuous volume preserving map to the 3D-ball. These maps can be further used in constructing uniform and refinable grids on the sphere and on the ball, starting from uniform and refinable grids on the elongated dipyramids. In particular, we show that HEALPix grids can be obtained from these maps. We also study the optimality of the logarithmic energy of the configurations of points obtained from these grids.

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Cluj-Napoca, str. Memorandumului 28, 400114, Cluj-Napoca, Romania

    Adrian Holhoş & Daniela Roşca

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  1. Adrian Holhoş
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  2. Daniela Roşca
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Correspondence to Adrian Holhoş.

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Communicated by: Yang Wang

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Holhoş, A., Roşca, D. Area preserving maps and volume preserving maps between a class of polyhedrons and a sphere. Adv Comput Math 43, 677–697 (2017). https://doi.org/10.1007/s10444-016-9502-z

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  • DOI: https://doi.org/10.1007/s10444-016-9502-z

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