Area preserving maps and volume preserving maps between a class of polyhedrons and a sphere
| Autor: | Adrian Holhoş, Daniela Roşca |
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| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Mathematics::Combinatorics Logarithm Applied Mathematics HEALPix 010102 general mathematics Inverse Metric Geometry (math.MG) 010103 numerical & computational mathematics 01 natural sciences Visualization Computational Mathematics Polyhedron Mathematics - Metric Geometry FOS: Mathematics Bijection Computational Science and Engineering Ball (mathematics) 65D18 68U05 65M55 0101 mathematics Computer Science::Databases Mathematics |
| Zdroj: | Advances in Computational Mathematics. 43:677-697 |
| ISSN: | 1572-9044 1019-7168 |
| Popis: | For a class of polyhedrons denoted $\mathbb K_n(r,\varepsilon)$, we construct a bijective continuous area preserving map from $\mathbb K_n(r,\varepsilon)$ to the sphere $\mathbb S^{2}(r)$, together with its inverse. Then we investigate for which polyhedrons $\mathbb K_n(r',\varepsilon)$ the area preserving map can be used for constructing a bijective continuous volume preserving map from $\bar{\mathbb K}_n(r',\varepsilon)$ to the ball $\bar{\mathbb S^{2}}(r)$. 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 of the polyhedrons $\mathbb K_n(r,\varepsilon)$ and $\bar{\mathbb K}_{n}(r',\varepsilon)$, respectively. In particular, we show that HEALPix grids can be obtained by mappings polyhedrons $\mathbb K_n(r,\varepsilon)$ onto the sphere. Comment: 25 pages, 6 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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