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- W2469716007 abstract "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." @default.
- W2469716007 created "2016-07-22" @default.
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- W2469716007 date "2015-04-07" @default.
- W2469716007 modified "2023-10-17" @default.
- W2469716007 title "Area preserving maps and volume preserving maps between a class of polyhedrons and a sphere" @default.
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