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

Content Provider	Semantic Scholar
Author	Holhocs, Adrian Rocsca, Daniela
Copyright Year	2015
Abstract	For a class of polyhedrons denoted Kn(r, ε), we construct a bijective continuous area preserving map from Kn(r, ε) to the sphere S (r), together with its inverse. Then we investigate for which polyhedrons Kn(r , ε) the area preserving map can be used for constructing a bijective continuous volume preserving map from Kn(r , ε) to the ball S2(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 Kn(r, ε) and Kn(r , ε), respectively. In particular, we show that HEALPix grids can be obtained by mappings polyhedrons Kn(r, ε) onto the sphere.
File Format	PDF HTM / HTML
Alternate Webpage(s)	https://arxiv.org/pdf/1504.01517v1.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article