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- W3210881109 abstract "Consider a random set of points on the unit sphere in Rd, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the case d = 3, for which there are elementary proofs and fascinating formulas for metric properties. In particular, we study the fraction of acute facets, the expected intrinsic volumes, the total edge length, and the distance to a fixed point. Finally we generalize the results to the ellipsoid with homeoid density." @default.
- W3210881109 created "2021-11-08" @default.
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- W3210881109 date "2021-10-25" @default.
- W3210881109 modified "2023-10-16" @default.
- W3210881109 title "The Beauty of Random Polytopes Inscribed in the 2-Sphere" @default.
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- W3210881109 doi "https://doi.org/10.1080/10586458.2021.1980459" @default.
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