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Towards Uniform Online Spherical Tessellations

Bell, PC and Potapov, I Towards Uniform Online Spherical Tessellations. In: Lecture Notes in Computer Science . (Computability in Europe, 15 July 2019 - 19 July 2019, Durham, UK). (Accepted)

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Abstract

The problem of uniformly placing N points onto a sphere finds applications in many areas. An online version of this problem was recently studied with respect to the gap ratio as a measure of uniformity. The proposed online algorithm of Chen et al. was upper-bounded by 5.99 and then improved to 3.69, which is achieved by considering a circumscribed dodecahedron followed by a recursive decomposition of each face. We analyse a simple tessellation technique based on the regular icosahedron, which decreases the upper-bound for the online version of this problem to around 2.84. Moreover, we show that the lower bound for the gap ratio of placing up to three points is approx. 1.618. The uniform distribution of points on a sphere also corresponds to uniform distribution of unit quaternions which represent rotations in 3D space and has numerous applications in many areas.

Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: 08 Information and Computing Sciences
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Computer Science
Publisher: Springer Verlag
Date Deposited: 14 Jun 2019 10:27
Last Modified: 14 Jun 2019 10:27
Editors: Primiero, G, Martin, B, Paulusma, D and Manea, F
URI: http://researchonline.ljmu.ac.uk/id/eprint/10879

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