Towards Uniform Online Spherical Tessellations



Bell, Paul C and Potapov, Igor
(2019) Towards Uniform Online Spherical Tessellations. In: 15th Conference on Computability in Europe, CiE 2019, 2019-07-15 - 2019-07-19, Durham, UK.

[img] Text
1810.01786v1.pdf - Submitted Version

Download (388kB) | Preview

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 1+5√2≈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 (Unspecified)
Uncontrolled Keywords: Online algorithms, Discrepancy theory, Spherical trigonometry, Uniform point placement
Depositing User: Symplectic Admin
Date Deposited: 01 Oct 2019 14:55
Last Modified: 23 Aug 2021 12:16
DOI: 10.1007/978-3-030-22996-2_11
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3056453