Online inserting points uniformly on the sphere

Chun Chen, Francis C.M. Lau, Sheung Hung Poon, Yong Zhang, Rong Zhou

Research output: Chapter in Book/Conference proceedingConference contributionpeer-review

2 Citations (Scopus)


In many scientific and engineering applications, there are occasions where points need to be inserted uniformly onto a sphere. Previous works on uniform point insertion mainly focus on the offline version, i.e., to compute N positions on the sphere for a given interger N with the objective to distribute these points as uniformly as possible. An example application is the Thomson problem where the task is to find the minimum electrostatic potential energy configuration of N electrons constrained on the surface of a sphere. In this paper, we study the online version of uniformly inserting points on the sphere. The number of inserted points is not known in advance, which means the points are inserted one at a time and the insertion algorithm does not know when to stop. As before, the objective is achieve a distribution of the points that is as uniform as possible at each step. The uniformity is measured by the gap ratio, the ratio between the maximal gap and the minimal gap of any pair of inserted points. We give a two-phase algorithm by using the structure of the regular dodecahedron, of which the gap ratio is upper bounded by 5.99. This is the first result for online uniform point insertion on the sphere.

Original languageEnglish
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings
EditorsMd. Saidur Rahman, Hsu-Chun Yen, Sheung-Hung Poon
PublisherSpringer Verlag
Number of pages11
ISBN (Print)9783319539249
Publication statusPublished - 2017
Externally publishedYes
Event11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017 - Hsinchu, Taiwan, Province of China
Duration: 29 Mar 201731 Mar 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10167 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017
Country/TerritoryTaiwan, Province of China

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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