TY - GEN

T1 - Online inserting points uniformly on the sphere

AU - Chen, Chun

AU - Lau, Francis C.M.

AU - Poon, Sheung Hung

AU - Zhang, Yong

AU - Zhou, Rong

N1 - Publisher Copyright:
© Springer International Publishing AG 2017.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85014303589&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-53925-6_19

DO - 10.1007/978-3-319-53925-6_19

M3 - Conference contribution

AN - SCOPUS:85014303589

SN - 9783319539249

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 243

EP - 253

BT - WALCOM

A2 - Rahman, Md. Saidur

A2 - Yen, Hsu-Chun

A2 - Poon, Sheung-Hung

PB - Springer Verlag

T2 - 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017

Y2 - 29 March 2017 through 31 March 2017

ER -