Discrete & Computational Geometry

, Volume 34, Issue 1, pp 87–96

Equipartitions of Measures by 2-Fans


DOI: 10.1007/s00454-004-1151-1

Cite this article as:
Bereg, S. Discrete Comput Geom (2005) 34: 87. doi:10.1007/s00454-004-1151-1


We study the problem of computing an equitable 2-fan for three masses distributed on the 2-sphere. The existence of an equitable 2-fan was shown by Barany and Matousek. The contribution of this paper is twofold. (i) We prove the existence of an infinite set of equitable 2-fans. (ii) We present an efficient algorithm for finding an equitable 2-fan when the mass distributions are discrete, i.e. finite sets of points. Both (i) and (ii) can be easily extended to mass distributions in the plane instead of the sphere.

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Computer Science, University of Texas at Dallas, Box 830688, Richardson, TX 75083USA