BetaConcept: A Program for Voronoi Diagrams, Dual Structures, and Complexes in the Plane

Voronoi diagrams are powerful for solving spatial problems among particles with different sizes. In particular, the Voronoi diagram of spheres, also called the additively-weighted Voronoi diagram, has proven its powerful capability for solving molecular biology/material science problems in an unified framework. Beta-complex is a generalization of (weighted) alpha-complex and they share similarities and dissimilarities. This paper presents the Beta Concept program which facilitates easy understanding of the powerful capability of the Voronoi diagram, its dual structure, and the beta-complex in the plane. Beta Concept is a Windows program with a graphic user interface written in the standard C++ language and is freely available at the Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr).