Voronoi Diagrams: Didactical and Artistic Applications

Abstract

Research on Voronoi Diagrams evolved a great deal from the original setting where a network of polygons marks the separation of points by regions of influence. Multiple approaches have been taken to solve the elementary geometry problems of bisecting segments and intersecting half-planes.The methods vary according to the type of point, the distance used and the type of bisector. In this work we propose some didactical tasks based on creating Voronoi diagrams. We also present some artistic quilt work, designed with the help of a Wolfram demonstrations project applet, based on a convenient choice of the generating points of a Voronoi Diagram.