Aplicacions didàctiques del diagrama de Voronoi i del problema invers

Abstract

[en] This paper about Voronoi diagrams begins with a brief historical context and actual applications. After introducing previous and necessary concepts, the properties of Voronoi diagrams are described, including different algorithms for its construction. In the main part of the paper, it is developed the distinction of a partition of the two-dimensional space as a Voronoi diagram, from the necessary and base conditions. Afterwards, different methods are proposed for the resolution of reverse problem of Voronoi, both for Voronoi diagrams and for partitions of two-dimensional space which do not satisfy the conditions set previously. In the final part, didactic applications are proposed for elementary and high school students.