Voronoi cell constructions on the map

Abstract

This bachelor’s thesis deals with study of Voronoi cell and its representation in Voronoi diagrams and their construction on the model of Earth’s surface. At first, Voronoi diagrams and their characteristics are explained in a plane, we describe their construction using Fortune’s algorithm, then spherical geometry is explained. Then we take a look at some equations that are useful for calculating on a sphere, and we use them for calculating distances on Earth, which we approximate with a sphere. Finally we apply Fortune’s algorithm on a sphere, we explain the principles of construction of Voronoi diagrams with this algorithm on a sphere and changes compared to the planar case that must be taken care of. The goal of the thesis is to display Voronoi diagram on Google maps, thus we work with Google Maps API