Diagrama de Voronoi para dois pontos com um obstáculo circular

Abstract

In this work, we first present a highly important geometric data structure in the solution of proximity problems called the Voronoi diagram. Through a set of generating points in the plane, we analyze how to construct them without the presence of obstacles among these points, presenting their properties and which characteristics. are important. We then analyze the consequences of such a structure when we insert obstacles between its generating points. First, we observe this situation considering polygonal obstacles. And we end by determining the boundary of this diagram when we consider two generative points and a circular obstacle.