Generalized voronoi diagram of the construction site Download

The Voronoi Diagram of P is the subdivision of the plane induced by the voronoi cells V(p i), for i = 1;2;:::;n. The vertices, edges, and faces of this subdivision are called voronoi vertices, voronoi edges, and voronoi cells. It is easy to see that the (interior of) cells of two points are disjoint, and the union of all the cells tiles the plane.. Dans ce texte, on pr´esente plusieurs aspects des diagrammes de Voronoi. On ´etudie d'abord l'espace des sph`eres de E, les faisceaux de sph`eres et la repr`esentation d'un diagramme de Voronoi comme projection de l'intersection de certains demi-espaces de l'espace des sph`eres (th´eor`eme 1).

Figure 3. Construction of a Voronoi Region Using Half-Planes [6]. every point of the plane that is closer to pi than pj or equidistant from the two. H(pj;pi), or Dom(pj;pi), is the dominance region of pj over pi. In the basic Voronoi diagram, H(pj;pi) is a half-plane. From our de nition of dominance regions, we can de ne Voronoi regions in yet.. A Voronoi diagram shows the region containing the set of all points which are closer to one given site than to any other site on the diagram. A site is located at the coordinates of a specific place of interest on a Voronoi diagram. It will be partitioned into a number of regions. These regions are often called Voronoi cells and will be polygons