Dynamic Detection of Topological Information from Grid-Based Generalized Voronoi Diagrams

Figure 1

Those points which are equidistant from at least three sites are denoted as GVD vertices. As a consequence, a plane can be represented as a partition and thus is called the GVD of 𝑆. As an example, Figure 1 represents the GVD of an indoor environment which first appeared in [5] and we build its GVD here by our proposed algorithm, Dynamic Topology Detector (DTD). The GVD of an indoor environment; red lines denote the GVD edges, blue dots are GVD vertices, and black polygons represents walls and furniture, that is, the GVD sites.