Granular Floor Plan Representation for Evacuation Modeling

In this paper we describe the architecture of a simple evacuation model which is based on a graph representation of the scene. Such graphs are typically constructed using Medial Axis Transform (MAT) or Straight Medial Axis Transform (S-MAT) transformations, the former being a part of the Voronoi diagram (Dirichlet tessellation) of the floor plan. In our work we construct such graphs for floor plans using Voronoi diagram along with the dual Delaunay triangulation of a set of points approximating the scene. Information supplied by Delaunay triangulation complements the graph in two ways: it determines capacities of some paths associated with edges, and provides a bijection between graph vertices and a set of regions forming a partition of the floor plan. We call the representation granular for this reason. We provide an exposition of the representation of fire scene that aids egress time calculations, discuss the algorithm of construction of this representation and briefly discuss the applicability of network flow models (e.g. the Ford-Fulkerson method or the push-relabel method) in our setting.