Separating a walkable environment into layers

Abstract

A multi-layered environment is a representation of the walkable environment in a 3D virtual environment that comprises a set of two-dimensional layers together with the locations where the different layers touch, which are called connections. This representation can be used for crowd simulations, e.g. to determine evacuation times in complex buildings, or for finding the shortest routes. The running times of these algorithms depend on the number of connections. Finding an environment with the smallest number of connections, is an NP-Hard problem. Our first algorithm tackles this problem by using an integer linear program which is capable of finding the best possible solution, but naturally takes a long time. Hence, we provide two heuristics that search for multi-layered environments with a low number of connections. One algorithm uses local search to gradually improve the found solution. The other one, called the height heuristic, is very fast and gives good solutions in practical environments.