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Path planning for walking characters in complicated virtual environments is afundamental task in simulations and games. A navigation mesh is a datastructure that allows efficient path planning. The Explicit Corridor Map (ECM)is a navigation mesh based on the medial axis. It enables path planning fordisk-shaped characters of any radius.  In this paper, we formally extend the medial axis (and therefore the ECM) to3D environments in which characters are constrained to walkable surfaces.Typical examples of such environments are multi-storey buildings, trainstations, and sports stadiums. We give improved definitions of a walkableenvironment (WE: a description of walkable surfaces in 3D) and a multi-layeredenvironment (MLE: a subdivision of a WE into connected layers). We define themedial axis of such environments based on projected distances on the groundplane. For an MLE with $n$ boundary vertices and $k$ connections, we show thatthe medial axis has size $O(n)$, and we present an improved algorithm thatconstructs the medial axis in $O(n \log n \log k)$ time.  The medial axis can be annotated with nearest-obstacle information to obtainthe ECM navigation mesh. Our implementations show that the ECM can be computedefficiently for large 2D and multi-layered environments, and that it can beused to compute paths within milliseconds. This enables simulations of largevirtual crowds of heterogeneous characters in real-time.

The Medial Axis of a Multi-Layered Environment and its Application as a Navigation Mesh