The Explicit Corridor Map: A Medial Axis-Based Navigation Mesh for Multi-Layered Environments.

Path planning for walking characters in complicated virtual environments is a fundamental task in simulations and games. In this paper, we present an improved definition of the Explicit Corridor Map (ECM), a navigation mesh that allows efficient path planning and crowd simulation for disk-shaped characters of any radius. The ECM is a medial axis (MA) annotated with nearest-obstacle information. For a planar environment with $n$ obstacle vertices, the ECM has size $O(n)$ and can be computed in $O(n log n)$ time. also introduce multi-layered environments (MLEs), in which multiple planar layers are connected by line segment connections. Typical real-world examples are multi-storey buildings, train stations, and sports stadiums. We define the MA and the ECM for multi-layered environments, based on projected distances on the ground plane. For an MLE with $n$ obstacle points and $k$ connections, the MA has size $O(n)$. We present an improved algorithm that constructs the MA and ECM in $O(n log n log k)$ time. Our implementations show that the ECM can be computed efficiently for large 2D and multi-layered environments, and that it can be used to compute paths within milliseconds. This enables simulations of large virtual crowds of heterogeneous characters in real-time.