COMPUTER ANIMATION AND VIRTUAL WORLDS Comp. Anim. Virtual Worlds 2012; 23:535–546 Published online 12 June 2012 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/cav.1468 SPECIAL ISSUE PAPER A navigation mesh for dynamic environments † Wouter G. van Toll, Atlas F. Cook IV and Roland Geraerts * Department of Information and Computing Sciences, Utrecht University, 3584 CC Utrecht, The Netherlands ABSTRACT Games and simulations frequently model scenarios where obstacles move, appear, and disappear in an environment. A city environment changes as new buildings and roads are constructed, and routes can become partially blocked by small obstacles many times in a typical day. This paper studies the effect of using local updates to repair only the affected regions of a navigation mesh in response to a change in the environment. The techniques are inspired by incremental methods for Voronoi diagrams. The main novelty of this paper is that we show how to maintain a 2D or 2.5D navigation mesh in an environment that contains dynamic polygonal obstacles. Experiments show that local updates are fast enough to permit real-time updates of the navigation mesh. Copyright © 2012 John Wiley & Sons, Ltd. KEYWORDS navigation mesh; dynamic environments; medial axis; Voronoi diagram *Correspondence Roland Geraerts, Department of Information and Computing Sciences, Utrecht University, 3584 CC Utrecht, The Netherlands. E-mail: R.J.Geraerts@uu.nl 1. INTRODUCTION A navigation mesh is a data structure that uses a set of two-dimensional (2D) regions to represent the walkable space in an environment [1]. These regions are commonly used to plan visually convincing paths through complicated environments [2–6]. Current environments are largely static because it is a relatively expensive operation to recompute the entire nav- igation mesh each time the environment changes. The goal of this paper is to show that a navigation mesh that is based on a medial axis can be updated very quickly. We locally repair only the affected regions of the navigation mesh each time the environment changes. Our experiments show that local operations can be performed quickly enough to support dynamic environments where many obstacles are frequently moved, added, and removed. The navigation mesh that we choose to locally repair is the Explicit Corridor Map (ECM) [2,6]. The ECM was chosen because it can quickly produce smooth and short paths with any feasible amount of clearance to the obsta- cles. This navigation mesh can be used to plan paths for characters that may have a variety of widths and clearance preferences. The ECM has a small memory footprint and has previously been used to plan visually convincing paths for thousands of virtual characters in real time [7]. † Supporting information may be found in the online version of this paper. To the best of our knowledge, this paper is the first to describe how to perform dynamic updates in an exact 2.5D navigation mesh. As illustrated in Figure 1, such a mesh describes the walkable areas for a connected set of 2D floors. Such a multilayered structure can be used to model buildings with multiple floors. 1.1. Static Environments Most path planners assume that the obstacles in an environ- ment are fixed. This means that the environment is static. Graph-based techniques such as probabilistic roadmaps [8], rapidly exploring random trees [9], waypoint graphs [10], and reactive deformation roadmaps [11] represent the walkable environment (or a high-dimensional config- uration space) using a set of one-dimensional edges. By contrast, a navigation mesh partitions the walkable envi- ronment into a set of 2D walkable areas. These walkable areas permit virtual characters to control their movements inside each 2D region so that they can more easily avoid other moving characters [12,13]. There are many techniques to construct navigation meshes. Pettré et al. [5] use a set of overlapping disks to describe the walkable space. Mononen’s [3] open-source Recast Navigation project discretizes the environment into cubic voxels, extracts the walkable surfaces, and connects all adjacent cells. Hale et al. [14] seed the environment with a series of quads, and each quad grows until it is as large Copyright © 2012 John Wiley & Sons, Ltd. 535