Abstract — Virtual characters often need to plan visually convincing paths through a complicated environment. For example, a traveler may need to walk from an airport entrance to a staircase, descend the staircase, walk to a shuttle, ride the shuttle to a destination, ride an elevator back to the ground floor, and finally move on the ground floor again to reach the desired airplane. Most previous research only supports path planning in a single plane because the underlying data structures are two-dimensional. The goal of this paper is to permit visually convincing paths to be efficiently computed in a multi-layered environment such as an airport or a multistorey building. We describe an algorithm to create a navigation mesh, and our implementation demonstrates the feasibility of the approach. A multi-layered environment is represented by a set of twodimensional layers and a set of connections. Each layer is a collection of two-dimensional polygons that all lie in a single plane, and each connection provides a means of moving between layers. We first compute the traditional medial axis of each twodimensional layer in the environment. The connections are then used to iteratively merge this collection of medial axes into a single data structure. By adding a linear number of line segments to this structure, we obtain a navigation mesh that mathematically describes the walkable areas in a multilayered environment. This mesh can easily be input into existing planners to generate visually convincing paths for thousands of virtual characters in real-time. I.

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A relatively new area within the field of path planning deals with computing a stealthy path for a character moving in a virtual environment. Besides efficiently obtaining a path that is collision-free, short and smooth, the added difficulty is that the path must have little or no exposure to observers. We propose a new algorithm for computing such a path in the plane, and show that real-time performance can be achieved.

Virtual characters often need to plan visually convincing paths through a complicated environment. For example, a traveler may need to walk from an airport entrance to a staircase, descend the staircase, walk to a shuttle, ride the shuttle to a destination, ride an elevator back to the ground floor, and finally move on the ground floor again to reach the desired airplane. Most previous research only supports path planning in a single plane because the underlying data structures are two-dimensional. The goal of this paper is to permit visually convincing paths to be efficiently computed in a multi-layered environment such as an airport or a multistorey building. We describe an algorithm to create a navigation mesh, and our implementation demonstrates the feasibility of the approach. A multi-layered environment is represented by a set of two-dimensional layers and a set of connections. Each layer is a collection of two-dimensional polygons that all lie in a single plane, and each connection provides a means of moving between layers. We first compute the traditional medial axis of each twodimensional layer in the environment. The connections are then used to iteratively merge this collection of medial axes into a single data structure. By adding a linear number of line segments that connect the medial axis to the nearest obstacles, we obtain a navigation mesh that mathematically describes the walkable areas in a multi-layered environment. This mesh can easily be input into existing planners to generate visually convincing paths for thousands of characters in real-time. 1

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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.

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Virtual characters in games and simulations often need to plan visually convincing paths through a crowded environment. This paper describes how crowd density information can be used to guide a large number of characters through a crowded environment. Crowd density information helps characters avoid congested routes that could lead to traffic jams. It also encourages characters to use a wide variety of routes to reach their destination. Our technique measures the desirability of a route by combining distance information with crowd density information. We start by building a navigation mesh for the walkable regions in a polygonal 2D or multi-layered 3D environment. The skeleton of this navigation mesh is the medial axis. Each walkable region in the navigation mesh maintains an up-to-date density value, given by the fraction of the area that is being occupied by characters. These density values are mapped onto the medial axis to form a weighted graph. An A * search on this graph yields a backbone path for each character, and forces are used to guide the characters through the weighted environment. The characters periodically replan their routes as the density values are updated. Our experiments show that we can compute congestionavoiding paths for tens of thousands of characters in real-time. 1

Abstract We present a novel approach for planning and directing heterogeneous groups of virtual agents based on techniques from linear programming. Our method efficiently identifies the most promising paths in both time and space and provides an optimal distribution of the groups ’ members over these paths such that their average traveling time is minimized. The computed space-time plan is combined with an agent-based steering method to handle collisions and generate the final motions of the agents. Our overall solution is applicable to a variety of virtual environment applications, such as computer games and crowd simulators. We highlight its potential on different scenarios and evaluate the results from our simulations using a number of quantitative quality metrics. In practice, our system runs at interactive rates and can solve complex planning problems involving one or multiple groups. 1