Wouter van Toll

Real-time density-based crowd simulation

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 two‐dimensional (2‐D) or multilayered three‐dimensional (3‐D) 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. This density value is equal to the area occupied by all the characters inside a given region divided by the total area of this region. 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 congestion‐avoiding paths for tens of thousands of characters in real‐time. Copyright

Navigation meshes for realistic multi-layered environments

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 multi-storey building. We describe an algorithm to create a navigation mesh, and our implementation demonstrates the feasibility of the approach.

A navigation mesh for dynamic environments

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

A comparative study of navigation meshes

A navigation mesh is a representation of a 2D or 3D virtual environment that enables path planning and crowd simulation for walking characters. Various state-of-the-art navigation meshes exist, but there is no standardized way of evaluating or comparing them. Each implementation is in a different state of maturity, has been tested on different hardware, uses different example environments, and may have been designed with a different application in mind. In this paper, we conduct the first comparative study of navigation meshes. First, we give general definitions of 2D and 3D environments and navigation meshes. Second, we propose theoretical properties by which navigation meshes can be classified. Third, we introduce metrics by which the quality of a navigation mesh implementation can be measured objectively. Finally, we use these metrics to compare various state-of-the-art navigation meshes in a range of 2D and 3D environments. We expect that this work will set a new standard for the evaluation of navigation meshes, that it will help developers choose an appropriate navigation mesh for their application, and that it will steer future research on navigation meshes in interesting directions.

Dynamically Pruned A* for re-planning in navigation meshes

Modern simulations feature crowds of AI-controlled agents moving through dynamic environments, with obstacles appearing or disappearing at run-time. A dynamic navigation mesh can represent the traversable space of such environments. The A* algorithm computes optimal paths through the dual graph of this mesh. When an obstacle is inserted or deleted, the mesh changes and agents should re-plan their paths. Many existing re-planning algorithms are too memory-intensive for crowds, or they cannot easily be used on graphs where vertices and edges are added or removed. In this paper, we present Dynamically Pruned A* (DPA*), an extension of A* for re-planning optimal paths in dynamic navigation meshes. DPA* has similarities to adaptive algorithms that make the A* heuristic more informed based on previous queries. However, DPA* prunes the search using only the previous path and its relation to the dynamic event. We describe the four re-planning scenarios that can occur; DPA* uses different rules in each scenario. Our algorithm is memory-friendly and robust against structural changes in the graph, which makes it suitable for crowds in dynamic navigation meshes. Experiments show that DPA* performs particularly well in complex environments and when the dynamic event is visible to the agent. We integrate the algorithm into crowd simulation software to model large crowds in dynamic environments in real-time.

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

Path planning for walking characters in complicated virtual environments is a fundamental task in simulations and games. A navigation mesh is a data structure that allows efficient path planning. The Explicit Corridor Map (ECM) is a navigation mesh based on the medial axis. It enables path planning for disk-shaped characters of any radius. In this article, we formally extend the medial axis (and therefore the ECM) to 3D environments in which characters are constrained to walkable surfaces. Typical examples of such environments are multi-storey buildings, train stations, and sports stadiums. We give improved definitions of a walkable environment (WE: a description of walkable surfaces in 3D) and a multi-layered environment (MLE: a subdivision of a WE into connected layers). We define the medial axis of such environments based on projected distances on the ground plane. For an MLE with n boundary vertices and k connections, we show that the medial axis has size O(n), and we present an improved algorithm that constructs the medial axis in O(n log n log k) time. The medial axis can be annotated with nearest-obstacle information to obtain the ECM navigation mesh. 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.

The Explicit Corridor Map: Using the Medial Axis for Real-Time Path Planning and Crowd Simulation

We describe and demonstrate the Explicit Corridor Map (ECM), a navigation mesh for path planning and crowd simulation in virtual environments. For a bounded 2D environment with polygonal obstacles, the ECM is the medial axis of the free space annotated with nearest-obstacle information. It can be used to compute short and smooth paths for disk-shaped characters of any radius. It is also well-defined for multi-layered 3D environments that consist of connected planar layers. We highlight various operations on the ECM, such as dynamic updates, visibility queries, and the computation of paths (indicative routes). We have implemented the ECM as the basis of a real-time crowd simulation framework with path following and collision avoidance. Our implementation has been successfully used to simulate real-life events involving large crowds of heterogeneous characters. The enclosed demo application displays various features of our software.

GPGPU-accelerated construction of high-resolution generalized voronoi diagrams and navigation meshes

This paper presents a GPU-accelerated approach for improving the approximated construction of Generalized Voronoi Diagrams (GVDs). Previous work has shown how to render a GVD onto the GPU framebuffer, and copy it to the CPU for extraction of a high-quality diagram. We improve upon this technique by performing more computations in parallel on the GPU, and reducing the amount of data transferred to the CPU. We also design a multi-tiled construction technique that overcomes hardware limitations and enables much higher rendering resolutions, thus reducing discretization errors. Next, we extend our approach to create an Explicit Corridor Map navigation mesh, which is an efficient data structure for path planning in modern crowd simulation systems. The new implementation allows much faster construction of GVDs and navigation meshes at virtually infinite resolutions.