Modern virtual environments can contain a variety of characters and traversable regions. Each character may have different preferences for the traversable region types. Pedestrians may prefer to walk on sidewalks, but they may occasionally need to traverse roads and dirt paths. By contrast, wild animals might try to stay in forest areas, but they are able to leave their protective environment when necessary. This paper presents a novel path planning method named MIRAN (Modified Indicative Routes and Navigation) that takes a character's region preferences into account. Given an indicative route as a rough estimation of a character's preferred route, MIRAN efficiently computes a visually convincing path that is smooth, keeps clearance from obstacles, avoids unnecessary detours, and allows local changes to avoid other characters. To the best of our knowledge, MIRAN is the first path planning method that supports the above features while using an exact representation of the navigable space. Experiments show that with our approach a wide range of different character behaviors can be simulated. It also overcomes problems that occur in previous path planning methods such as the Indicative Route Method. The resulting paths are well-suited for real-time simulations and gaming applications.

We present Social Groups and Navigation (SGN), a method to simulate the walking behavior of small pedestrian groups in virtual environments. SGN is the first method to simulate group behavior on both global and local levels of an underlying planning hierarchy. We define quantitative metrics to measure the coherence and the sociality of a group based on existing empirical data of real crowds. SGN does not explicitly model coherent and social formations, but it lets such formations emerge from simple geometric rules. In addition to a previous version, SGN also handles group-splitting to smaller groups throughout navigation as well as social subgroup behavior whenever a group has to temporarily split up to re-establish its coherence. For groups of four, SGN generates between 13% and 53% more socially-friendly behavior than previous methods, measured over the lifetime of a group in the simulation. For groups of three, the gain is between 15% and 31%, and for groups of two, the gain is between 1% and 4%. SGN is designed in a flexible way, and it can be integrated into any crowd-simulation framework that handles global path planning and any path following as separate steps. Experiments show that SGN enables the simulation of thousands of agents in real time.

We present a new method, Social Groups and Navigation (SGN), to simulate the walking behavior of small pedestrian groups in virtual environments. SGN is the first method to simulate group behavior on both global and local levels. We define quantitative metrics to measure the coherence and the sociality of a group based on existing empirical data of real crowds. SGN is designed to let groups stay in coherent and social formations without explicitly modeling such formations. For groups of four, SGN generates between 13% and 53% more socially-friendly behavior than existing methods, measured over the lifetime of a group in the simulation. For groups of three, the gain is between 15% and 31%, and for groups of two, the gain is between 1% and 4%. SGN can be used with any existing global path planner and any existing path following method. Experiments show that SGN enables the simulation of thousands of agents in real time. Due to its flexible design, it can be easily integrated into a larger crowd simulation framework.

The Weighted Region Problem is defined as the problem of finding a cost-optimal path in a weighted planar polygonal subdivision. Searching for paths on a grid representation of the scene is fast and easy to implement. However, grid representations do not capture the exact geometry of the scene. Hence, grid paths can be inaccurate or might not even exist at all. Methods that work on an exact representation of the scene can approximate an optimal path up to an arbitrarily small -error. However, these methods are computationally inefficient and thus not well-suited for real-time applications. In this paper, we analyze the quality of optimal paths on a 8-neighbor-grid. We prove that the costs of such a path in a scene with weighted regions can be arbitrarily high in the general case. If all regions are aligned with the grid, we prove that the costs are at most 4 + 4 − 2 √ 2 times the costs of an optimal path. In addition, we present a new hybrid method called Vertex-based Pruning (VBP). VBP computes paths that are -optimal inside a pruned subset of the scene. Experiments show that VBP paths can be computed at interactive rates, and are thus well-suited as an input for advanced path-following strategies in robotics, crowd simulation or gaming applications.

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