Incremental collision detection for polygonal models

1 Introduction Fast and accurate collision detection between general polygonal models is a fundamental problem for computational geometry, robotics, and computer-simulated environments. Most earlier algorithms are either restricted to a class of models, such as convex polytopes, or are not fast enough for practical applications. We outline and demonstrate an incremental algorithm for collision detection between general polygonal models in dynamic environments. The algorithm combines hierarchical representation with incremental frame to frame computation to rapidly detect collisions. It makes use of coherence between successive instances to efficiently determine the number of objects interacting. For each pair of objects , it localizes the interference regions on their convex hulls. The features associated with these regions are represented in a precomputed hierarchy. The algorithm uses a coherence based approach to quickly traverse the pre-computed hierarchy to check for collisions between the features. More details of the algorithm are given in [5]. The algorithm builds on our previous work for pairs of convex polytopes [6] and multiple moving convex poly-topes [4]. For each non-convex polyhedral model, we compute its convex hull and the axis-aligned bounding box enclosing the convex hull. A four level hierarchical and incremental algorithm is used to detect collisions [5]: 1. We determine which pairs of bounding boxes are colliding, using the sweep and prune algorithm described in [3, 4]. 2. For each intersecting bounding box pair, we determine if the objects' convex hulls are colliding by walking across the external and pseudo-internal Voronoi regions of the polytopes. When one poly-tope's feature is within another polytopes pseudo-internal Voronoi regions, interpenetration is detected. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copyin is by permission of the Association of Computing ? Machinery. o copy otherwise, or to republish, requires a fee and/or specific ermission. For each colliding hull pair, we determine the areas of intersection on the convex hulls. There are several algorithms in the literature for intersection computation [2, 7]. We extend these algorithms using a coherence based scheme. For each intersection region, we examine the vertex, edge, and face features associated with it to determine precise contact points. These features are represented as a bounding box hierarchy, and we apply a hierarchical …