Incremental algorithms for collision detection between solid models

TL;DR: An incremental algorithm for collision detection between general polygonal models in dynamic environments is presented, which combines a hierarchical representation with incremental computation to rapidly detect collisions.

Abstract: Fast and accurate collision detection between general polygonal models is a fundamental problem in physically based and geometric modeling, robotics, animation, and computer-simulated environments. Most earlier collision detection algorithms are either restricted to a class of models (such as convex polytopes) or are not fast enough for practical applications. We present an incremental algorithm for collision detection between general polygonal models in dynamic environments. The algorithm combines a hierarchical representation with incremental computation to rapidly detect collisions. It makes use of coherence between successive instances to efficiently determine the number of object features interacting. For each pair of objects, it tracks the closest features between them on their respective convex hulls. It detects the objects' penetration using pseudo internal Voronoi cells and constructs the penetration region, thus identifying the regions of contact on the 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 precomputed hierarchy and check for possible collisions between the features. We highlight its performance on different applications. Index Terms—Collision detection, contacts, interference, dynamic simulation, physically based modeling, convex hulls, hierarchical representation. —————————— ✦ —————————— 1I NTRODUCTION realistic visual simulation system, which couples geometric modeling and physical prototyping, can provide a useful toolset for applications in robotics, CAD/CAM design, molecular modeling, manufacturing design simulations, etc. Such systems create electronic rep- resentations of mechanical parts, tools, and machines, which need to be tested for interconnectivity, functionality, and reliability. The goal of these virtual and electronic simula- tion systems is to save processing time and manufacturing costs by avoiding the production of actual physical proto- types (1), (2). This is similar to the goal of CAD tools for VLSI. It requires a complete test environment for simulat- ing hundreds of parts interacting.