Collision detection framework using model simplification

(see, for example, Gottschalk, et al. OBBTree: A Hierarchical Structure for Rapid Interference Detection. SIGGRAPH 96, 171-179), there remain many controversial design issues, such as top-down versus bottom-up, and the choice of bounding volume (Klosowski et al. Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPs, State University of New York, Stony Brook, Dept. Applied Math. and Statistics, July 1997). This project proposes a new framework to resolve some of these design issues, using output from model simplification. It differs from the previous work of, for example, Klosowski et al. in looking beyond constructing different types of (possibly computationally expensive) bounding volumes to better understand the importance of shapes of objects in collision detection. Our proposed framework uses output from simplification in the construction of bounding volume hierarchies. The basic idea is to use clues from simplified models to partition the given polygonal model into components with tight bounding volumes. A simplified model S contains elements such as points, edges, and triangles derived from the original model. We obtain a partition of these elements based on an equivalence relation, where element x and y are related if and only if x is connected to y by triangles in S. From parts of the partition , we then obtain components where each component contains those triangles of the original model that are simplified to elements in a same part. This process can be recur-sively applied, each time with a simplified model of higher level of detail, to obtain sub-components of components. All these components and sub-components can be arranged into a few topmost levels of the bounding volume hierarchy, and the remaining levels of the hierarchy can be computed using some other standard bounding volume hierarchy algorithms. The above process exploits the fact that the set of triangles, edges, and points in a simplified model shows a sketch of the object, and its vertices are also more uniformly distributed compared to the original model. As such, computation to derive a bounding volume hierarchy with simplified model can be (1) effective due to its "shape" information captured by its essential elements, (2) unbiased for uniformly distributed ver-tices, and (3) faster due to the smaller number of vertices in the simplified model. The overall construction has the unique flavor of bottom-up in that triangles are distributed into various components, followed by top-down in that triangles are partitioned as in, for example, the RAPID …