The need to perform fast and accurate proximity queries arises frequently in physically-based modeling, simulation, animation, real-time interaction within a virtual environment, and game dynamics. The set of proximity queries include intersection detection, tolerance verification, exact and approximate minimum distance computation, and (disjoint) contact determination. Specialized data structures and algorithms have often been designed to perform each type of query separately. We present a unified approach to perform any of these queries seamlessly for general, rigid polyhedral objects with boundary representations which are orientable 2-manifolds. The proposed method involves a hierarchical data structure built upon a surface decomposition of the models. Furthermore, the incremental query algorithm takes advantage of coherence between successive frames. It has been applied to complex benchmarks and compares very favorably with earlier algorithms and systems.

Many applications in Computer Graphics require fast and robust 3D collision detection algorithms. These algorithms can be grouped into four approaches: space-time volume intersection, swept volume interference, multiple interference detection and trajectory parameterization. While some approaches are linked to a particular object representation scheme (e.g., space-time volume intersection is particularly suited to a CSG representation), others do not. The multiple interference detection approach has been the most widely used under a variety of sampling strategies, reducing the collision detection problem to multiple calls to static interference tests. In most cases, these tests boil down to detecting intersections between simple geometric entities, such as spheres, boxes aligned with the coordinate axes, or polygons and segments. The computational cost of a collision detection algorithm depends not only on the complexity of the basic interference test used, but also on the ...

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We propose a technique for performing view-dependent geometry and topology simplifications for level-of-detail-based renderings of large models. The algorithm proceeds by preprocessing the input dataset into a binary tree, the view-dependence tree of general vertex-pair collapses. A subset of the Delaunay edges is used to limit the number of vertex pairs considered for topology simplification. Dependencies to avoid mesh foldovers in manifold regions of the input object are stored in the view-dependence tree in an implicit fashion. We have observed that this not only reduces the space requirements by a factor of two, it also highly localizes the memory accesses at run time. The view-dependence tree is used at run time to generate the triangles for display. We also propose a cubic-spline-based distance metric that can be used to unify the geometry and topology simplifications by considering the vertex positions and normals in an integrated manner.

This paper describes an algorithm for morphing polyhedral surfaces based on their decompositions into patches.

Mesh segmentation has become an important component in many applications in computer graphics. In the last several years, many algorithms have been proposed in this growing area, offering a diversity of methods and various evaluation criteria. This paper provides a comparative study of some of the latest algorithms and results, along several axes. We evaluate only algorithms whose code is available to us, and thus it is not a comprehensive study. Yet, it sheds some light on the vital properties of the methods and on the challenges that future algorithms should face.

We present a novel and fast algorithm to compute penetration depth (PD) between two polyhedral models for physically-based animation. Given two overlapping polyhedra, it computes the minimal translation distance to separate them using a combination of object-space and image-space techniques. The algorithm computes pairwise Minkowski sums of decomposed convex pieces and performs a closest point query using rasterization hardware. It uses bounding volume hierarchies, object-space and image-space culling algorithms to further accelerate the computation and refines the estimated PD in a hierarchical manner. We demonstrate its application to contact response computation and a time-stepping method for dynamic simulation.

We introduce a novel "sensation preserving" simplification algorithm for faster collision queries between two polyhedral objects in haptic rendering. Given a polyhedral model, we construct a multiresolution hierarchy using "filtered edge collapse", subject to constraints imposed by collision detection. The resulting hierarchy is then used to compute fast contact response for haptic display. The computation model is inspired by human tactual perception of contact information. We have successfully applied and demonstrated the algorithm on a time-critical collision query framework for haptically displaying complex object-object interaction. Compared to existing exact contact query algorithms, we observe noticeable performance improvement in update rates with little degradation in the haptic perception of contacts.

We present a formulation of boundary mesh segmentation as an optimization problem. Previous segmentation solutions are classified according to the different segmentation goals, the optimization criteria and the various algorithmic techniques used. We identify two primarily distinct types of mesh segmentation, namely parts segmentation and patch segmentation. We also define generic algorithms for the major techniques used for segmentation.

This paper addresses the problem of decomposing a polyhedral surface into “meaningful ” patches. We describe two decomposition algorithms – flooding convex decomposition and watershed decomposition, and show experimental results. Moreover, we discuss three applications which can highly benefit from surface decomposition. These applications include content-based retrieval of threedimensional models, metamorphosis of three-dimensional models and simplification.