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.

Given a planar spline curve and local tolerances, a matched pair of polygons is computed that encloses the curve and whose width (distance between corresponding break points) is below the tolerances. This is the simplest instance of a subdividable linear efficient variety enclosure, short sleve.

This paper surveys a new, computationally efficient technique for linearizing curved spline geometry, bounding such geometry from one side and constructing curved spline geometry that stays to one side of a barrier or inside a given channel. Combined with a narrow error bound, these reapproximations tightly couple linear and nonlinear representations and allow them to be substituted when reasoning about the other. For example, a subdividable linear efficient variety enclosure (sleve, pronounced like Steve) of a composite spline surface is a pair of matched triangulations that sandwich a surface and may be used for interference checks. The average of the sleve components, the mid-structure, is a good max-norm linearization and, similar to a control polytope, has a welldefined, associated curved geometry representation. Finally, the ability to fit paths through given channels or keep surfaces near but outside forbidden regions, allows extending many techniques of linear computational geometry to the curved, nonlinear realm.

An enclosure of a composite spline surface is a pair of simpler approximations that sandwich the surface. In particular, we are interested in efficiently constructing two triangulations, so that matched triangle pairs enclose a piece of the curved surface. The width of the enclosure, i,e. the distance between inner and outer hull, can be easily measured, because it is taken on at a vertex. Enclosures are therefore approximate implicitizations with known error; such bounding constructs are useful to support, say, collision detection, re-approximation for format conversion, meshing with tolerance, or silhouette detection. The surface enclosure developed in this paper is effective, because it is optimized and refinable: an optimization specific to a given geometry representation is done off-line and tabulated once and for all. Moreover, given an enclosure of a smooth surface, the number and location of refinement steps can be announced that guarantee that the distance to the object falls below a given tolerance, because the width generically shrinks to 1/4 under subdivision at midpoints. CR Categories: I.3.5 [surface representation, splines]: I.3.6--- graphics data structures Keywords: curved spline surface enclosure, 2-sided bounds, triangulated surface enclosure, approximate implicitization 1 Motivation Measuring closeness to the silhouette or determining the distance between objects are fundamental issues in computer graphics. While efficient algorithms exist for piecewise linear surfaces with not too many pieces, objects in B-spline, Bezier or generalized subdivision representation pose numerical and implementation challenges due to the curved geometry. Naive linearization of a curved surface, say triangulation by sampling, incurs an error that is difficult to quantif...

Collision detection is fundamental to many kinds of simulation. Any simulation that needs to model interactions between solid objects needs some form of collision detection. However, despite this need, a general-purpose collision detection framework has not been developed for the High Level Architecture (HLA). This research paper proposes a framework which facilitates this need. The framework differs from previous solutions by conforming to the principles of low coupling and high cohesion, which are cornerstones of the HLA ideology, which promotes reuse of simulation components. To this end, the framework does not bind itself to the existing Object Model of the simulation it supports. The HLA Data Distribution Management (DDM) services are used to increase the network and processing efficiency of the solution. By incorporation of advanced spatial partitioning and collision detection algorithms, the solution provides an accurate, fast collision detection service to HLA federates.