. We present new algorithms for creating and rendering visual hulls in real-time. Unlike voxel or sampled approaches, we compute an exact polyhedral representation for the visual hull directly from the silhouettes. This representation has a number of advantages: 1) it is a view-independent representation, 2) it is well-suited to rendering with graphics hardware, and 3) it can be computed very quickly. We render these visual hulls with a view-dependent texturing strategy, which takes into account visibility information that is computed during the creation of the visual hull. We demonstrate these algorithms in a system that asynchronously renders dynamically created visual hulls in real-time. Our system outperforms similar systems of comparable computational power. 1

We show how (now familiar) hierarchical representations of (convex) polyhedra can be used to answer various separation queries efficiently (in a number of cases, optimally). Our emphasis is i) the uniform treatment of polyhedra separation problems, ii) the use of hierarchical representations of primitive objects to provide implicit representations of composite or transformed objects, and iii) applications to natural problems in graphics and robotics. Among the specific results is an O(log jP j 1 log jQj) algorithm for determining the sepa- ration of polyhedra P and Q (which have been individually preprocessed in at most linear time).

: We present novel algorithms for fast proximity queries using swept sphere volumes. The set of proximity queries includes collision detection and both exact and approximate separation distance computation. We introduce a new family of bounding volumes that correspond to a core primitive shape grown outward by some offset. The set of core primitive shapes includes a point, line, and rectangle. This family of bounding volumes provides varying tightness of fit to the underlying geometry. Furthermore, we describe efficient and accurate algorithms to perform different queries using these bounding volumes. We present a novel analysis of proximity queries that highlights the relationship between collision detection and distance computation. We also present traversal techniques for accelerating distance queries. These algorithms have been used to perform proximity queries for applications including virtual prototyping, dynamic simulation, and motion planning on complex models. As compared to ...

solid models

: Many applications in computer graphics and virtual environments need to render datasets with large numbers of primitives and high depth complexity at interactive rates. However, standard techniques like view frustum culling and a hardware z-buffer are unable to display datasets composed of hundred of thousands of polygons at interactive frame rates on current high-end graphics systems. We add a "conservative" visibility culling stage to the rendering pipeline, attempting to identify and avoid processing of occluded polygons. Given a moving viewpoint, the algorithm dynamically chooses a set of occluders. Each occluder is used to compute a shadow frustum, and all primitives contained within this frustum are culled. The algorithm hierarchicallytraverses the model, culling out parts not visible from the current viewpoint using efficient, robust, and in some cases specialized interference detection algorithms. The algorithm's performance varies with the location of the viewpoint and the ...

This paper proposes new methods to answer approximate nearest neighbor queries on a set of n points in d-dimensional Euclidean space. For any fixed constant d, a data structure with O(" (1\Gammad)=2 n log n) preprocessing time and O(" (1\Gammad)=2 log n) query time achieves approximation factor 1 + " for any given 0 ! " ! 1; a variant reduces the "-dependence by a factor of " \Gamma1=2 . For any arbitrary d, a data structure with O(d 2 n log n) preprocessing time and O(d 2 log n) query time achieves approximation factor O(d 3=2 ). Applications to various proximity problems are discussed. 1 Introduction Let P be a set of n point sites in d-dimensional space IR d . In the well-known post office problem, we want to preprocess P into a data structure so that a site closest to a given query point q (called the nearest neighbor of q) can be found efficiently. Distances are measured under the Euclidean metric. The post office problem has many applications within computational...

Genus-reducing simplifications are important in constructing multiresolution hierarchies for level-of-detail-based rendering, especially for datasets that have several relatively small holes, tunnels, and cavities. We present a genus-reducing simplification approach that is complementary to the existing work on genus-preserving simplifications. We propose a simplification framework in which genus-reducing and genus-preserving simplifications alternate to yield much better multiresolution hierarchies than would have been possible by using either one of them. In our approach we first identify the holes and the concavities by extending the concept of #- hulls to polygonal meshes under the L1 distance metric and then generate valid triangulations to fill them. CR Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/Image Generation --- Display algorithms; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling --- Curve, surface, solid, and object represent...

Improving on a recent breakthrough of Sharir, we find two minimum-radius circular disks covering a planar point set, in randomized expected time O(n log 2 n). 1 Introduction The k-center problem for a point set S is to find k points (called centers, usually not required to be a subset of S) such that the maximum distance from any point in S to the nearest center is minimized. A case of particular interest is the planar two-center problem [4], which can be viewed less abstractly as one of covering a set of points in the plane by two congruent circular disks, in such a way as to minimize the radius r # of the disks. For a long time the best algorithms for this problem had time bounds of the form O(n 2 log c n) [1, 5, 12, 11]. In a recent breakthrough, Sharir [16] greatly improved all of these algorithms, giving a two-center algorithm with running time O(n log c n). The basic idea is to search for different types of partition depending on the relative positions of the two disk...

: We present new distance computation algorithms using hierarchies of rectangular swept spheres. Each bounding volume of the tree is described as the Minkowski sum of a rectangle and a sphere, and fits tightly to the underlying geometry. We present accurate and efficient algorithms to build the hierarchies and perform distance queries between the bounding volumes. We also present traversal techniques for accelerating distance queries using coherence and priority directed search. These algorithms have been used to perform proximity queries for applications including virtual prototyping, dynamic simulation, and motion planning on complex models. As compared to earlier algorithms based on bounding volume hierarchies for separation distance and approximate distance computation, our algorithms have achieved significant speedups on many benchmarks. 1

We present simple output-sensitive algorithms that construct the convex hull of a set of n points in two or three dimensions in worst-case optimal O(n log h) time and O(n) space, where h denotes the number of vertices of the convex hull.