-Collision detection is of paramount importance for many applications in computer graphics and visualization. Typically, the input to a collision detection algorithm is a large number of geometric objects comprising an environment, together with a set of objects moving within the environment. In addition to determining accurately the contacts that occur between pairs of objects, one needs also to do so at real-time rates. Applications such as haptic force-feedback can require over 1000 collision queries per second.In this paper, we develop and analyze a method, based on bounding-volume hierarchies, for efficient collision detection for objects moving within highly complex environments. Our choice of bounding volume is to use a "discrete orientation polytope" (" -dop"), a convex polytope whose facets are determined by halfspaces whose outward normals come from a small fixed set of orientations. We compare a variety of methods for constructing hierarchies ("BVtrees") of bounding -dops. Further, we propose algorithms for maintaining an effective BV-tree of -dops for moving objects, as they rotate, and for performing fast collision detection using BV-trees of the moving objects and of the environment.Our algorithms have been implemented and tested. We provide experimental evidence showing that our approach yields substantially faster collision detection than previous methods.

No abstract

We discuss the design and implementation of a topology-oriented algorithm for the computation of Voronoi diagrams of points and line segments in the two-dimensional Euclidean space. The main focus of our work was on designing and engineering an algorithm that is completely reliable and fast in practice. The algorithm was implemented in ANSI C, using standard floating-point arithmetic. In addition to Sugihara and Iri's topologyoriented approach, it is based on a very careful implementation of the numerical computations required, an automatic relaxation of epsilon thresholds, and a multi-level recovery process combined with "desperate mode". The resulting code, named vroni , was tested extensively on real-world data and turned out to be reliable. CPU-time statistics document that it is always faster than other popular Voronoi codes. In our computing environment, vroni needs about 0.01n log 2 n milliseconds to compute the Voronoi diagram of n line segments, and this formula holds for a wide variety of synthetic and real-world data. In particular, its CPU-time consumption is hardly affected by the actual distribution of the input data. Vroni also features a function for computing offset curves, and it has been successfully tested within and integrated into several industrial software packages. 

No abstract

No abstract

No abstract

No abstract

A fundamental algorithmic problem in computer graphics is that of computing a succinct encoding of a triangulation of a polygonal surface model in order to be able to transmit and render it efficiently. The goal is to take a given polygonal surface model, whose facets are given by (possibly multiply-connected) polygons, triangulate its facets, and then decompose the triangulation into a small number of "tristrips," each of which has its connectivity stored implicitly in the ordering of the data points. We develop methods that are effective in solving the stripification problem, both in theory (provably good encodings) and in practice. Our methods are based on carefully constructed search trees in the dual graph, followed by algorithms to decompose dual trees into tristips. One decomposition algorithm is provably optimal (based on dynamic programming), allowing us a sound basis of comparison among our other (heuristic) algorithms. We demonstrate the speed and effectiveness of our algorithms through a battery of experiments. In comparison with the recently released STRIPE system for stripification, we find that our stripifier, FTSG, produces comparable or better quality encodings, while requiring significantly less computing time on a large variety of datasets. Further, FTSG is carefully engineered and implemented to be robust, even in the face of highly degenerate and corrupted real-world data.