Narrow Results

We present fast implementations of a hybrid algorithm for reporting box and cube intersections. Our algorithm initially takes a divide-and-conquer approach and switches to simpler algorithms for low numbers of boxes. We use our implementations as engines to solve problems about geometric primitives. We look at two such problems in the category of quality analysis of surface triangulations.

Collision detection optimization in an event-driven simulation of a multi-particle system is one of the crucial tasks, determining the efficiency of the simulation. We present the event-driven simulation algorithm that employs dynamic computational geometry data structures as a tool for collision detection optimization (CDO). The first successful application of the dynamic generalized Voronoi diagram method for collision detection optimization in a system of moving particles is discussed. A comprehensive comparision of four kinetic data structures in d-dimensional space, performed in a framework of an event-driven simulation of a granular-type materials system, is supported by the experimental results.

We consider problems on intervals which can be solved by dynamic programming. Specifically, we give an efficient implementation of dynamic programming on intervals. As an application, an optimal sequential partition of a graph G=(V, E) can be obtained in O(m log n) time, where n=|V| and m=|E|. We also present an O(n log n) time algorithm for finding a minimum weight dominating set of an interval graph G=(V, E), and an O(m log n) time algorithm for finding a maximum weight clique of a circular-arc graph G=(V, E), provided their intersection models of n intervals (arcs) are given.

We define a new model of complexity, called object complexity, for measuring the performance of hidden-surface removal algorithms. This model is more appropriate for predicting the performance of these algorithms on current graphics rendering systems than the standard measure of scene complexity used in computational geometry.

We also consider the problem of determining the set of visible windows in scenes consisting of n axis-parallel windows in ℝ³. We present an algorithm that runs in optimal Θ(n log n) time. The algorithm solves in the object complexity model the same problem that Bern³ addressed in the scene complexity model.