A simple and efficient algorithm for finding the closest points between two convex polyhedra is described here. Data from numerous experiments tested on a broad set of convex polyhedra on ! 3 show that the running time is roughly constant for finding closest points when nearest points are approximately known and is linear in total number of vertices if no special initialization is done. This algorithm can be used for collision detection, computation of the distance between two polyhedra in three-dimensional space, and other robotics problems. It forms the heart of the motion planning algorithm of [1]. 1 Introduction In this paper we present a simple method for finding and tracking the closest points on a pair of convex polyhedra. The method is generally applicable, but is especially well suited to repetitive distance calculation as the objects move in a sequence of small, discrete steps. The method works by finding and maintaining the pair of closest features (vertex, edge, or face)...

We present efficient algorithms for collision detection and contact determination between geometric models, described by linear or curved boundaries, undergoing rigid motion. The heart of our collision detection algorithm is a simple and fast incremental method to compute the distance between two convex polyhedra. It utilizes convexity to establish some local applicability criteria for verifying the closest features. A preprocessing procedure is used to subdivide each feature's neighboring features to a constant size and thus guarantee expected constant running time for each test. The expected constant time performance is an attribute from exploiting the geometric coherence and locality. Let n be the total number of features, the expected run time is between O( p n) and O(n) ...

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 ...

solid models

Please note: This document is ©2001 by David Baraff. This chapter may be freely duplicated and distributed so long as no consideration is received in return, and this copyright notice remains intact.

Abstract not found

Abstract not found

This paper presents fast algorithms for penetration and contact determination between general polyhedral models in dynamic environments. The main contribution is an extension of an earlier expected constant time algorithm between convex polytopes to detect penetrations and contacts. For each pair of non-convex polyhedral models, the algorithm uses the convex hull of each object to determine which regions of the objects are colliding. After identifying these regions, it uses a new dynamic technique, sweep and prune, to overcome the bottleneck of O(n 2 ) pairwise feature checks of these regions. The resulting algorithm has been implemented and in practice its performance in dynamic environments is O(n +m), where m corresponds to the number of feature pairs close to each other. 1 Introduction The problem of determining whether objects are penetrating or separated is of great importance in many areas. It has been extensively studied in robotics, molecular-based modeling, computational ...

: We describe models and algorithms designed to produce efficient and physically consistent dynamic simulations. These models and algorithms have been implemented within the Robot\Phi system[55] which can potentially be configured for a large variety of intervention-style tasks such as dextrous manipulations with a robot hand; manipulation of non-rigid objects; tele-programming of the motions of an all-terrain vehicle; and some robot assisted surgery tasks (e.g. positioning of an artificial ligament in knee surgery). The approach uses a novel physically based modeling technique to produce dynamic simulations which are both efficient and consistent according to the laws of the Physics. The main advances over previous works in Robotics and Computer Graphics fields are twofold: the development of a unique framework for simultaneously processing motions, deformations, and physical interactions; and the incorporation of appropriate models and algorithms for obtaining efficient processing ti...