Results 1  10
of
85
Efficient collision detection using bounding volume hierarchies of kdops
 IEEE Transactions on Visualization and Computer Graphics
, 1998
"... Abstract—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 ..."
Abstract

Cited by 289 (4 self)
 Add to MetaCart
(Show Context)
Abstract—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 realtime rates. Applications such as haptic forcefeedback can require over 1,000 collision queries per second. In this paper, we develop and analyze a method, based on boundingvolume hierarchies, for efficient collision detection for objects moving within highly complex environments. Our choice of bounding volume is to use a “discrete orientation polytope” (“kdop”), a convex polytope whose facets are determined by halfspaces whose outward normals come from a small fixed set of k orientations. We compare a variety of methods for constructing hierarchies (“BVtrees”) of bounding kdops. Further, we propose algorithms for maintaining an effective BVtree of kdops for moving objects, as they rotate, and for performing fast collision detection using BVtrees 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. Index Terms—Collision detection, intersection searching, bounding volume hierarchies, discrete orientation polytopes, bounding boxes, virtual reality, virtual environments. 1
Optimal search in planar subdivisions
 SIAM Journal of Computing, Voltune
, 1983
"... Abstract. A planar subdivision is any partition of the plane into (possibly unbounded) polygonal regions. The subdivision search problem is the following: given a subdivision S with n line segments and a query point P, determine which region of S contains P. We present a practical algorithm for subd ..."
Abstract

Cited by 283 (3 self)
 Add to MetaCart
(Show Context)
Abstract. A planar subdivision is any partition of the plane into (possibly unbounded) polygonal regions. The subdivision search problem is the following: given a subdivision S with n line segments and a query point P, determine which region of S contains P. We present a practical algorithm for subdivision search that achieves the same (optimal) worst case complexity bounds as the significantly more complex algorithm of Lipton and Tarjan, namely O (log n) search time with O (n) storage. Our subdivision search structure can be constructed in linear time from the subdivision representation used in many applications. Key words, computational geometry, analysis of algorithms, point location, planar graphs, hierarchical search
Approximating Polyhedra with Spheres for TimeCritical Collision Detection
 ACM Transactions on Graphics
, 1996
"... This paper presents a method for approximating polyhedral objects to support a timecritical collisiondetection algorithm. The approximations are hierarchies of spheres, and they allow the timecritical algorithm to progressively refine the accuracy of its detection, stopping as needed to maintain ..."
Abstract

Cited by 212 (1 self)
 Add to MetaCart
(Show Context)
This paper presents a method for approximating polyhedral objects to support a timecritical collisiondetection algorithm. The approximations are hierarchies of spheres, and they allow the timecritical algorithm to progressively refine the accuracy of its detection, stopping as needed to maintain the realtime performance essential for interactive applications. The key to this approach is a preprocess that automatically builds tightly fitting hierarchies for rigid and articulated objects. The preprocess uses medialaxis surfaces, which are skeletal representations of objects. These skeletons guide an optimization technique that gives the hierarchies accuracy properties appropriate for collision detection. In a sample application, hierarchies built this way allow the timecritical collisiondetection algorithm to have acceptable accuracy, improving significantly on that possible with hierarchies built by previous techniques. The performance of the timecritical algorithm in this appli...
Collision Detection for Interactive Graphics Applications
 IEEE Transactions on Visualization and Computer Graphics
, 1995
"... ..."
(Show Context)
Fast proximity queries with swept sphere volumes
, 1999
"... 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 ..."
Abstract

Cited by 128 (20 self)
 Add to MetaCart
(Show Context)
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 t 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 earlier algorithms based on bounding volume hierarchies for separation distance and approximate distance computation, our algorithms have
Determining the Separation of Preprocessed Polyhedra  A Unified Approach
, 1990
"... 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 prim ..."
Abstract

Cited by 118 (5 self)
 Add to MetaCart
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).
Optimal OutputSensitive Convex Hull Algorithms in Two and Three Dimensions
, 1996
"... We present simple outputsensitive algorithms that construct the convex hull of a set of n points in two or three dimensions in worstcase optimal O(n log h) time and O(n) space, where h denotes the number of vertices of the convex hull. ..."
Abstract

Cited by 78 (7 self)
 Add to MetaCart
(Show Context)
We present simple outputsensitive algorithms that construct the convex hull of a set of n points in two or three dimensions in worstcase optimal O(n log h) time and O(n) space, where h denotes the number of vertices of the convex hull.
OutputSensitive Results on Convex Hulls, Extreme Points, and Related Problems
, 1996
"... . We use known data structures for rayshooting and linearprogramming queries to derive new outputsensitive results on convex hulls, extreme points, and related problems. We show that the f face convex hull of an npoint set P in a fixed dimension d # 2 can be constructed in O(n log f + (nf) ..."
Abstract

Cited by 74 (12 self)
 Add to MetaCart
(Show Context)
. We use known data structures for rayshooting and linearprogramming queries to derive new outputsensitive results on convex hulls, extreme points, and related problems. We show that the f face convex hull of an npoint set P in a fixed dimension d # 2 can be constructed in O(n log f + (nf) 11/(#d/2#+1) log O(1) n) time; this is optimal if f = O(n 1/#d/2# / log K n) for some sufficiently large constant K . We also show that the h extreme points of P can be computed in O(n log O(1) h + (nh) 11/(#d/2#+1) log O(1) n) time. These results are then applied to produce an algorithm that computes the vertices of all the convex layers of P in O(n 2# ) time for any constant #<2/(#d/2# 2 + 1). Finally, we obtain improved time bounds for other problems including levels in arrangements and linear programming with few violated constraints. In all of our algorithms the input is assumed to be in general position. 1. Introduction Let P be a set of n points in ddimen...
Fast Distance Queries with Rectangular Swept Sphere Volumes
 Proc. of IEEE Int. Conference on Robotics and Automation
, 2000
"... : 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 hier ..."
Abstract

Cited by 66 (15 self)
 Add to MetaCart
(Show Context)
: 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
Computing the IntersectionDepth of Polyhedra
 Algorithmica
, 1993
"... Given two intersecting polyhedra P , Q and a direction d, find the smallest translation of Q along d that renders the interiors of P and Q disjoint. The same problem can also be posed without specifying the direction, in which case the minimum translation over all directions is sought. These are fun ..."
Abstract

Cited by 58 (2 self)
 Add to MetaCart
(Show Context)
Given two intersecting polyhedra P , Q and a direction d, find the smallest translation of Q along d that renders the interiors of P and Q disjoint. The same problem can also be posed without specifying the direction, in which case the minimum translation over all directions is sought. These are fundamental problems that arise in robotics and computer vision. We develop techniques for implicitly building and searching convolutions and apply them to derive efficient algorithms for these problems. 1 Introduction The computation of spatial relationships among geometric objects is a fundamental problem in such areas as robotics, computeraided design, VLSI layout, and computer graphics. In a dynamic environment where objects are mobile, intersection or proximity among objects has obvious applications. Consider, for instance, the problem of collision detection in robot motion planning. The Euclidean distance is a commonly used measure in these areas. Numerous efficient algorithms are known...