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A Fast Algorithm for Incremental Distance Calculation
 In IEEE International Conference on Robotics and Automation
, 1991
"... 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 approxim ..."
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Cited by 166 (4 self)
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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 threedimensional 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)...
Efficient Collision Detection for Animation and Robotics
, 1993
"... 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 ..."
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Cited by 115 (19 self)
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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) ...
3D Collision Detection: A Survey
 Computers and Graphics
, 2000
"... Many applications in Computer Graphics require fast and robust 3D collision detection algorithms. These algorithms can be grouped into four approaches: spacetime volume intersection, swept volume interference, multiple interference detection and trajectory parameterization. While some approaches ar ..."
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Cited by 94 (3 self)
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Many applications in Computer Graphics require fast and robust 3D collision detection algorithms. These algorithms can be grouped into four approaches: spacetime volume intersection, swept volume interference, multiple interference detection and trajectory parameterization. While some approaches are linked to a particular object representation scheme (e.g., spacetime 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 ...
Incremental algorithms for collision detection between solid models
 IEEE Transactions on Visualization and Computer Graphics
, 1995
"... solid models ..."
An introduction to physically based modeling: Rigid body simulation i  unconstrained rigid body dynamics
 In An Introduction to Physically Based Modelling, SIGGRAPH '97 Course Notes
, 1997
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Rigid body simulation
 SIGGRAPH 95 Course Note 34. ACM SIGGRAPH
, 1992
"... 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. ..."
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Cited by 19 (0 self)
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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.
Collision Detection Algorithms for Motion Planning
 LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES, 229
, 1998
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Fast algorithms for penetration and contact determination between nonconvex polyhedral models
 Robotics and Automation, IEEE International Conference
, 1995
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1 An Incremental Distance Computation Algorithm
"... In this chapter we present a simple and efficient method to compute the distance between two convex polyhedra by finding and tracking the closest points. The method is generally applicable, but is especially well suited to repetitive distance calculation as the objects move in a sequence of small, d ..."
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In this chapter we present a simple and efficient method to compute the distance between two convex polyhedra by finding and tracking the closest points. 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 due to its incremental nature. The method works by finding and maintaining a pair of closest features (vertex, edge, or face) on the two polyhedra as the they move. We take advantage of the fact that the closest features change only infrequently as the objects move along finely discretized paths. By preprocessing the polyhedra, we can verify that the closest features have not changed or performed an update to a neighboring feature in expected constant time. Our experiments show that, once initialized, the expected running time of our incremental algorithm is constant independent of the complexity of the polyhedra, provided the motion is not abruptly large. Our method is very straightforward in its conception. We start with a candidate pair of features, one from each polyhedron, and check whether the closest points lie on these features. Since the objects are convex, this is a local test involving only the neighboring features (boundary and coboundary as defined in Sec.??) of the candidate features. If the features fail the test, we step to a neighboring feature of one or both candidates, and try again. With some simple preprocessing, we can guarantee that every feature has a constant number of neighboring features. This is how we can verify a closest feature pair in expected constant time. When a pair of features fails the test, the new pair we choose is guaranteed to be closer than the old one. Usually when the objects move and one of the closest features changes, we can find it after a single iteration. Even if the closest features are changing rapidly, say once per step along the path, our algorithm will take only slightly longer. It is also clear that in any situation the algorithm must terminate in a number of steps at most equal to the number of feature pairs. This algorithm is a key part of our general planning algorithm, described in Chap.?? That algorithm creates a onedimensional roadmap of the free space of a robot by tracing out curves of maximal clearance from obstacles. We use the algorithm in this chapter to compute distances and closest points.