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17
Enhancing GJK: Computing Minimum and Penetration Distances between Convex Polyhedra
 Proceedings of International Conference on Robotics and Automation
, 1997
"... The problem of tracking the distance between two convex polyhedra is finding applications in many areas of robotics, including intersection detection, collision detection, and path planning. We present new results that confirm an almostconstant time complexity for an enhanced version of Gilbert, Jo ..."
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Cited by 117 (5 self)
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The problem of tracking the distance between two convex polyhedra is finding applications in many areas of robotics, including intersection detection, collision detection, and path planning. We present new results that confirm an almostconstant time complexity for an enhanced version of Gilbert, Johnson and Keerthi's algorithm, and also describe modifications to the algorithm to compute measures of penetration distance.
Incremental algorithms for collision detection between solid models
 IEEE Transactions on Visualization and Computer Graphics
, 1995
"... solid models ..."
Collision and Proximity Queries
, 2003
"... In a geometric context, a collision or proximity query reports information about the relative configuration or placement of two objects. Some of the common examples of such queries include checking whether two objects overlap in space, or whether their boundaries intersect, or computing the minimum ..."
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Cited by 74 (15 self)
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In a geometric context, a collision or proximity query reports information about the relative configuration or placement of two objects. Some of the common examples of such queries include checking whether two objects overlap in space, or whether their boundaries intersect, or computing the minimum Euclidean separation distance between their boundaries. Hundreds of papers have been published on di#erent aspects of these queries in computational geometry and related areas such as robotics, computer graphics, virtual environments, and computeraided design. These queries arise in di#erent applications including robot motion planning, dynamic simulation, haptic rendering, virtual prototyping, interactive walkthroughs, computer gaming, and molecular modeling. For example, a largescale virtual environment, e.g., a walkthrough, creates a model of the environment with virtual objects. Such an environment is used to give the user a sense of presence in a synthetic world and it s
Penetration Depth of Two Convex Polytopes in 3D
 Nordic J. Computing
, 2000
"... with m and n facets, respectively. The penetration depth of A and B, denoted as (A; B), is the minimum distance by which A has to be translated so that A and B do not intersect. We present a randomized algorithm that computes (A; B) in O(m + m ) expected time, for any constant " > 0. I ..."
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Cited by 24 (2 self)
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with m and n facets, respectively. The penetration depth of A and B, denoted as (A; B), is the minimum distance by which A has to be translated so that A and B do not intersect. We present a randomized algorithm that computes (A; B) in O(m + m ) expected time, for any constant " > 0. It also computes a vector t such that ktk = (A; B) and int(A + t) \ B = ;. We show that if the Minkowski sum B ( A) has K facets, then the expected running time of our algorithm is O K , for any " > 0.
DEEP: Dualspace Expansion for Estimating Penetration depth between convex polytopes
 In IEEE Conference on Robotics and Automation
, 2002
"... We present an incremental algorithm to estimate the penetration depth between convex polytopes in 3D. The algorithm incrementally seeks a "locally optimal solution" by walking on the surface of the Minkowski sums. The surface of the Minkowski sums is computed implicitly by constructing a local Gauss ..."
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Cited by 22 (7 self)
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We present an incremental algorithm to estimate the penetration depth between convex polytopes in 3D. The algorithm incrementally seeks a "locally optimal solution" by walking on the surface of the Minkowski sums. The surface of the Minkowski sums is computed implicitly by constructing a local Gauss map. In practice, the algorithm works well when there is high motion coherence in the environment and is able to compute the optimal solution in most cases.
Haptic display of interaction between textured models
 Proceedings of IEEE Visualization Conference
, 2004
"... Surface texture is among the most salient haptic characteristics of objects; it can induce vibratory contact forces that lead to perception of roughness. In this paper, we present a new algorithm to display haptic texture information resulting from the interaction between two textured objects. We co ..."
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Cited by 22 (8 self)
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Surface texture is among the most salient haptic characteristics of objects; it can induce vibratory contact forces that lead to perception of roughness. In this paper, we present a new algorithm to display haptic texture information resulting from the interaction between two textured objects. We compute contact forces and torques using lowresolution geometric representations along with texture images that encode surface details. We also introduce a novel force model based on directional penetration depth and describe an efficient implementation on programmable graphics hardware that enables interactive haptic texture rendering of complex models. Our force model takes into account important factors identified by psychophysics studies and is able to haptically display interaction due to fine surface textures that previous algorithms do not capture.
Incremental Penetration Depth Estimation Between Convex Polytopes Using Dualspace Expansion
, 2004
"... We present a fast algorithm to estimate the penetration depth between convex polytopes in 3D. The algorithm incrementally seeks a "locally optimal solution" by walking on the surface of the Minkowski sums. The surface of the Minkowski sums is computed implicitly by constructing a local dual mappin ..."
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Cited by 9 (1 self)
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We present a fast algorithm to estimate the penetration depth between convex polytopes in 3D. The algorithm incrementally seeks a "locally optimal solution" by walking on the surface of the Minkowski sums. The surface of the Minkowski sums is computed implicitly by constructing a local dual mapping on the Gauss map. We also present three heuristic techniques that are used to estimate the initial features used by the walking algorithm. We have implemented the algorithm and compared its performance with earlier approaches. In our experiments, the algorithm is able to estimate the penetration depth in about a millisecond on an 1 GHz Pentium PC. Moreover, its performance is almost independent of model complexity in environments with high coherence between successive instances.
Fast Algorithms for Penetration and Contact Determination Between NonConvex Polyhedral Models
 IEEE Int. Conf. on Robotics and Automation
, 1994
"... 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 ..."
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Cited by 5 (1 self)
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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 nonconvex 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, molecularbased modeling, computational ...
Haptic rendering of interaction between textured objects
 in SIGGRAPH: Sketches and Applications
, 2004
"... Surface texture is among the most salient haptic characteristics of objects; it can induce vibratory contact forces that lead to perception of roughness. In this paper, we present a new algorithm to compute contact forces and torques between textured objects using lowresolution geometric representa ..."
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Cited by 4 (1 self)
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Surface texture is among the most salient haptic characteristics of objects; it can induce vibratory contact forces that lead to perception of roughness. In this paper, we present a new algorithm to compute contact forces and torques between textured objects using lowresolution geometric representations with texture images that encode surface details. We introduce a novel force model based on directional penetration depth and describe an efficient implementation on programmable graphics hardware that enables interactive haptic texture rendering of complex models. Our algorithm takes into account important factors identified by psychophysics studies and is able to haptically display interaction due to fine surface textures that existing algorithms do not capture.
Computing Rotation Distance between Contacting Polytopes
 In Proc. IEEE Int. Conf. Robot. Autom. (ICRA
, 1996
"... Distance computation is essential for collision prediction and/or detection in realworld robotic tasks, computer simulation and animation, and CAD/CAM. This paper addresses distance computation to deal with a rarely researched type of collision prediction/detection problem: Given two objects in cer ..."
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Cited by 3 (2 self)
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Distance computation is essential for collision prediction and/or detection in realworld robotic tasks, computer simulation and animation, and CAD/CAM. This paper addresses distance computation to deal with a rarely researched type of collision prediction/detection problem: Given two objects in certain contact, determine if and when a relative rotation constrained by contact will cause a collision (which results in a new contact state) between the two objects. We use the positive angle of rotation as the measure of rotation distance and present a method to compute, given two contacting convex polytopes G and H and a rotation axis containing contact point(s) between them, the shortest rotation distance (SRD) of G which will cause new colllision between G and H . The method is fully implemented, and the algorithm is very efficient. If each vertex of G or H is the intersection of n e=v edges, then the worstcase time complexity of the algorithm is O(n 2 e=v ).