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29
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 ..."
Abstract

Cited by 108 (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) ...
Accurate and fast proximity queries between polyhedra using convex surface decomposition
, 2001
"... The need to perform fast and accurate proximity queries arises frequently in physicallybased modeling, simulation, animation, realtime interaction within a virtual environment, and game dynamics. The set of proximity queries include intersection detection, tolerance verification, exact and approxi ..."
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Cited by 97 (14 self)
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The need to perform fast and accurate proximity queries arises frequently in physicallybased modeling, simulation, animation, realtime interaction within a virtual environment, and game dynamics. The set of proximity queries include intersection detection, tolerance verification, exact and approximate minimum distance computation, and (disjoint) contact determination. Specialized data structures and algorithms have often been designed to perform each type of query separately. We present a unified approach to perform any of these queries seamlessly for general, rigid polyhedral objects with boundary representations which are orientable 2manifolds. The proposed method involves a hierarchical data structure built upon a surface decomposition of the models. Furthermore, the incremental query algorithm takes advantage of coherence between successive frames. It has been applied to complex benchmarks and compares very favorably with earlier algorithms and systems. 1.
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 84 (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 ..."
Strategies for Polyhedral Surface Decomposition: An Experimental Study
, 1995
"... This paper addresses the problem of decomposing a complex polyhedral surface into a small number of "convex" patches (ie, boundary parts of convex polyhedra). The corresponding optimization problem is shown to be NPcomplete and an experimental search for good heuristics is undertaken. 1 Introductio ..."
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Cited by 50 (5 self)
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This paper addresses the problem of decomposing a complex polyhedral surface into a small number of "convex" patches (ie, boundary parts of convex polyhedra). The corresponding optimization problem is shown to be NPcomplete and an experimental search for good heuristics is undertaken. 1 Introduction Convex shapes are easiest to represent, manipulate, and render. Even though they form the building blocks of bottomup solid modelers, it is more often the case that the convex structure of a geometric shape is lost in its representation. We are then presented, not with the solidmodeling problem of putting together primitive convex objects, but with the reverse problem of extracting convexity out of a complex shape. The classical example is that of cutting up a 3polyhedron into convex pieces. This is often a useful, sometimes a required, preprocessing step in graphics, manufacturing, and mesh generation. The problem has been exhaustively researched in the last few years [2][18]. Despi...
WellSpaced Points for Numerical Methods
, 1997
"... mesh generation, mesh coarsening, multigrid Abstract A numerical method for the solution of a partial differential equation (PDE) requires the following steps: (1) discretizing the domain (mesh generation); (2) using an approximation method and the mesh to transform the problem into a linear system; ..."
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Cited by 44 (2 self)
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mesh generation, mesh coarsening, multigrid Abstract A numerical method for the solution of a partial differential equation (PDE) requires the following steps: (1) discretizing the domain (mesh generation); (2) using an approximation method and the mesh to transform the problem into a linear system; (3) solving the linear system. The approximation error and convergence of the numerical method depend on the geometric quality of the mesh, which in turn depends on the size and shape of its elements. For example, the shape quality of a triangular mesh is measured by its element's aspect ratio. In this work, we shift the focus to the geometric properties of the nodes, rather than the elements, of well shaped meshes. We introduce the concept of wellspaced points and their spacing functions, and show that these enable the development of simple and efficient algorithms for the different stages of the numerical solution of PDEs. We first apply wellspaced point sets and their accompanying technology to mesh coarsening, a crucial step in the multigrid solution of a PDE. A good aspectratio coarsening sequence of an unstructured mesh M0 is a sequence of good aspectratio meshes M1; : : : ; Mk such that Mi is an approximation of Mi\Gamma 1 containing fewer nodes and elements. We present a new approach to coarsening that guarantees the sequence is also of optimal size and width up to a constant factor the first coarsening method that provides these guarantees. We also present experimental results, based on an implementation of our approach, that substantiate the theoretical claims.
Control Volume Meshes using Sphere Packing: Generation, Refinement and Coarsening
 In Fifth International Meshing Roundtable
, 1996
"... . In this paper we present a spherepacking technique for Delaunaybased mesh generation, refinement and coarsening. We have previously established [10] that a bounded radius of ratio of circumscribed sphere to smallest tetrahedra edge is sufficient to get optimal rates of convergence for approximat ..."
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Cited by 41 (8 self)
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. In this paper we present a spherepacking technique for Delaunaybased mesh generation, refinement and coarsening. We have previously established [10] that a bounded radius of ratio of circumscribed sphere to smallest tetrahedra edge is sufficient to get optimal rates of convergence for approximate solutions of Poisson's equation constructed using control volume (CVM) techniques. This translates to Delaunay meshes whose dual, the Voronoi cells diagram, is wellshaped. These meshes are easier to generate in 3D than finite element meshes, as they allow for an element called a sliver. We first support our previous results by providing experimental evidence of the robustness of the CVM over a mesh with slivers. We then outline a simple and efficient sphere packing technique to generate a 3D boundary conforming Delaunaybased mesh. We also apply our spherepacking technique to the problem of automatic mesh coarsening. As an added benefit, we obtain a simple 2D mesh coarsening algorithm t...
Polyhedral surface decomposition with applications
 Computers and Graphics
"... This paper addresses the problem of decomposing a polyhedral surface into “meaningful ” patches. We describe two decomposition algorithms – flooding convex decomposition and watershed decomposition, and show experimental results. Moreover, we discuss three applications which can highly benefit from ..."
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Cited by 36 (5 self)
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This paper addresses the problem of decomposing a polyhedral surface into “meaningful ” patches. We describe two decomposition algorithms – flooding convex decomposition and watershed decomposition, and show experimental results. Moreover, we discuss three applications which can highly benefit from surface decomposition. These applications include contentbased retrieval of threedimensional models, metamorphosis of threedimensional models and simplification.
Approximate convex decomposition of polyhedra
 In Proc. of ACM Symposium on Solid and Physical Modeling
, 2005
"... Decomposition is a technique commonly used to partition complex models into simpler components. While decomposition into convex components results in pieces that are easy to process, such decompositions can be costly to construct and can result in representations with an unmanageable number of compo ..."
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Cited by 29 (2 self)
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Decomposition is a technique commonly used to partition complex models into simpler components. While decomposition into convex components results in pieces that are easy to process, such decompositions can be costly to construct and can result in representations with an unmanageable number of components. In this paper, we explore an alternative partitioning strategy that decomposes a given model into “approximately convex ” pieces that may provide similar benefits as convex components, while the resulting decomposition is both significantly smaller (typically by orders of magnitude) and can be computed more efficiently. Indeed, for many applications, an approximate convex decomposition (ACD) can more accurately represent the important structural features of the model by providing a mechanism for ignoring less significant features, such as surface texture. We describe a technique for computing ACDs of threedimensional polyhedral solids and surfaces of arbitrary genus. We provide results illustrating that our approach results in high quality decompositions with very few components and applications showing that comparable or better results can be obtained using ACD decompositions in place of exact convex decompositions (ECD) that are several orders of magnitude larger. 1 ECD Figure 1: The approximate convex decompositions (ACD) of the Armadillo and the David models consist of a small number of nearly convex components that characterize the important features of the models better than the exact convex decompositions (ECD) that have orders of magnitude more components. The Armadillo (500K edges, 12.1MB) has a solid ACD with 98 components (14.2MB) that was computed in 232 seconds while the solid “ECD ” has more than 726,240 components (20+ GB) and could not be completed because disk space was exhausted after nearly 4 hours of computation. The David (750K edges, 18MB) has a surface ACD with 66 components (18.1MB) while the surface ECD has 85,132 components (20.1MB). 1
Six DegreeofFreedom Haptic Display of Polygonal Models
 in Proc. IEEE Visualization
, 2000
"... : We present an algorithm for haptic display of moderately complex polygonal models with a six degree of freedom (DOF) force feedback device. We make use of incremental algorithms for contact determination between convex primitives. The resulting contact information is used for calculating the rest ..."
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Cited by 25 (0 self)
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: We present an algorithm for haptic display of moderately complex polygonal models with a six degree of freedom (DOF) force feedback device. We make use of incremental algorithms for contact determination between convex primitives. The resulting contact information is used for calculating the restoring forces and torques and thereby used to generate a sense of virtual touch. To speed up the computation, our approach exploits a combination of geometric locality, temporal coherence, and predictive methods to compute objectobject contacts at kHz rates. The algorithm has been implemented and interfaced with a 6DOF PHANToM Premium 1.5. We demonstrate its performance on force display of the mechanical interaction between moderately complex geometric structures that can be decomposed into convex primitives. CR Categories: I.3.6 [Computer Graphics]: Methodology and Techniques  Interaction Techniques Additional Keywords: haptics, virtual reality, forcefeedback devices, interactive comput...