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Collision Detection Between Geometric Models: A Survey
 In Proc. of IMA Conference on Mathematics of Surfaces
, 1998
"... In this paper, we survey the state of the art in collision detection between general geometric models. The set of models include polygonal objects, spline or algebraic surfaces, CSG models, and deformable bodies. We present a number of techniques and systems available for contact determination. We a ..."
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Cited by 184 (15 self)
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In this paper, we survey the state of the art in collision detection between general geometric models. The set of models include polygonal objects, spline or algebraic surfaces, CSG models, and deformable bodies. We present a number of techniques and systems available for contact determination. We also describe several Nbody algorithms to reduce the number of pairwise intersection tests. 1 Introduction The goal of collision detection (also known as interference detection or contact determination) is to automatically report a geometric contact when it is about to occur or has actually occurred. The geometric models may be polygonal objects, splines, or algebraic surfaces. The problem is encountered in computeraided design and machining (CAD/CAM), robotics and automation, manufacturing, computer graphics, animation and computer simulated environments. Collision detection enables simulationbased design, tolerance verification, engineering analysis, assembly and disassembly, motion pla...
Incremental algorithms for collision detection between solid models
 IEEE Transactions on Visualization and Computer Graphics
, 1995
"... solid models ..."
Affine Arithmetic and its Applications to Computer Graphics
, 1993
"... We describe a new method for numeric computations, which we call affine arithmetic (AA). This model is similar to standard interval arithmetic, to the extent that it automatically keeps track of rounding and truncation errors for each computed value. However, by taking into account correlations betw ..."
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Cited by 66 (6 self)
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We describe a new method for numeric computations, which we call affine arithmetic (AA). This model is similar to standard interval arithmetic, to the extent that it automatically keeps track of rounding and truncation errors for each computed value. However, by taking into account correlations between operands and subformulas, AA is able to provide much tighter bounds for the computed quantities, with errors that are approximately quadratic in the uncertainty of the input variables. We also describe two applications of AA to computer graphics problems, where this feature is particularly valuable: namely, ray tracing and the construction of octrees for implicit surfaces.
Rapid and Accurate Contact Determination between Spline Models using ShellTrees
, 1998
"... In this paper, we present an efficient algorithm for contact determination between spline models. We make use of a new hierarchy, called ShellTree, that comprises of spherical shells and oriented bounding boxes. Each spherical shell corresponds to a portion of the volume between two concentric spher ..."
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Cited by 24 (5 self)
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In this paper, we present an efficient algorithm for contact determination between spline models. We make use of a new hierarchy, called ShellTree, that comprises of spherical shells and oriented bounding boxes. Each spherical shell corresponds to a portion of the volume between two concentric spheres. Given large spline models, our algorithm decomposes each surface into Bezier patches as part of preprocessing. At runtime it dynamically computes a tight fitting axisaligned bounding box across each Bezier patch and efficiently checks all such boxes for overlap. Using offline and online techniques for tree construction, our algorithm computes ShellTrees for Bezier patches and performs fast overlap tests between them to detect collisions. The overall approach can trade off runtime performance for reduced memory requirements. We have implemented the algorithm and tested itonlarge models, each composed of hundred ofpatches. Its performance varies with the configurations of the objects. For many complex models composed of hundreds of patches, it can accurately compute the contacts in a few milliseconds.
Surface Intersection Using Affine Arithmetic
 In Graphics Interface
, 1996
"... We describe a variant of a domain decomposition method proposed by Gleicher and Kass for intersecting and trimming parametric surfaces. Instead of using interval arithmetic to guide the decomposition, the variant described here uses affine arithmetic, a tool recently proposed for range analysis. Aff ..."
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Cited by 18 (7 self)
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We describe a variant of a domain decomposition method proposed by Gleicher and Kass for intersecting and trimming parametric surfaces. Instead of using interval arithmetic to guide the decomposition, the variant described here uses affine arithmetic, a tool recently proposed for range analysis. Affine arithmetic is similar to standard interval arithmetic, but takes into account correlations between operands and subformulas, generally providing much tighter bounds for the computed quantities. As a consequence, the quadtree domain decompositions are much smaller and the intersection algorithm runs faster. keywords: surface intersection, trimming surfaces, range analysis, interval analysis, CAGD.
Sampling Implicit Objects With PhysicallyBased Particle Systems
 Computers & Graphics
, 1996
"... . After reviewing three classical sampling methods for implicit objects, we describe a new sampling method that is not based on scanning the ambient space. In this method, samples are "randomly" generated using physicallybased particle systems. Introduction In computer graphics, an object is desc ..."
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Cited by 9 (7 self)
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. After reviewing three classical sampling methods for implicit objects, we describe a new sampling method that is not based on scanning the ambient space. In this method, samples are "randomly" generated using physicallybased particle systems. Introduction In computer graphics, an object is described either by a set of sample points or by an analytic scheme that uses mathematical equations to define its geometry and topology. Descriptions based on samples occur in areas such as medical images and terrain models. Analytical descriptions are usually found in applications of geometric modeling, such computeraided design and manufacture. When an object is described by samples, a reconstruction scheme is needed to recover its geometry and topology from the samples. This problem, called structuring, consists of providing a combinatorial structure to the samples in order to (ideally) recover the exact topology of the object and an approximation of its geometry. When the object is describe...
Parallel Spatial Enumeration of Implicit Surfaces Using Interval Arithmetic for Octree Generation and its Direct Visualisation
, 1998
"... This article presents a new parallel method for implicit surface voxelization  the determination of which cells of a regular grid in 3space intersect the zeroset of an implicit function. The serial version of the method uses interval arithmetic to rapidly prune regions of space where the surface ..."
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Cited by 6 (0 self)
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This article presents a new parallel method for implicit surface voxelization  the determination of which cells of a regular grid in 3space intersect the zeroset of an implicit function. The serial version of the method uses interval arithmetic to rapidly prune regions of space where the surface does not lie, and a novel octree generation#storage scheme for recording the voxels the surface meets. In the parallelization, good speedups on up to 7 processors are achieved, although the serial version is also very e#cient. The parallelization is accomplished through a masterslave scheme with dynamic loadbalancing. We also describe a method for rendering voxels directly. This method is e#ective when the voxels are small compared to pixels, hence is appropriate for very highdensityvoxel grids. Even though an octree is used in this paper, the algorithm can also be used for 3D grids or other chosen data structures. This #exibility arrives from the fact that the voxels storage is indepen...
BOOLE: A Boundary Evaluation System for Boolean Combinations of Sculptured Solids
, 2000
"... In this paper we describe a system, BOOLE, that generates the boundary representations (Breps) of solids given as a CSG expression in the form of trimmed B'ezier patches. The system makes use of techniques from computational geometry, numerical linear algebra and symbolic computation to generate ..."
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Cited by 5 (2 self)
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In this paper we describe a system, BOOLE, that generates the boundary representations (Breps) of solids given as a CSG expression in the form of trimmed B'ezier patches. The system makes use of techniques from computational geometry, numerical linear algebra and symbolic computation to generate the Breps. Given two solids, the system first computes the intersection curve between the two solids using our surface intersection algorithm. Using the topological information of each solid, it computes various components within each solid generated by the intersection curve and their connectivity. The component classification step is performed by rayshooting. Depending on the Boolean operation performed, appropriate components are put together to obtain the final solid. We also present techniques to parallelize this system on shared memory multiprocessor machines. The system has been successfully used to generate Breps for a number of large industrial models including parts of ...
Robust Voxelization of Surfaces
, 1997
"... Voxelization is the transformation of geometric surfaces into voxels. Up to date this process has been done, essentially using incremental algorithms. Incremental algorithms have the reputation of being very ecient but they lack an important property: robustness. The voxelized representation should ..."
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Cited by 4 (0 self)
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Voxelization is the transformation of geometric surfaces into voxels. Up to date this process has been done, essentially using incremental algorithms. Incremental algorithms have the reputation of being very ecient but they lack an important property: robustness. The voxelized representation should envelop its continuous model. However, without robust methods this cannot be guaranteed. This technical report presents several techniques to voxelize dierent kinds of surfaces guaranteeing robustness. Keywords: Voxel,Voxelization Algorithms, 3D Visualization, Interval Arithmetic, Implicit Surfaces, Parametric Surfaces, Polygonal meshes, Parallel Processing 1
A Methodology for Piecewise Linear Approximation of Surfaces
, 1997
"... We discuss the problem of adaptive polygonization of regular surfaces of the euclidean 3D space, and present effective algorithms for computing optimal polygonizations of surfaces described in parametric or implicit form. Keywords: Surface approximation, polygonization, parametric surfaces, implici ..."
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Cited by 3 (2 self)
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We discuss the problem of adaptive polygonization of regular surfaces of the euclidean 3D space, and present effective algorithms for computing optimal polygonizations of surfaces described in parametric or implicit form. Keywords: Surface approximation, polygonization, parametric surfaces, implicit surfaces, geometric modeling. 1 Introduction The polygonization of surfaces is a classical problem in computer graphics and geometric modeling that has many practical applications. The problem is computing a piecewise linear approximation for a smooth surface described either in parametric or implicit form. In this paper, we present a conceptual framework for the piecewise linear approximation of surfaces and also a methodology for computing good polygonal approximations while keeping the number of polygons low. Based on the general principles in this methodology, we describe two specific new algorithms for the adaptive polygonization of parametric and implicit surfaces. 1.1 Importance...