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147
C.H.: Visibility Preprocessing For Interactive Walkthroughs
 In: Computer Graphics (SIGGRAPH 91 Proceedings
, 1991
"... The number of polygons comprising interesting architectural models is many more than can be rendered at interactive frame rates. However, due to occlusion by opaque surfaces (e.g., walls), only a small fraction of atypical model is visible from most viewpoints. We describe a method of visibility pre ..."
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Cited by 281 (15 self)
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The number of polygons comprising interesting architectural models is many more than can be rendered at interactive frame rates. However, due to occlusion by opaque surfaces (e.g., walls), only a small fraction of atypical model is visible from most viewpoints. We describe a method of visibility preprocessing that is efficient andeffective foraxisaligned oril.ria / architectural m[}dels, A model is subdivided into rectangular cc//.$whose boundaries coincide with major opaque surfaces, Nonopaque p(~rtc~/.rare identified rm cell boundaries. and used to form ana~ju{~’n~y,q)f~/>//con nectingthe cells nfthesubdivisicm. Next. theccl/r/~cc/ / visibility is computed for each cell of the subdivisirrn, by linking pairs of cells between which unobstructed.si,q/~t/inr. ~exist. During an interactive ww/krhrm/,q/~phase, an observer with a known ~~sition and\it)M~~~)~t>mov esthrc>ughthe model. At each frame, the cell containingthe observer is identified, and the contents {]fp{>tentially visible cells areretrieved from storage. The set of potentially visible cells is further reduced by culling it against theobserver’s view cone, producing the ~)yt>r~]t(>// \ i,$ibi/ify, The contents of the remaining visible cells arc then sent to a graphics pipeline for hiddensurface removal and rendering, Tests onmoderatelyc mnplex 2D and 3D axial models reveal substantially reduced rendering loads,
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...
Smallest Enclosing Disks (balls and Ellipsoids)
 Results and New Trends in Computer Science
, 1991
"... A simple randomized algorithm is developed which computes the smallest enclosing disk of a finite set of points in the plane in expected linear time. The algorithm is based on Seidel's recent Linear Programming algorithm, and it can be generalized to computing smallest enclosing balls or ellipsoids ..."
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Cited by 175 (5 self)
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A simple randomized algorithm is developed which computes the smallest enclosing disk of a finite set of points in the plane in expected linear time. The algorithm is based on Seidel's recent Linear Programming algorithm, and it can be generalized to computing smallest enclosing balls or ellipsoids of point sets in higher dimensions in a straightforward way. Experimental results of an implementation are presented. 1 Introduction During the recent years randomized algorithms have been developed for a host of problems in computational geometry. Many of these algorithms are not only attractive because of their efficiency, but also because of their appealing simplicity. This feature makes them easier to access for nonexperts in the field, and for actual implementation. One of these simple algorithms is Seidel's Linear Programming algorithm, [Sei1], which solves a Linear Program with n constraints and d variables in expected O(n) time, provided d is constant
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 154 (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 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) ...
A Library for Doing Polyhedral Operations
, 1993
"... Polyhedra are geometric representations of linear systems of equations and inequalities. Since polyhedra are used to represent the iteration domains of nested loop programs, procedures for operating on polyhedra are useful for doing loop transformations and other program restructuring transformatio ..."
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Cited by 107 (13 self)
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Polyhedra are geometric representations of linear systems of equations and inequalities. Since polyhedra are used to represent the iteration domains of nested loop programs, procedures for operating on polyhedra are useful for doing loop transformations and other program restructuring transformations which are needed in parallelizing compilers. Thus a need for a library of polyhedral operations has recently been recognized in the parallelizing compiler community. Polyhedra are also used in the definition of domains of variables in systems of affine recurrence equations (SARE). Alpha is a language which is based on the SARE formalism in which all variables are declared over finite unions of polyhedra. This report describes a library of polyhedral functions which was developed to support the Alpha language environment, and which is general enough to satisfy the needs of researchers doing parallelizing compilers. This report describes the data structures used to represent domains, gives...
Las Vegas algorithms for linear and integer programming when the dimension is small
 J. ACM
, 1995
"... Abstract. This paper gives an algcmthm for solving linear programming problems. For a problem with tz constraints and d variables, the algorithm requires an expected O(d’n) + (log n)o(d)d’’+(’(’) + o(dJA log n) arithmetic operations, as rz ~ ~. The constant factors do not depend on d. Also, an algor ..."
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Cited by 103 (2 self)
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Abstract. This paper gives an algcmthm for solving linear programming problems. For a problem with tz constraints and d variables, the algorithm requires an expected O(d’n) + (log n)o(d)d’’+(’(’) + o(dJA log n) arithmetic operations, as rz ~ ~. The constant factors do not depend on d. Also, an algorlthm N gwen for integer hnear programmmg. Let p bound the number of bits required to specify the ratmnal numbers defmmg an input constraint or the ob~ective function vector. Let n and d be as before. Then, the algorithm requires expected 0(2d dn + S~dm In n) + dc)’d) ~ in H operations on numbers with O(1~p bits d ~ ~ ~z + ~, where the constant factors do not depend on d or p. The expectations are with respect to the random choices made by the algorithms, and the bounds hold for any gwen input. The techmque can be extended to other convex programming problems. For example, m algorlthm for finding the smallest sphere enclosing a set of /z points m Ed has the same t]me bound
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.
On LinearTime Deterministic Algorithms for Optimization Problems in Fixed Dimension
, 1992
"... We show that with recently developed derandomization techniques, one can convert Clarkson's randomized algorithm for linear programming in fixed dimension into a lineartime deterministic one. The constant of proportionality is d O(d) , which is better than for previously known such algorithms. We s ..."
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Cited by 94 (11 self)
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We show that with recently developed derandomization techniques, one can convert Clarkson's randomized algorithm for linear programming in fixed dimension into a lineartime deterministic one. The constant of proportionality is d O(d) , which is better than for previously known such algorithms. We show that the algorithm works in a fairly general abstract setting, which allows us to solve various other problems (such as finding the maximum volume ellipsoid inscribed into the intersection of n halfspaces) in linear time.
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 ..."
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Cited by 94 (19 self)
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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