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37
Spatial Data Structures
, 1995
"... An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarch ..."
Abstract

Cited by 287 (13 self)
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An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarchical data structures are based on the principle of recursive decomposition. They are attractive because they are compact and depending on the nature of the data they save space as well as time and also facilitate operations such as search. Examples are given of the use of these data structures in the representation of different data types such as regions, points, rectangles, lines, and volumes.
Collision Detection for Interactive Graphics Applications
 IEEE Transactions on Visualization and Computer Graphics
, 1995
"... Solid objects in the real world do not pass through each other when they collide. Enforcing this property of "solidness" is important in many interactive graphics applications; for example, solidness makes virtual reality more believable, and solidness is essential for the correctness of vehicle sim ..."
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Cited by 173 (5 self)
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Solid objects in the real world do not pass through each other when they collide. Enforcing this property of "solidness" is important in many interactive graphics applications; for example, solidness makes virtual reality more believable, and solidness is essential for the correctness of vehicle simulators. These applications use a collisiondetection algorithm to enforce the solidness of objects. Unfortunately, previous collisiondetection algorithms do not adequately address the needs of interactive applications. To work in these applications, a collisiondetection algorithm must run at realtime rates, even when many objects can collide, and it must tolerate objects whose motion is specified "on the fly" by a user. This dissertation describes a new collisiondetection algorithm that meets these criteria through approximation and graceful degradation, elements of timecritical computing. The algorithm is not only fast but also interruptible, allowing an application to trade accuracy ...
Accelerating Volume Animation by SpaceLeaping
, 1993
"... f i In this paper we present a method for speeding the process of volume rendering a sequence o mages. Speedup is based on exploiting coherency between consecutive images to shorten the n path rays take through the volume. This is achieved by providing each ray with information eeded to leap over th ..."
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Cited by 66 (9 self)
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f i In this paper we present a method for speeding the process of volume rendering a sequence o mages. Speedup is based on exploiting coherency between consecutive images to shorten the n path rays take through the volume. This is achieved by providing each ray with information eeded to leap over the empty space and commence volume traversal at the vicinity of mean  b ingful data. The algorithm starts by projecting the volume into a Cbuffer (Coordinates uffer) which stores, at each pixel location, the objectspace coordinates of the first nonempty s t voxel visible from that pixel. For each change in the viewing parameters, the Cbuffer i ransformed accordingly. In the case of rotation the transformed Cbuffer goes through a pro  b cess of eliminating coordinates that possibly became hidden. The remaining values in the C uffer serve as an estimate of the point where the new rays should start their volume traverc sal. This spaceleaping method can be combined with existing accele...
Nonuniform Dynamic Discretization in Hybrid Networks
 In Proc. UAI
, 1997
"... We consider probabilistic inference in general hybrid networks, which include continuous and discrete variables in an arbitrary topology. We reexamine the question of variable discretization in a hybrid network aiming at minimizing the information loss induced by the discretization. We show that a n ..."
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Cited by 64 (3 self)
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We consider probabilistic inference in general hybrid networks, which include continuous and discrete variables in an arbitrary topology. We reexamine the question of variable discretization in a hybrid network aiming at minimizing the information loss induced by the discretization. We show that a nonuniform partition across all variables as opposed to uniform partition of each variable separately reduces the size of the data structures needed to represent a continuous function. We also provide a simple but efficient procedure for nonuniform partition. To represent a nonuniform discretization in the computer memory, we introduce a new data structure, which we call a Binary Split Partition (BSP) tree. We show that BSP trees can be an exponential factor smaller than the data structures in the standard uniform discretization in multiple dimensions and show how the BSP trees can be used in the standard join tree algorithm. We show that the accuracy of the inference process can be significa...
Filling Gaps in the Boundary of a Polyhedron
 Computer Aided Geometric Design
, 1993
"... In this paper we present an algorithm for detecting and repairing defects in the boundary of a polyhedron. These defects, usually caused by problems in CAD software, consist of small gaps bounded by edges that are incident to only one polyhedron face. The algorithm uses a partial curve matching t ..."
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Cited by 38 (4 self)
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In this paper we present an algorithm for detecting and repairing defects in the boundary of a polyhedron. These defects, usually caused by problems in CAD software, consist of small gaps bounded by edges that are incident to only one polyhedron face. The algorithm uses a partial curve matching technique for matching parts of the defects, and an optimal triangulation of 3D polygons for resolving the unmatched parts. It is also shown that finding a consistent set of partial curve matches with maximum score, a subproblem which is related to our repairing process, is NPHard. Experimental results on several polyhedra are presented. Keywords: CAD, polyhedra, gap filling, curve matching, geometric hashing, triangulation. 1 Introduction The problem studied in this paper is the detection and repair of "gaps" in the boundary of a polyhedron. This problem usually appears in polyhedral approximations of CAD objects, whose boundaries are described using curved entities of higher leve...
Buckettree: Improving collision detection between deformable objects
 In Proceedings of SCCG2000: Spring Conference on Computer Graphics, Budmerice
"... In recent years, thanks to the increasing computational power available, real time computer animation has naturally evolved to model more complex and computationally expensive scenes. Consequently, all the problems concerning physical modelling need further research to tackle these new requirements, ..."
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Cited by 27 (2 self)
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In recent years, thanks to the increasing computational power available, real time computer animation has naturally evolved to model more complex and computationally expensive scenes. Consequently, all the problems concerning physical modelling need further research to tackle these new requirements, especially the problem of collision detection for deformable objects. Most existing solutions cannot not be trivially extended, because they are strongly based on the assumption that the shape of the object is fixed. In this paper we propose a general approach to reduce the cost of collision detection between deformable objects explicitly represented, regardless of the specific geometrical and physical manner in which they are modelled.
Implementing ray tracing with octrees and neighbor finding
 Computers And Graphics
, 1989
"... AbstractA ray tracing implementation is described that is based on an octree representation of a scene. Rays are traced through the scene by calculating the blocks through which they pass. This calculation is performed in a bottomup manner through the use of neighbor finding. The octrees are assu ..."
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Cited by 18 (4 self)
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AbstractA ray tracing implementation is described that is based on an octree representation of a scene. Rays are traced through the scene by calculating the blocks through which they pass. This calculation is performed in a bottomup manner through the use of neighbor finding. The octrees are assumed to be implemented by a pointer representation. The most basic operation in computer graphics is the conversion of an internal model of a threedimensional scene into a twodimensional scene that lies on the viewplane. The purpose is to generate an image of the
Neighbour finding in images represented by octrees
 Computer Vision, Graphics and Image Processing
, 1989
"... Algorithms are presented for moving between adjacent blocks in an octree representation of an image. Motion is possible in the direction of a face, edge, and a vertex, and between blocks of arbitrary size. The algorithms are based on a generalization and simplification of techniques developed earlie ..."
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Cited by 16 (6 self)
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Algorithms are presented for moving between adjacent blocks in an octree representation of an image. Motion is possible in the direction of a face, edge, and a vertex, and between blocks of arbitrary size. The algorithms are based on a generalization and simplification of techniques developed earlier for two dimensions (i.e., in quadtrees). They are also applicable to quadtrees. The difference lies in the graphtheoretical classification of adjacenciesi.e., in terms of vertices, edges, and faces. Algorithms are given for octrees that are implemented with pointers and with pointerless representations such as the linear octree. 0 1989 Academic PRSS. ITIC. 1.
Shape intrinsic fingerprints for freeform object matching
 in Proc. 8th ACM Symposium on Solid Modeling and Applications
, 2003
"... This paper presents matching and similarity evaluation methods between two NURBS surfaces, and their application to copyright protection of digital data representing solids or NURBS surfaces. Two methods are employed to match objects:the moment and the curvature methods. The moment method uses integ ..."
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Cited by 10 (3 self)
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This paper presents matching and similarity evaluation methods between two NURBS surfaces, and their application to copyright protection of digital data representing solids or NURBS surfaces. Two methods are employed to match objects:the moment and the curvature methods. The moment method uses integral properties, i.e. the volume, the principal moments of inertia and directions, to find the rigid body transformation as well as the scaling factor. The curvature method is based on the Gaussian and the mean curvatures to establish correspondence between two objects. The matching algorithms are applied to problems of copyright protection. A suspect model is aligned to an original model through the matching methods so that similarity between two models can be assessed to determine if the suspect
Dynamic data structures for realtime management of large geometric scenes (Extended Abstract)
, 1997
"... ) M: Fischer, F: Meyer auf der Heide, and W:B. Strothmann Heinz Nixdorf Institute and Department of Computer Science University of Paderborn, D33095 Paderborn, Germany fmafi,fmadh,willyg@unipaderborn.de Abstract We present a data structure problem which describes the requirements of a simple va ..."
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Cited by 9 (1 self)
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) M: Fischer, F: Meyer auf der Heide, and W:B. Strothmann Heinz Nixdorf Institute and Department of Computer Science University of Paderborn, D33095 Paderborn, Germany fmafi,fmadh,willyg@unipaderborn.de Abstract We present a data structure problem which describes the requirements of a simple variant of fully dynamic walkthrough animation: We assume the scene to consist of unit size balls in IR 2 or higher dimensions. The scene may be arbitrarily large and has to be stored in secondary memory (discs) with relatively slow access. We allow a visitor to walk in the scene, and a modeler to update the scene by insertions and deletions of balls. We focus on the realtime requirement of animation systems: For some t (specified by the computation power of (the rendering hardware of) the graphic workstation) the data structure has to guarantee that the balls within distance t of the current visitor's position are presented to the rendering hardware, 20 times per second. Insertions and del...