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Formulae and Growth Rates of High-Dimensional Polycubes

Electronic Notes in Discrete Mathematics 2009年 34卷 459-463页

作者： Barequet, Ronnie Barequet, Gill Rote, Günter Depts. of Mathematics and Computer Science Tel Aviv University Tel Aviv 69978 Israel Center for Graphics and Geometric Computing Dept. of Computer Science The Technion-Israel Inst. of Technology Haifa 32000 Israel Institut für Informatik Freie Universität Berlin D-14195 Berlin Takustraße 9 Germany

A d-dimensional polycube is a facet-connected set of cubes in d dimensions. Fixed polycubes are considered distinct if they differ in shape or orientation. A proper d-D polycube spans all d dimensions. In this paper we prove some formulae for fixed (proper and improper) polycubes, show that the growth-rate limit of the number of polycubes in d dimensions is 2 ed - o (d), and estimate it at (2 d - 3) e + O (1 / d). © 2009 Elsevier B.V. All rights reserved.

关键词： lattice animals Polyominoes

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On Voronoi Diagrams for Lines in the Plane

On Voronoi Diagrams for Lines in the Plane

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International Conference on Computational Science and its Applications (ICCSA)

作者： Gill Barequet Kira Vyatkina Center of Graphics and Geometric Computing Department of Computer Science Technion-Israel Institute of Technology Haifa Israel Department of Mathematics and Mechanics Saint Petersburg State University Saint Petersburg Russia

We describe a method based on the wavefront propagation, which computes a multiplicatively weighted Voronoi diagram for a set L of n lines in the plane in O(n 2 log n) time and O(n 2 ) space. In the process, we derive complexity bounds and certain structural properties of such diagrams. An advantage of our approach over the general purpose machinery, which requires computation of the lower envelope of a set of halfplanes in three-dimensional space, lies in its relative simplicity. Besides, we point out that the unweighted Voronoi diagram for n lines in the plane has a simple structure, and can be obtained in optimal thetas(n 2 ) time and space.

关键词： Machinery Euclidean distance Application software Computer graphics Computer science Mathematics

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GPU-assisted z-field simplification

GPU-assisted z-field simplification

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International Symposium on 3D Data Processing Visualization and Transmission

作者： A. Bogomjakov C. Gotsman Center of Graphics and Geometric Computing Computer Science Department Technion-Israel Institute of Technology Haifa Israel

Height fields and depth maps which we collectively refer to as z-fields, usually carry a lot of redundant information and are often used in real-time applications. This is the reason why efficient methods for their simplification are necessary. On the other hand, the computation power and programmability of commodity graphics hardware has significantly grown. We present an adaptation of an existing real-time z-field simplification method for execution in graphics hardware. The main parts of the algorithm are implemented as fragment programs which run on the GPU. The resulting polygonal models are identical to the ones obtained by the original method. The main benefit is that the computation load is imposed on the GPU, freeing-up the CPU for other tasks. Additionally, the new method exhibits a performance improvement when compared to a pure CPU implementation.

关键词： Hardware Rendering (computer graphics) Concurrent computing Computer graphics Computer science Application software Computer aided instruction Throughput Physics computing Pipelines

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Explicit surface remeshing 03

Explicit surface remeshing

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Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing

作者： Vitaly Surazhsky Craig Gotsman Center for Graphics and Geometric Computing Technion---Israel Institute of Technology

ISBN: (纸本)9781581136876

We present a new remeshing scheme based on the idea of improving mesh quality by a series of local modifications of the mesh geometry and connectivity. Our contribution to the family of local modification techniques is an area-based smoothing technique. Area-based smoothing allows the control of both triangle quality and vertex sampling over the mesh, as a function of some criteria, e.g. the mesh curvature. To perform local modifications of arbitrary genus meshes we use dynamic patch-wise parameterization. The parameterization is constructed and updated on-the-fly as the algorithm progresses with local updates. As a post-processing stage, we introduce a new algorithm to improve the regularity of the mesh connectivity. The algorithm is able to create an unstructured mesh with a very small number of irregular vertices. Our remeshing scheme is robust, runs at interactive speeds and can be applied to arbitrary complex meshes.

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On graph partitioning, spectral analysis, and digital mesh processing

On graph partitioning, spectral analysis, and digital mesh p...

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International Conference on Shape Modeling and Applications

作者： C. Gotsman Center for Graphics and Geometric Computing Department of Computer Science Technion-Israel Institute of Technology Israel

Partitioning is a fundamental operation on graphs. In this paper we briefly review the basic concepts of graph partitioning and its relationship to digital mesh processing. We also elaborate on the connection between ... 详细信息

关键词： Spectral analysis Shape

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A comparison of Gaussian and mean curvatures estimation methods on triangular meshes

A comparison of Gaussian and mean curvatures estimation meth...

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IEEE International Conference on Robotics and Automation (ICRA)

作者： T. Surazhsky E. Magid O. Soldea G. Elber E. Rivlin Center for Graphics and Geometric Computing Israel Institute of Technology Haifa Israel Applied Mathematics Department Faculty of Computer Science

Estimating intrinsic geometric properties of a surface from a polygonal mesh obtained from range data is an important stage of numerous algorithms in computer and robot vision, computer graphics, geometric modeling, industrial and biomedical engineering. This work considers different computational schemes for local estimation of intrinsic curvature geometric properties. Five different algorithms and their modifications were tested on triangular meshes that represent tessellations of synthetic geometric models. The results were compared with the analytically computed values of the Gaussian and mean curvatures of the non-uniform rational B-spline (NURBs) surfaces, these meshes originated from. This work manifests the best algorithms suited for that indeed different algorithms should be employed to compute the Gaussian and mean curvatures.

关键词： Biomedical computing Solid modeling Spline Computer vision Service robots Robot vision systems Computer graphics Computer industry Biomedical engineering Testing

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Drawing graphs with large vertices and thick edges

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8th International Workshop on Algorithms and Data Structures, WADS 2003

作者： Barequet, Gill Goodrich, Michael T. Riley, Chris Center for Graphics and Geometric Computing Dept. of Computer Science The Technion-Israel Institute of Technology Haifa32000 Israel Dept. of Information and Computer Science Univ. of California IrvineCA92697 United States Center for Algorithm Engineering Dept. of Computer Science Johns Hopkins University BaltimoreMD21218 United States

ISBN: (纸本)3540405453

We consider the problem of representing size information in the edges and vertices of a planar graph. Such information can be used, for example, to depict a network of computers and information traveling through the network. We present an efficient linear-time algorithm which draws edges and vertices of varying 2-dimensional areas to represent the amount of information flowing through them. The algorithm avoids all occlusions of nodes and edges, while still drawing the graph on a compact integer grid. © Springer-Verlag Berlin Heidelberg 2003.

关键词： Clustering algorithms

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Efficient compression and rendering of multi-resolution meshes 02

Efficient compression and rendering of multi-resolution mesh...

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Proceedings of the conference on Visualization '02

作者： Zachi Karni Alexander Bogomjakov Craig Gotsman Center for Graphics and Geometric Computing The Faculty of Computer Science Technion -- Israel Institute of Technology

ISBN: (纸本)9780780374980

We present a method to code the multiresolution structure of a 3D triangle mesh in a manner that allows progressive decoding and efficient rendering at a client machine. The code is based on a special ordering of the mesh vertices which has good locality and continuity properties, inducing a natural multiresolution structure. This ordering also incorporates information allowing efficient rendering of the mesh at all resolutions using the contemporary vertex buffer mechanism. The performance of our code is shown to be competitive with existing progressive mesh compression methods, while achieving superior rendering speed.

关键词： rendering wavelets geometry coding progressive compression

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Efficient compression and rendering of multi-resolution meshes

Efficient compression and rendering of multi-resolution mesh...

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IEEE Conference on Visualization

作者： Z. Karni A. Bogomjakov C. Gotsman Center for Graphics and Geometric Computing The Faculty of Computer Science Technion-Israel Institute of Technology Israel

关键词： Rendering (computer graphics) Geometry Decoding Solid modeling Multiresolution analysis Computer graphics Computer science Internet Web server Rough surfaces

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computing the penetration depth of two convex polytopes in 3d 7th

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7th Scandinavian Workshop on Algorithm Theory, SWAT 2000

作者： Agarwal, Pankaj K. Guibas, Leonidas J. Har-Peled, Sariel Rabinovitch, Alexander Sharir, Micha Center for Geometric Computing Department of Computer Science Duke University Box 90129 DurhamNC27708-0129 United States Computer Graphics Laboratory Computer Science Department Stanford University StanfordCA94305 United States Synopsys Inc 154 Crane Meadow Rd Suite 300 MarlboroMA01752 United States School of Mathematical Sciences Tel Aviv University Tel Aviv69978 Israel Courant Institute of Mathematical Sciences New York University NY10012 United States

ISBN: (纸本)3540676902

Let A and B be two convex polytopes in R3 with m and n facets, respectively. The penetration depth of A and B, denoted as π(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 π(A,B) in O(m3/4+ɛn3/4+ɛ + m1+ɛ + n1+ɛ) expected time, for any constant ɛ > 0. It also computes a vector t such that ||t|| = π(A,B) and int(A + t) ⊓ B = θ. We show that if the Minkowski sum B ⊗ (—A) has K facets, then the expected running time of our algorithm is O (K1/2+ɛm1/4n1/4 + m1+ɛ + n1+ɛ), for any ɛ > 0. We also present an approximation algorithm for computing π(A,B). For any δ > 0, we can compute, in time O(m + n + (log2(m + n))/δ), a vector t such that ||t|| 2 n)/δ), which is simpler and slightly faster than the recent algorithm by Chan. © Springer-Verlag Berlin Heidelberg 2000.

关键词： Approximation algorithms

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