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The Growth Rate of High-Dimensional Tree Polycubes

Electronic Notes in Discrete Mathematics 2011年 38卷 25-30页

作者： Aleksandrowicz, Gadi Barequet, Gill Center for Graphics and Geometric Computing Dept. of Computer Science The Technion-Israel Inst. of Technology Haifa 32000 Israel

A d-dimensional polycube is a (d-1)-face-connected set of cubes in d dimensions. Fixed polycubes are considered distinct if they differ in shape or orientation. The cube-adjacency graph of a tree polycube is a tree. In this paper we investigate the asymptotic growth rate of d-dimensional tree polycubes, and estimate it at (2. d-3.5). e+. O(1/d). © 2011 Elsevier B.V.

关键词： Lattice animals Polyominoes

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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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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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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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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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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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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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On 2-site Voronoi diagrams under arithmetic combinations of point-to-point distances

On 2-site Voronoi diagrams under arithmetic combinations of ...

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7th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2010

作者： Vyatkina, Kira Barequet, Gill Dept. of Mathematics and Mechanics Saint Petersburg State University 28 Universitetsky pr. Stary Peterhof St Petersburg 198504 Russia Center for Graphics and Geometric Computing Dept. of Computer Science Technion-Israel Institute of Technology Haifa 32000 Israel

ISBN: (纸本)9780769541129

We consider a generalization of Voronoi diagrams, recently introduced by Barequet et al., in which the distance is measured from a pair of sites to a point. An easy way to define such distance was proposed together with the concept: it can be the sum-of, the product-of, or (the absolute value of) the difference-between Euclidean distances from either site to the respective point. We explore further the last definition, and analyze the complexity of the nearest- and the furthest- neighbor 2-site Voronoi diagrams for points in the plane with Manhattan or Chebyshev underlying metrics, providing extensions to general Minkowsky metrics and, for the nearest- neighbor case, to higher dimensions. In addition, we point out that the observation made earlier in the literature that 2-point site Voronoi diagrams under the sum-of and the product-of Euclidean distances are identical and almost identical to the second order Voronoi diagrams, respectively, holds in a much more general statement. © 2010 IEEE.

关键词： Graphic methods

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Minimal-Perimeter Lattice Animals and the Constant-Isomer Conjecture

arXiv

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arXiv 2022年

作者： Barequet, Gill Ben-Shachar, Gil Center for Graphics and Geometric Computing Dept. of Computer Science The Technion—Israel Inst. of Technology Haifa3200003 Israel

We consider minimal-perimeter lattice animals, providing a set of conditions which are sufficient for a lattice to have the property that inflating all minimal-perimeter animals of a certain size yields (without repetitions) all minimal-perimeter animals of a new, larger size. We demonstrate this result on the two-dimensional square and hexagonal lattices. In addition, we characterize the sizes of minimal-perimeter animals on these lattices that are not created by inflating members of another set of minimal-perimeter animals. © 2022, CC BY.

关键词： Isomers

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On the Triangle-Perimeter Two-Site Voronoi Diagram

On the Triangle-Perimeter Two-Site Voronoi Diagram

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International Symposium on Voronoi Diagrams in Science and Engineering (ISVD)

作者： Iddo Hanniel Gill Barequet Research Group Solid Works Corporation Concord MA USA Center of Graphics and Geometric Computing Department of Computer Science Technion-Israel Institute of Technology Israel

The triangle-perimeter 2-site distance function defines the "distance" P(x, (p, q)) from a point x to two other points p, q as the perimeter of the triangle whose vertices are x, p, q. Accordingly, given a set S of n points in the plane, the Voronoi diagram of S with respect to P, denoted as V P (S), is the subdivision of the plane into regions, where the region of p, q ¿ S is the locus of all points closer to p, q (according to P) than to any other pair of sites in S. In this paper we prove a theorem about the perimeters of triangles, two of whose vertices are on a given circle. We use this theorem to show that the combinatorial complexity of V P (S) is O(n 2+¿ ) (for any ¿ > 0). Consequently, we show that one can compute V P (S) on O(n 2+¿ ) time and space.

关键词： Computer science Q measurement Mobile antennas Transmitting antennas Computer graphics Crystallography Geography Metrology Biology Mathematics

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