检索结果-内蒙古大学图书馆

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

来源：评论

学校读者我要写书评

暂无评论

Improved Upper Bounds on the Growth Constants of Polyominoes and Polycubes

arXiv

引用

arXiv 2019年

作者： Barequet, Gill Shalah, Mira Center for Graphics Geometric Computing Computer Science Department Technion—Israel Institute of Technology Haifa3200003 Israel Computer Science Department Stanford University CA United States

A d-dimensional polycube is a facet-connected set of cells (cubes) on the d-dimensional cubical lattice Zd. Let Ad(n) denote the number of d-dimensional polycubes (distinct up to translations) with n cubes, and λd denote the limit of the ratio Ad(n+1)/Ad(n) as n → ∞. The exact value of λd is still unknown rigorously for any dimension d ≥ 2;the asymptotics of λd, as d → ∞, also remained elusive as of today. In this paper, we revisit and extend the approach presented by Klarner and Rivest in 1973 to bound A2(n) from above. Our contributions are: • Using available computing power, we prove that λ2 ≤ 4.5252. This is the first improvement of the upper bound on λ2 in almost half a century;• We prove that λd ≤ (2d−2)e+o(1) for any value of d ≥ 2, using a novel construction of a rational generating function which dominates that of the sequence (Ad(n));• For d = 3, this provides a subtantial improvement of the upper bound on λ3 from 12.2071 to 9.8073;• However, we implement an iterative process in three dimensions, which improves further the upper bound on λ3 to 9.3835;Copyright © 2019, The Authors. All rights reserved.

关键词： Rational functions

来源：评论

学校读者我要写书评

暂无评论

Kinetic binary space partitions for intersecting segments and disjoint triangles 98

Kinetic binary space partitions for intersecting segments an...

引用

Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms

作者： Pankaj K. Agarwal Jeff Erickson Leonidas J. Guibas Center for Geometric Computing Computer Science Department Duke University Box 90129 Durham NC Computer Graphics Laboratory Computer Science Department Stanford University Stanford CA

来源：评论

学校读者我要写书评

暂无评论

On Voronoi Diagrams for Lines in the Plane

On Voronoi Diagrams for Lines in the Plane

引用

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

来源：评论

学校读者我要写书评

暂无评论

Drawing graphs with large vertices and thick edges

引用

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

来源：评论

学校读者我要写书评

暂无评论

On 2-Site Voronoi Diagrams under Arithmetic Combinations of Point-to-Point Distances

On 2-Site Voronoi Diagrams under Arithmetic Combinations of ...

引用

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

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

ISBN: (纸本)9781424476060;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.

关键词： Computer science Digital arithmetic Mathematics Computer graphics Mechanical variables measurement Chebyshev approximation Application software History Information resources Books

来源：评论

学校读者我要写书评

暂无评论

Finite cell method for functionally graded materials based on V-models and homogenized microstructures

引用

Advanced Modeling and Simulation in Engineering Sciences 2020年第1期7卷 1-33页

作者： Wassermann, Benjamin Korshunova, Nina Kollmannsberger, Stefan Rank, Ernst Elber, Gershon Chair for Computation in Engineering Technical University of Munich Arcisstr. 21 München 80333 Germany Chair of Computational Modeling and Simulation Technical University of Munich Arcisstr. 21 München 80333 Germany Institute for Advanced Study Technical University of Munich Lichtenbergstr. 2a Garching 85748 Germany Center for Graphics and Geometric Computing Technion Israel Institute of Technology Haifa 3200003 Israel

This paper proposes an extension of the finite cell method (FCM) to V-rep models, a novel geometric framework for volumetric representations. This combination of an embedded domain approach (FCM) and a new modeling framework (V-rep) forms the basis for an efficient and accurate simulation of mechanical artifacts, which are not only characterized by complex shapes but also by their non-standard interior structure. These types of objects gain more and more interest in the context of the new design opportunities opened by additive manufacturing, in particular when graded or micro-structured material is applied. Two different types of functionally graded materials (FGM) are considered: The first one, multi-material FGM is described using the inherent property of V-rep models to assign different properties throughout the interior of a domain. The second, single-material FGM—which is heterogeneously micro-structured—characterizes the effective material behavior of representative volume elements by homogenization and performs large-scale simulations using the embedded domain approach. © 2020, The Author(s).

关键词： Additive manufacturing Direct simulation Finite cell method Functionally Ggraded material Homogenization V-models V-reps

来源：评论

学校读者我要写书评

暂无评论

Kinetic collision detection between two simple polygons 99

Kinetic collision detection between two simple polygons

引用

Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms

作者： Julien Basch Jeff Erickson Leonidas J. Guibas John Hershberger Li Zhang Computer Science Department Stanford University Stanford CA and Center for Geometric Computing Department of Computer Science Duke University Durham NC Center for Geometric Computing Department of Computer Science Duke University Durham NC and Department of Computer Science University of Illinois Urbana IL Computer Science Department Stanford University Stanford CA Mentor Graphics Corp. 8005 SW Boeckman Road Wilsonville OR

来源：评论

学校读者我要写书评

暂无评论

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

引用

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

来源：评论

学校读者我要写书评

暂无评论

Single breathhold, three-dimensional measurement of left atrial volume and function using sparse CINE CMR imaging with iterative reconstruction

引用

Journal of Cardiovascular Magnetic Resonance 2015年第SUPPL 1期17卷 Q35-Q35页

作者： Pierre Monney Orestis Vardoulis Davide Piccini Amit Bermano Amir Vaxman Craig Gotsman Janine Schwitter Michael O Zenge Michaela Schmidt Mariappan S Nadar Matthias Stuber Nikolaos Stergiopulos Juerg Schwitter Center for Cardiac Magnetic Resonance Cardiology University Hospital Lausanne (CHUV) Lausanne Switzerland Laboratory of Hemodynamics and Cardiovascular Technology Swiss Federal Institute of Technology Lausanne Switzerland Center for Biomedical Imaging (CIBM) University of Lausanne Lausanne Switzerland Advanced Clinical Imaging Technology Siemens Healthcare Lausanne Switzerland Center for Graphics and Geometric Computing Technion Haifa Israel Geometric Modelling and Industrial Geometry Vienna University of Technology Vienna Austria University of Fribourg Fribourg Switzerland Healthcare sector Siemens AG Erlangen Germany Imaging and Computer Vision Siemens Corporation Princeton NJ USA Radiology University Hospital Lausanne Lausanne Switzerland

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：