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

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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

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Improved Upper Bounds on the Growth Constants of Polyominoes and Polycubes

arXiv

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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

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Finite Cell Method for functionally graded materials based on V-models and homogenized microstructures

arXiv

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arXiv 2020年

作者： Wassermann, Benjamin Korshunova, Nina Kollmannsberger, Stefan Rank, Ernst Elber, Gershon Chair for Computation in Engineering Technical University of Munich Arcisstr. 21 München80333 Germany Chair of Computational Modeling and Simulation Technical University of Munich Arcisstr. 21 München80333 Germany Institute for Advanced Study Technical University of Munich Lichtenbergstr. 2a Garching85748 Germany Center for Graphics and Geometric Computing Technion Israel Institute of Technology Haifa3200003 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 objects gain more and more interest in the context of the new design opportunities opened by additive manufacturing, mainly 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 V-rep models’ inherent property 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. Copyright © 2020, The Authors. All rights reserved.

关键词： Functionally graded materials

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

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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

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The Growth Rate of High-Dimensional Tree Polycubes

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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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On multiplicatively weighted voronoi diagrams for lines in the plane

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Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 2011年 6750 LNCS卷 44-71页

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 Dept. of Computer Science Tufts University 161 College Ave. Medford MA 02155 United States

ISBN: (纸本)9783642226182

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(n2 logn) time and O(n2) 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 Θ(n2) time and space. © 2011 Springer-Verlag Berlin Heidelberg.

关键词： Machinery

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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

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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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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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

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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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