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Computing optimal shortcuts for networks

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第1期279卷 26-37页

作者： Garijo, Delia Marquez, Alberto Rodriguez, Natalia Silveira, Rodrigo, I Univ Seville Dept Matemat Aplicada 1 Avda Reina Mercedes S-N E-41012 Seville Spain Univ Buenos Aires Dept Computat Pabellon 1Ciudad UnivC1428EGA Buenos Aires DF Argentina Univ Politecn Cataluna Dept Matemat Jordi Girona 1-3 ES-08034 Barcelona Spain

We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received considerable attention recently, mostly for discrete variants of the problem. We consider a fully continuous setting, where the problem of computing distances and placing a shortcut is much harder as all points on the network, instead of only the vertices, must be taken into account. We present the first results on the computation of optimal shortcuts for general networks in this model: a polynomial time algorithm and a discretization of the problem that leads to an approximation algorithm. We also improve the general method for networks that are paths, restricted to two types of shortcuts: those with a fixed orientation and simple shortcuts. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Networks geometric algorithm Complexity Discrete optimization Graph augmentation

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A fast and efficient particle packing generation algorithm with controllable gradation for discontinuous deformation analysis

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GEOMECHANICS AND GEOPHYSICS FOR GEO-ENERGY AND GEO-RESOURCES 2023年第1期9卷 1-27页

作者： Ma, Jianjun Ding, Wenjie Lin, Yuexiang Chen, Wanxiang Huang, Linchong Sun Yat Sen Univ Guangdong Res Ctr Underground Space Exploitat Tech Sch Civil Engn Southern Marine Sci & Engn Guangdong Lab ZhuhaiGu Zhuhai 519082 Peoples R China Sun Yat Sen Univ Sch Civil Engn Guangzhou 510275 Peoples R China Sun Yat Sen Univ Sch Aeronaut & Astronaut Shenzhen 518107 Peoples R China Hong Kong Polytech Univ Dept Civil & Environm Engn Hong Kong Peoples R China

A systematic geometric algorithm is developed to generate particle packing with high density, controllable gradation, and uniform spatial distribution for discontinuous deformation analysis (DDA). The algorithm incorporates a lattice searching technique to expedite overlap detection and reduce computational costs during particle packing generation. Additionally, a Fourier transformation method is utilized to analytically handle overlap detections on arbitrary irregular boundaries. To evaluate the efficiency and accuracy of the proposed method, a series of comparisons are made between existing methods and the proposed approach. Numerical modelling of engineering problems is conducted using the proposed method and a self-developed numerical program called DDA. The modelling results demonstrate that the proposed particle generation method has wide applications in generating complex particle models for discontinuous numerical analysis. The algorithm exhibits excellent performance in both geometric and numerical analyses, further confirming its efficiency and accuracy.

关键词： geometric algorithm Lattice searching algorithm Particle packing generation Discrete Fourier transforms

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Support slimming for single material based additive manufacturing

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COMPUTER-AIDED DESIGN 2015年 65卷 1-10页

作者： Hu, Kailun Jin, Shuo Wang, Charlie C. L. Chinese Univ Hong Kong Dept Mech & Automat Engn Hong Kong Hong Kong Peoples R China

In layer-based additive manufacturing (AM), supporting structures need to be inserted to support the overhanging regions. The adding of supporting structures slows down the speed of fabrication and introduces artifacts onto the finished surface. We present an orientation-driven shape optimizer to slim down the supporting structures used in single material-based AM. The optimizer can be employed as a tool to help designers to optimize the original model to achieve a more self-supported shape, which can be used as a reference for their further design. The model to be optimized is first enclosed in a volumetric mesh, which is employed as the domain of computation. The optimizer is driven by the operations of reorientation taken on tetrahedra with 'facing-down' surface facets. We formulate the demand on minimizing shape variation as global rigidity energy. The local optimization problem for determining a minimal rotation is analyzed on the Gauss sphere, which leads to a closed-form solution. Moreover, we also extend our approach to create the functions of controlling the deformation and searching for optimal printing directions. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： geometric algorithm Shape optimization Design tool Additive manufacturing

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Islamic geometric Patterns in Higher Dimensions

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NEXUS NETWORK JOURNAL 2020年第3期22卷 777-798页

作者： Moradzadeh, Sam Ebrahimi, Ahad Nejad Tabriz Islamic Art Univ Dept Architecture & Urbanism Azadi BlvdHak Nizami Ganjavi Sq Tabriz Iran

The purpose of this paper is to develop the Islamic geometric patterns from planar coordinates to three or higher dimensions through their repeat units. We use historical plane methods, polygons in contact (PIC) and point-joined, in our deductive approaches. The mentioned approach makes use of a novel method of tessellation that generates 3D Islamic patterns called "interior polyhedral stellations". The outputs showed that both the PIC and point-joined methods have strengths and weaknesses. Point-joined stellations are more efficient for regular repeat units and PIC is suitable for complex designs. These two methods can produce a large range of patterns and can be employed simultaneously. This study effectively answers the question regarding the gap between planar design from Muslim achievements and contemporary demands in modern art and architecture. We also propose techniques for constructing aperiodic three-dimension Islamic geometric patterns tessellation and two-point family.

关键词： Islamic ornaments geometric algorithm Space tessellation Dimensions Symmetry

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Efficient Hausdorff Distance computation for freeform geometric models in close proximity

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COMPUTER-AIDED DESIGN 2013年第2期45卷 270-276页

作者： Kim, Yong-Joon Oh, Young-Taek Yoon, Seung-Hyun Kim, Myung-Soo Elber, Gershon Seoul Natl Univ Sch Comp Sci & Engn Seoul 151744 South Korea Samsung Adv Inst Technol Yongin 446712 Gyeonggi South Korea Dongguk Univ Dept Multimedia Engn Seoul 100715 South Korea Technion Israel Inst Technol Dept Comp Sci IL-32000 Haifa Israel

We present an interactive-speed algorithm for computing the Hausdorff Distance (HD) between two freeform geometric models represented with NURBS surfaces. The algorithm is based on an effective technique for matching a surface patch from one model to the corresponding nearby surface patch on the other model. To facilitate the matching procedure, we employ a bounding volume hierarchy (BVH) for freeform NURBS surfaces, which provides a hierarchy of Coons patches and bilinear surfaces approximating the NURBS surfaces (Kim et al., 2011 [1]). Comparing the local HD upper bound against a global HD lower bound, we can eliminate the majority of redundant surface patches from further consideration. The resulting algorithm and the associated data structures are considerably simpler than the previous BVH-based HD algorithms. As a result, we can compute the HD of two freeform geometric models efficiently and robustly even when the two models are in close proximity. We demonstrate the effectiveness of our approach using several experimental results. (C) 2012 Published by Elsevier Ltd

关键词： Hausdorff Distance NURBS surface Coons patch Bounding volume hierarchy (BVH) Hierarchical data structure geometric algorithm

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Precise Hausdorff distance computation between polygonal meshes

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COMPUTER AIDED geometric DESIGN 2010年第8期27卷 580-591页

作者： Barton, Michael Hanniel, Iddo Elber, Gershon Kim, Myung-Soo Technion Israel Inst Technol IL-32000 Haifa Israel SolidWorks Corp Concord MA 01742 USA Seoul Natl Univ Seoul 151744 South Korea

We present an exact algorithm for computing the precise Hausdorff distance between two general polyhedra represented as triangular meshes. The locus of candidate points, events where the Hausdorff distance may occur, is fully classified. These events include simple cases where foot points of vertices are examined as well as more complicated cases where extreme distance evaluation is needed on the intersection curve of one mesh with the medial axis of the other mesh. No explicit reconstruction of the medial axis is conducted and only bisectors of pairs of primitives (i.e. vertex, edge, or face) are analytically constructed and intersected with the other mesh, yielding a set of conic segments. For each conic segment, the distance functions to all primitives are constructed and the maximum value of their low envelope function may correspond to a candidate point for the Hausdorff distance. The algorithm is fully implemented and several experimental results are also presented. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Hausdorff distance Polygonal mesh geometric algorithm Bisector surface Medial axis Low envelope

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An algorithm to find the number of the digitizations of discs with a fixed radius

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Electronic Notes in Discrete Mathematics 2005年 20卷 607-622页

作者： Nagy, Benedek Department of Computer Science University of Debrecen Debrecen Hungary Research Group on Mathematical Linguistics Rovira i Virgili University Tarragona Spain

For digitizations a grid is given, usually it is considered as Z2. The digital image of a real object depends on the respective position of the object and the grid. In this paper we consider the simplest objects of th... 详细信息

For digitizations a grid is given, usually it is considered as Z². The digital image of a real object depends on the respective position of the object and the grid. In this paper we consider the simplest objects of the plane: the Euclidean circles (real and open discs) are given by a fixed radius. We present an algorithm which results all possible digital images of these real discs. Moreover discrete data-sets of these digital images are presented. © 2005 Elsevier B.V. All rights reserved.

关键词： combinatorial image processing Digital discs enumeration geometric algorithm inverse discrete tomography lattice points

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Transmitting Particles in a Polygonal Domain by Repulsion 12th

Transmitting Particles in a Polygonal Domain by Repulsion

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12th Annual International Conference on Combinatorial Optimization and Applications (COCOA)

作者： Mozafari, Amirhossein Shermer, Thomas C. Simon Fraser Univ Sch Comp Sci Burnaby BC Canada

ISBN: (纸本)9783030046514;9783030046507

In this paper, we introduce the problem of transmitting particles to a target point by the effect of a repulsion actuator (RA). In this problem, we are given a polygonal domain P and a target point t inside it. Also, there is a particle at each point of P. The question is which particles can get to the target point t by activating a RA in P. We present the first polynomial time algorithm to solve this problem.

关键词： geometric algorithm Polygonal domain Repulsion actuator Polynomial time algorithm

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Parallel Sphere Packing for Arbitrary Domains 16th

Parallel Sphere Packing for Arbitrary Domains

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16th International Symposium on Visual Computing (ISVC)

作者： Cuba Lajo, Ruben Adrian Loaiza Fernandez, Manuel Eduardo Univ Catolica San Pablo Dept Comp Sci Arequipa Peru

ISBN: (纸本)9783030904364;9783030904357

Particle packings are methods used to fill a container with particles. These are used to simulate granular matter, which has various uses. Particle packings seek to be dense, however, particle packings are slow, they don't become completely dense, and most only work in simple containers. Currently, several techniques have been proposed to achieve a dense packing, significantly reducing packing construction time, but little progress has been seen in increasing the density of the packing. Particle packings reach an average maximum density of approximately 70% in rectangular and cylindrical containers, and 60% in arbitrary containers. The density of the packings is also known as compaction or solid fraction. The objective of this work is to make a compact packing that in arbitrary containers reaches between 60% and 70% of compaction. For this, a compact periodic packing of spheres is taken as a basis, which from the use of spheres of the same size achieves the highest compaction, that is, it is the most dense. Searched packing is made following a periodic hexagonal pattern, to this are added three sizes of spheres, which are smaller than the initial size, these spheres go in the empty spaces left by the hexagonal packing. The proposed method, reaches densities in arbitrary containers between 60% and 70% in times less than 5 min using a parallel optimization on GPU resource.

关键词： Sphere packing geometric algorithm Parallel

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A complete and improved mathematical framework of the geometric approach based on the Scaled convex hull (SCH) and its application to large medical data sets

A complete and improved mathematical framework of the geomet...

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International Conference on Mechatronics Engineering and Computing Technology (ICMECT)

作者： Guo, Haoyan Cheng, Yuanzhi Wang, Dazheng Xu, Jiacheng Harbin Inst Technol Sch Mech Elect Harbin 150001 Peoples R China Harbin Inst Technol Sch Comp Harbin 150001 Peoples R China Harbin Inst Technol Sch Mech Elect Harbin 150001 Peoples R China Harbin Inst Technol Sch Math Harbin 150001 Peoples R China

ISBN: (纸本)9783038351153

In this paper a complete and improved mathematical framework of the geometric approach based on the Scaled convex hull (SCH), which includes two parts, SCH-based geometric algorithms for SVM and a fast and novel geometric method for model selection in SCH-based SVM, is developed to solve SCH-based SVM classification of large data sets. On the basis of this framework, these geometric algorithms are more suitable for classification task of large data sets. Results of numerical experiments show that the proposed geometric algorithms can reduce kernel calculations and display nice performances on large medical data sets, such as computer assisted screening for lung cancer.

关键词： Kernel methods scaled convex hull (SCH) support vector machines (SVMs) geometric algorithm

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