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A new constructive algorithm for random polydisperse dense disk pack generation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2021年第20期122卷 5812-5843页

作者： Lozano, Elias Gattass, Marcelo Tecgraf Inst Tech Sci Software DevelopmentPUC Rio Rio De Janeiro Brazil Pontificia Univ Catolica Rio de Janeiro Dept Informat Rio de Janeiro Brazil

This article presents a novel strategy for the non-overlapping disk-packing problem for generating dense random assemblies. The proposed geometric algorithm adopts an advancing-front approach that uses novel heuristics to determine the next positions for incoming particles with support from a polygonal mesh. Additionally, we propose strategies to improve generation at the pack's interior and near container borders. Experiments demonstrate that our algorithm outperforms previous methods in terms of the desired particle radius distribution function, packing density, and mean number of particle contacts.

关键词： advancing-front approach disk packing geometric algorithm polygonal mesh

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A generalized Mitchell-Dem'yanov-Malozemov algorithm for one-class support vector machine

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KNOWLEDGE-BASED SYSTEMS 2016年第0期109卷 17-24页

作者： Zeng, Ming Yang, Yu Cheng, Junsheng Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Hunan Univ Coll Mech & Vehicle Engn Changsha 410082 Hunan Peoples R China

The dual problem of one-class support vector machine (OCSVM) can be interpreted as a minimum norm problem associated with the reduced convex hull. Based on this geometric interpretation, a generalized Mitchell-Dem'yanov-Malozemov (GMDM) algorithm is proposed for OCSVM. The GMDM algorithm finds the minimum norm point in the reduced convex hull of training samples and employs such a point to construct the separating hyper-plane. Numerical experiments are conducted to compare the proposed geometric algorithm with some existing algorithms such as two modified sequential minimal optimization algorithms and the generalized Gilbert algorithm. The experimental results show that the GMDM algorithm exhibits better performance in terms of computational efficiency while achieving comparable classification accuracies to other algorithms. (C) 2016 Elsevier B.V. All rights reserved.

关键词： One-class support vector machine Generalized Mitchell-Dem'yanov-Malozemov algorithm Minimum norm problem geometric algorithm

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Mesh-driven resampling and regularization for robust point cloud-based flow analysis directly on scanned objects

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2024年 432卷

作者： Jaiswal, Monu Corpuz, Ashton M. Hsu, Ming-Chen Iowa State Univ Dept Mech Engn 2043 Black Engn Ames IA 50011 USA

Point cloud representations of three-dimensional objects have remained indispensable across a diverse array of applications, given their ability to represent complex real-world geometry with just a set of points. The high fidelity and versatility of point clouds have been utilized in directly performing numerical analysis for engineering applications, bypassing the laborintensive and time-consuming tasks of creating analysis-suitable CAD models. However, point clouds exhibit various levels of quality, often containing defects such as holes, noise, and sparse regions, leading to sub-optimal geometry representation that can impact the stability and accuracy of any analysis study. This paper aims to overcome such challenges by proposing a novel method that expands upon our recently developed direct point cloud-to-CFD approach based on immersogeometric analysis. The proposed method features a mesh-driven resampling technique to fill any unintended gaps and regularize the point cloud, making it suitable for CFD analysis. Additionally, ghost penalty stabilization is employed for incompressible flow to improve the conditioning and stability compromised by the small cut elements in immersed methods. The developed method is validated against standard benchmark geometries and real- world point clouds obtained in-house with photogrammetry. Results demonstrate the proposed framework's robustness in facilitating CFD simulations directly on point clouds of varying quality, underscoring its potential for practical applications in analyzing real-world structures.

关键词： Point cloud Scanned object geometric algorithm CFD Immersed method Ghost penalty

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Efficient method of adaptive sign detection for 4x4 determinants using a standard arithmetic processing unit

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VISUAL COMPUTER 2004年第1期20卷 37-46页

作者： Yamauchi, T Yoshida, N Doi, J Yamaguchi, F Waseda Univ Grad Sch Sci & Engn Shinjuku Ku Tokyo 1698555 Japan Nihon Univ Dept Ind Engn & Management Narashino Chiba 2758575 Japan IBM Japan Ltd Tokyo Res Lab Yamato Kanagawa 2428502 Japan Waseda Univ Sch Sci & Engn Dept Mech Engn Shinjuku Ku Tokyo 1698555 Japan

We propose an efficient and exact method for the adaptive sign detection of 4x4 determinants using a standard arithmetic unit. The entities of determinants are variable length integers (integers of arbitrary bit length). The integers are expressed in 16-bit data units, and the sign detection is reduced to the computation of 4x4 determinants of 16-bit integers. To accelerate the computation, the calculation is performed by using a standard arithmetic unit. We have implemented our method and confirmed that it significantly improves the computation time of 4x4 determinants. The method can be applicable to many geometric algorithms that need the exact sign evaluation of 4x4 determinants, especially to construct robust geometric algorithms.

关键词： solid modeling Boolean set operation exact integer arithmetic geometric algorithm

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Computing melodic templates in oral music traditions

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APPLIED MATHEMATICS AND COMPUTATION 2019年 344卷 219-229页

作者： Bereg, Sergey Diaz-Banez, Jose-Miguel Kroher, Nadine Ventura, Inmaculada Univ Texas Dallas Dept Comp Sci 800 West Campbell Rd Richardson TX 75080 USA Univ Seville Dept Appl Math 2 Camino Descubrimientos S-N Seville 41092 Spain

The term melodic template or skeleton refers to a basic melody which is subject to variation during a music performance. In many oral music traditions, these templates are implicitly passed throughout generations without ever being formalized in a score. In this work, we introduce a new geometric optimization problem, the spanning tube problem, to approximate a melodic template for a set of labeled performance transcriptions corresponding to a specific style in oral music traditions. Given a set of n piecewise linear functions, we solve the problem of finding a continuous function, f*, and a minimum value, epsilon*, such that, the vertical segment of length 2 epsilon* centered at (x, f*(x)) intersects at least p functions (p <= n). The method explored here also provide a novel tool for quantitatively assess the amount of melodic variation which occurs across performances. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Melodic skeleton geometric algorithm Oral music tradition

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An algebraic algorithm for point inclusion query

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COMPUTERS & GRAPHICS-UK 2000年第4期24卷 517-522页

作者： Wu, HY Gong, JY Li, DR Shi, WZ Hubei Univ Sch Econ Wuhan 430062 Peoples R China Wuhan Tech Univ Surveying & Mapping Natl Lab Informat Engn Surveying Mapping & Remote Wuhan 430079 Peoples R China Hong Kong Polytech Univ Dept Land Surveying & Geo Informat Hong Kong Hong Kong Peoples R China

Linking number is a basic invariant of a closed curve in topology. In this paper, linking number is generalized in a computational way to reflect the spatial relationship between a point and a line segment, an are, a plane subdivision, a three-dimensional shape, a three-dimensional object and a three-dimensional space subdivision. An algebraic algorithm for the point-in-polygon test is devised on the base of the generalized linking number. The algorithm is characterized by the algebraic property that the linking number of a point to a polygon is merely the arithmetic sum of the linking numbers of the point to all the line segments of the polygon. The algorithm takes intersection into consideration, but no intersection is actually computed. It calculates the linking number, but no trigonometric function is processed. Detailed time complexity analysis shows that this algorithm greatly improves currently existing algorithms for the point-in-polygon test. Another achievement of this paper is the consistent and successful extension of the algebraic algorithm for the point-in-polygon test to point inclusion queries in two-dimensional objects, plane subdivisions, three-dimensional shapes, three-dimensional objects and three-dimensional space subdivisions. All these algorithms retain the algebraic character. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： geometric algorithm complexity point-in-polygon test

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Gathering identical autonomous systems on a circle using stigmergy

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DISTRIBUTED COMPUTING 2012年第6期25卷 461-472页

作者： Kozlov, Dmitry N. Univ Bremen Dept Math D-28334 Bremen Germany

In this paper we provide a protocol solving the problem of gathering of identical autonomous systems (aka ants) on a circle. In our biologically inspired model the autonomous systems are unable to communicate directly, instead they employ the mechanism of pheromone marking. The gathering on a circle is not always solvable, however our protocol will terminate in finite time if ants are in a general initial position. Since the gathering problem on a line is unsolvable for obvious reasons for any non-degenerate initial position, this implies that if the ants are in generic initial position they will be able to decide in finite time whether they are on a line or on a circle. We give asymptotic bounds for the time our protocol needs to terminate, and show that for fixed number of ants, the termination time of any protocol can be arbitrarily long. Finally, our protocol may be adopted to the case of asynchronous drop-downs and starting times of the autonomous systems.

关键词： Distributed algorithm Protocol Gathering problem Swarm intelligence Pheromone communication geometric algorithm Ant algorithm

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algorithmic approach to discrete fracture network flow modeling in consideration of realistic connections in large-scale fracture networks

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Journal of Rock Mechanics and Geotechnical Engineering 2024年第9期16卷 3798-3811页

作者： Qihua Zhang Shan Dong Yaoqi Liu Junjie Huang Feng Xiong Badong National Observation and Research Station of Geohazards China University of GeosciencesWuhan430074China SINOPEC Shanghai Engineering Co. Ltd.Shanghai200120China Faculty of Engineering China University of GeosciencesWuhan430074China

Analyzing rock mass seepage using the discrete fracture network(DFN)flow model poses challenges when dealing with complex fracture *** paper presents a novel DFN flow model that incorporates the actual connections of large-scale ***,this model efficiently manages over 20,000 fractures without necessitating adjustments to the DFN *** geometric analyses,such as identifying connected fractures,dividing the two-dimensional domain into closed loops,triangulating arbitrary loops,and refining triangular elements,are fully *** analysis processes are comprehensively introduced,and core algorithms,along with their pseudo-codes,are outlined and explained to assist readers in their programming *** accuracy of geometric analyses is validated through topological graphs representing the connection relationships between *** practical application,the proposed model is employed to assess the water-sealing effectiveness of an underground storage cavern *** analysis results indicate that the existing design scheme can effectively prevent the stored oil from leaking in the presence of both dense and sparse ***,following extensive modification and optimization,the scale and precision of model computation suggest that the proposed model and developed codes can meet the requirements of engineering applications.

关键词： Discrete fracture network(DFN)flow model geometric algorithm Fracture flow Water-sealing effect

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An efficient dense and stable particular elements generation method based on geometry

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2017年第11期110卷 1003-1020页

作者： OuYang, Y. P. Yang, Q. Yu, L. Shanghai Jiao Tong Univ Collaborat Innovat Ctr Adv Ship & Deep Sea Explor State Key Lab Ocean Engn Shanghai 200240 Peoples R China

In this paper, a new discrete elements generation method based on geometry is proposed to fill geometric domains with particles (disks or spheres). By generating particles each one with a random radius or with a radius calculated from the iteration to ensure no overlaps exist between particles and identifying unstable particles and changing them to stable ones, a dense and stable packing can be created. A partitioning particle radius interval method and a particle stability inspection and improvement method are introduced to guarantee the algorithm's success and the stability of the particles. Some packings were created to evaluate the performances of the new method. The results showed that the algorithm was very efficient and was able to create isotropic packings of low porosities and large coordinate numbers. The partitioning particle radius interval method improved the generation efficiency significantly and increased the packing densities. Through the comparisons with several existing methods proposed recently, the method proposed in this work is found to be more efficient and can fill geometric domains with the lowest porosities. In addition, the stability of the particles is guaranteed and no complex triangular or tetrahedral mesh is required in particle generation, thereby making the new method simpler. Copyright (c) 2016 John Wiley & Sons, Ltd.

关键词： particle generation discrete elements geometric algorithm coordinate number porosity

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The robust and efficient adaptive normal direction support vector regression

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EXPERT SYSTEMS WITH APPLICATIONS 2011年第4期38卷 2998-3008页

作者： Peng, Xinjun Wang, Yifei Shanghai Normal Univ Dept Math Shanghai 200234 Peoples R China Shanghai Univ Sci Comp Key Lab Shanghai 200234 Peoples R China Shanghai Univ Dept Math Shanghai 200444 Peoples R China

The recently proposed reduced convex hull support vector regression (RH-SVR) treats support vector regression (SVR) as a classification problem in the dual feature space by introducing an epsilon-tube. In this paper, an efficient and robust adaptive normal direction support vector regression (AND-SVR) is developed by combining the geometric algorithm for support vector machine (SVM) classification. AND-SVR finds a better shift direction for training samples based on the normal direction of output function in the feature space compared with RH-SVR. Numerical examples on several artificial and UCI benchmark datasets with comparisons show that the proposed AND-SVR derives good generalization performance. Crown Copyright (C) 2010 Published by Elsevier Ltd. All rights reserved.

关键词： Support vector regression geometric algorithm Normal direction Epsilon-tube Sample shift

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