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Interpolation by geometric algorithm

COMPUTER-AIDED DESIGN 2007年第4期39卷 313-323页

作者： Maekawa, Takashi Matsumoto, Yasunori Namiki, Ken Yokohama Natl Univ Dept Mech Engn Yokohama Kanagawa 2408501 Japan

We present a novel geometric algorithm to construct a smooth surface that interpolates a triangular or a quadrilateral mesh of arbitrary topological type formed by n vertices. Although our method can be applied to B-spline surfaces and subdivision surfaces of all kinds, we illustrate our algorithm focusing on Loop subdivision surfaces as most of the meshes are in triangular form. We start our algorithm by assuming that the given triangular mesh is a control net of a Loop subdivision surface. The control points are iteratively updated globally by a simple local point-surface distance computation and an offsetting procedure without solving a linear system. The complexity of our algorithm is O(mn) where n is the number of vertices and at is the number of iterations. The number of iterations m depends on the fineness of the mesh and accuracy required. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： geometric algorithm surface interpolation loop subdivision surface Catmull-Clark subdivision surface B-spline curves and surfaces geometric modeling

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Local geometric algorithm for hole boundary detection in sensor networks

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SECURITY AND COMMUNICATION NETWORKS 2011年第9期4卷 1003-1012页

作者： Shirsat, Amit Bhargava, Bharat US Off Santa Clara CA 95054 USA US Off W Lafayette IN 47907 USA

We present a hole boundary detection algorithm for sensor network which identifies the geographical boundary of voids in the network assuming the relative geographic information of only 2-hop neighbors. We formalize the fuzzy notion of a hole by relating it to the graph theoretic concept of a chordless cycle enclosing a face in an arrangement of lines. Furthermore, the algorithm for detecting such topological holes is distributed, O(k) per node computation (for k 2-hop neighbors) and requires synchronization between nodes that are no more than 2-hops away. The algorithm takes a local best-effort approach and does not verify if the nodes indeed form a closed polygonal loop. We believe that this local effort is sufficient based on theoretical observations and experiments. In the simulation tests we conducted, this was hardly a restriction in correctly identifying the simple, closed polygonal loops. We discuss the security implications of the hole detection framework in the context of sensor networks. Copyright (C) 2011 John Wiley & Sons, Ltd.

关键词： geometric algorithm hole detection security sensor networks

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Norm-mixed twin support vector machine classifier and its geometric algorithm

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NEUROCOMPUTING 2013年 99卷 486-495页

作者： Peng, Xinjun Xu, Dong Shanghai Normal Univ Dept Math Shanghai 200234 Peoples R China

In this paper, a novel classifier named norm-mixed twin support vector machine (NMTWSVM) is presented. The main idea in each primal problem of this NMTWSVM is to replace the hinge loss of the other class with the L-1-norm-based loss, which are obtained from equality constraints, such that each hyperplane is closest to the corresponding class and is as possible as far from the other class. The geometric analysis shows that the dual problems of NMTWSVM can be interpreted as a pair of minimum generalized Mahalanobis-norm problems (MGMNPs) on the two reduced affine hulls (RAHs) composed of two classes of points. As the practical application of the geometric analysis for NMTWSVM, a novel geometric algorithm is suggested based on the geometric properties of RAHs. The experimental results on several artificial and benchmark datasets indicate that the proposed algorithm not only obtains comparable accuracy, but also needs less kernel operations compared with the geometric algorithm of classical support vector machine (SVM). (C) 2012 Elsevier B.V. All rights reserved.

关键词： Support vector machine Nonparallel hyperplanes Minimum norm problem Reduced affine hull geometric algorithm

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A geometric algorithm based on tetrahedral meshes to generate a dense polydisperse sphere packing

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GRANULAR MATTER 2009年第1期11卷 43-52页

作者： Jerier, Jean-Francois Imbault, Didier Donze, Frederic-Victor Doremus, Pierre Univ Grenoble 1 Lab Sols Solides Struct & Risques Inst Natl Polytech Grenoble Grenoble France

In the discrete element method, the packing generation of polydisperse spheres with a high packing density value is a major concern. Among the methods already developed, few algorithms can generate sphere packing with a high density value. The aim of this paper is to present a new geometric algorithm based on tetrahedral meshes to generate dense isotropic arrangements of non-overlapping spheres. The method consists of first filling in every tetrahedron with spheres in contact (i.e., hard-sphere clusters). Then, the algorithm increases the packing density value by detecting the large empty spaces and filling them with new spheres. This new geometric algorithm can also generate a complex shape structure.

关键词： Discrete element method Sphere packing geometric algorithm Polydisperse spheres

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Higher-order Extension of the Breiter-Nesborny-Vokrouhlicky geometric algorithm for Nonautonomous Poisson Systems and Its Application to the Exactly Solvable Model of a Classical Spin in a Rotating Magnetic Field

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JOURNAL OF THE KOREAN PHYSICAL SOCIETY 2012年第4期60卷 613-620页

作者： Oh, Suhk Kun Chungbuk Natl Univ Dept Phys Chonju 361763 South Korea Chungbuk Natl Univ Phys Program BK21 Chonju 361763 South Korea

The Breiter-Nesborny-Vokrouhlicky geometric algorithm for nonautonomous Poisson systems is extended to higher orders. The effectiveness of this extension is exemplified by numerically solving the exactly solvable model of a classical single spin in a rotating magnetic field. Because this model exhibits very complicated periodic motion, after long time elapsed, the usual fourth-order Runge-Kutta algorithm yields a decaying trajectory that has departed significantly from the exact trajectory. We found that the fourth-order Breiter-Nesborny-Vokrouhlicky geometric algorithm of type B remained close to the exact trajectory even when we chose large time-steps for which the Runge-Kutta fourth-order algorithm miserably fails even at relatively short times.

关键词： Classical spin dynamics Poisson system Numerical simulations geometric algorithm

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geometric algorithm for efficient coincident detection of gravitational waves

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Physical Review D 2008年第6期78卷 062002-062002页

作者： C. A. K. Robinson B. S. Sathyaprakash Anand S. Sengupta School of Physics and Astronomy Cardiff University 5 The Parade Cardiff United Kingdom CF24 3AA LIGO Laboratory California Institute of Technology Pasadena California 91125 USA

Data from a network of gravitational-wave detectors can be analyzed in coincidence to increase detection confidence and reduce nonstationarity of the background. We propose and explore a geometric algorithm to combine the data from a network of detectors. The algorithm makes optimal use of the variances and covariances that exist among the different parameters of a signal in a coincident detection of events. The new algorithm essentially associates with each trigger ellipsoidal regions in parameter space defined by the covariance matrix. Triggers from different detectors are deemed to be in coincidence if their ellipsoids have a nonzero overlap. Compared to an algorithm that uses uncorrelated windows separately for each of the signal parameters, the new algorithm greatly reduces the background rate thereby increasing detection efficiency at a given false alarm rate.

关键词： .false New algorithm overlap parameter space ellipsoids covariances detection of gravitational Gravitational-Wave Coherent Analysis Coincidence Analysis geometric algorithm efficient coincident background rate

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A geometric algorithm based on the advancing front approach for sequential sphere packing

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GRANULAR MATTER 2018年第4期20卷 59-59页

作者： Li, Yongjun Ji, Shunying Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dalian Peoples R China

The arrangement of calculation samples with a high initial solid fraction and lower computation times are the primary concern of discrete element simulations. When generating thousands of particles, the advancing front algorithm, as one of the effective constructive packing methods, provides a time-saving and non-overlapping packing methodology compared to dynamic approaches, which are extremely time consuming in these situations. This paper proposes a sequential packing algorithm based on the advancing front approach. New particles with random sizes are sequentially inserted into a predefined void space to make contact with at least three existing neighboring particles by analytically solving the trilateration equations. The algorithm allows for an arrangement of particles with random sizes to obtain a low-porosity particle assembly. To increase the algorithm efficiency, a feasible measure of the spatial gridding is proposed to simplify the detection of the advancing fronts. The generated packings can be isotropic, and the number of contacts per particle is sufficiently high to reach a stable state. When the generated packing structures are filled with particles, the physical properties, including the average coordination number, solid fraction, second-order fabric tensor, contact orientation and particle size distribution, are analyzed with different size ratios. Examples of practical geometric models for real industrial applications to railway ballast and a gear are presented.

关键词： Sequential sphere packing geometric algorithm Advancing front approach Spatial gridding Discrete element method geometrical isotropy

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Research on Post Nonlinear geometric algorithm for BSS of Mixed Vibration Simulation Signals from the Impeller Pumps

Research on Post Nonlinear Geometric Algorithm for BSS of Mi...

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The second International Symposium on Socially and Technically Symbiotic Systems (STSS2015);The 7th International Symposium on Symbiotic Nuclear Power Systems (ISSNP2015)

作者： Sun Shi-yan XIA Hong CHEN Zhi-hui YANG Bo LIU Mei-ru Fundamental Science on Nuclear Safety and Simulation Technology Laboratory College of Nuclear Science and TechnologyHarbin Engineering University Science and Technology on Reactor System Design Technology Laboratory Science and Technology on Reactor System Design Technology Laboratory Nuclear Power Institute of China

In nuclear power plants,for rotating equipment,a normal method for monitoring the modes and diagnosing its fault is monitoring and analyzing its vibration or noise ***,the detected signals are usually the non-linear mixed signals produced by multiple pieces of equipment or their different *** order to distinguish equipment's status,Blind Source Separation technique need to be applied to separate the mixed signals,then equipment's mode can be distinguished *** existing mature BSS algorithms are based on the assumption of the linear *** it to the nonlinear mixed problem directly may cause failure or result in totally wrong *** this paper,we apply geometric algorithm to separate the mixed vibration simulation *** method follows the post-nonlinear mixing model assumption,and develops its separating measure exploiting the difference between a linear mixture and a nonlinear one from their distributions in a three-dimensional *** impeller pump,which is a typical rotating machinery in nuclear power plants,is chosen as the study *** build a three-dimensional model of a kind of impeller pump,use Finite Element Analysis method to create some correlative stress and mode analysis,decorate appropriate monitoring points to get the most intense vibration simulation signal in the pump,and then construct the mixed *** using the post-nonlinear geometric algorithm,the mixed vibration simulation signals of the pump are *** with correlation coefficient,the algorithm performs *** can obtain the same vibration peak frequency from the result as that from the source signals.

关键词： Blind Source Separation post-nonlinear model geometric algorithm the impeller pump vibration simulation signal

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Approximation of triangular B-spline surfaces by local geometric fitting algorithm

Approximation of triangular B-spline surfaces by local geome...

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3rd National-Foundation-for-Science-and-Technology-Development Conference on Information and Computer Science (NICS)

作者： Nga Le-Thi-Thu Khoi Nguyen-Tan Thuy Nguyen-Thanh Danang Univ Sci & Technol Danang Vietnam Vietnam Natl Univ Hanoi Vietnam

ISBN: (纸本)9781509020980

Surfaces over triangular domain are a powerful and flexible tool for modeling of complex objects with non-rectangular topology. Due to the particular advantages of triangular parametric surfaces, they have wide application and prospect in computer aided design and reverse engineering. The interpolation or approximation problem for reconstructing an arbitrary topological parametric surface from scattered data points or polygonal mesh is one of the significant research areas. This paper deals with the approximation of triangular B-spline surfaces based on a local geometric fitting algorithm and an inverse Loop subdivision scheme. The reconstructed triangular B-spline with the low degree crosses through most of the given data points of an initial triangular mesh. The accuracy of the obtained triangular B-spline surfaces can he carried out by changing the position of control points in the local geometric algorithm as well as a number of the inverse subdivision times. Finally, we demonstrate the effectiveness of the proposed method with some experimental examples.

关键词： Parametric surface triangular B-splines geometric algorithm inverse subdivision approximation

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Exact and efficient search-based wall distance algorithm for partitioned unstructured grids

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COMPUTERS & FLUIDS 2025年 288卷

作者： Oh, Jun Seok Kung, Tae Yoon Kim, Kyu Hong Seoul Natl Univ Dept Aerosp Engn 105-401 Gwanak Ro Seoul 08826 South Korea Seoul Natl Univ Inst Adv Aerosp Technol Seoul 08826 South Korea

In this paper, we develop a novel search-based wall distance calculation algorithm. The algorithm is highly efficient and satisfies the crucial requirement of exactness in wall distance calculations, taking into account the full geometry of the discretized surface. Unlike conventional search-based algorithms that use element-wise bounding boxes or auxiliary grids, the developed algorithm employs only a set of zero-dimensional reference points representing the elements of the discretized surface. Reference points can be chosen as the centers of faces, the centers of edges, or the vertices. The conservative relation between the approximate distance using one of these references and the exact distance is established, allowing for the efficient extraction of element candidates using only low-level information. The algorithm does not require complex pre-processing of the surface or any information about the query points, ensuring high software modularity. An intuitive load balancing procedure is also proposed to address the load imbalance arising from partitioning-based parallelization. Numerical test demonstrates that the developed algorithm shows three orders of magnitude speed-up compared to exhaustive search and one to two orders of magnitude speed-up compared to other search-based algorithms. It also shows high parallel scalability on partitioned meshes, indicating its feasibility for large-scale problems.

关键词： geometric algorithm Minimum wall distance Tree-based algorithm Computational fluid dynamics Unstructured grids

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