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Design for rational B̀�zier harmonic and biharmonic surfaces

Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao/Journal of computer-Aided Design and computer graphics 2010年第8期22卷 1331-1338页

作者： Shi, Yanhui Wang, Guojin Institute of Computer Graphic and Image Processing Department of Mathematics Zhejiang University Hangzhou 310027 China State Key Laboratory of CAD and CG Zhejiang University Hangzhou 310027 China

Considering the complexity of the rational B´zier harmonic surfaces, in this paper an approximated algorithm for constructing rational B´zier harmonic surfaces is proposed. By using polynomial curves and surfaces to approximate rational curves and surfaces and constructing B´zier harmonic surfaces with the Monterde method, the rational B´zier harmonic surface modeling problem can be transformed into an optimization problem of how to minimize a nonlinear function with a limited number of variables under a linear constrained condition. The proposed algorithm is also extended into constructing the rational B´zier biharmonic surfaces. The method is validated by examples of biharmonic surfaces of degree three and harmonic surfaces of degree two and three .The experimental results show that the algorithm proposed performs well in the application of constructing rational B´zier harmonic surfaces and biharmonic surfaces.

关键词： Polynomial approximation

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Adaptive triangular mesh coarsening with centroidal Voronoi tessellations

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2009年第4期10卷 535-545页

作者： Zhen-yu SHU Guo-zhao WANG Chen-shi DONG Institute of Computer Graphics and lmage Processing Department of Mathematics Zhejiang University Hangzhou 310027 China Laboratory of Information and Optimization Technologies Ningbo Institute of Technology Zhejiang University Ningbo 315100 China

We present a novel algorithm for adaptive triangular mesh coarsening. The algorithm has two stages. First, the input triangular mesh is refined by iteratively applying the adaptive subdivision operator that performs a so-called red-green split. Second, the refined mesh is simplified by a clustering algorithm based on centroidal Voronoi tessellations (CVTs). The accuracy and good quality of the output triangular mesh are achieved by combining adaptive subdivision and the CVTs technique. Test results showed the mesh coarsening scheme to be robust and effective. Examples are shown that validate the method.

关键词： Triangular mesh Mesh coarsening Surface subdivision Centroidal Voronoi tessellations （CVTs）

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Weighted approximate developable minimal B̀�zier surfaces

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Journal of Computational Information Systems 2009年第4期5卷 1047-1052页

作者： Xu, Gang Wang, Guozhao Chen, Xiaodiao College of Computer Hangzhou Dianzi University Hangzhou 310018 China Institute of Image Processing and Computer Graphics Department of Mathematics Zhejiang University Hangzhou 310027 China

Developable surfaces and minimal surfaces have been employed in many areas such as sheet-metal and plate-metal based industries, architecture, aviation and ship manufacture. However, nonplanar minimal surfaces cannot be developable surfaces. In this paper, we firstly introduce the new concept of weighted approximate developable minimal surface. It contains approximate developable surface and approximate minimal surface as special cases. For the case of tensor product B´zier surface, given the boundary control points, the interior control points can be constructed using nonlinear optimization algorithm. We mainly adopt the trust-region method in this paper. We also present several examples and the corresponding numeric results on Gaussian curvature and mean curvature. © 2009 Binary Information Press August, 2009.

关键词： Plate metal

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Geometric parameters based cubic PH curve interpolation and approximation

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Journal of Information and Computational Science 2009年第6期6卷 2423-2432页

作者： Cheng, Min Wang, Guojin Department of Mathematics Zhejiang University Zhejiang Hangzhou 310000 China College of Science Zhejiang University of Technology Zhejiang Hangzhou 310000 China Institute of Computer Graphics and Image Processing Zhejiang University Zhejiang Hangzhou 310000 China

The Pythagorean-hodograph curves offer unique computational advantages in computer aided design and manufacturing. In this paper, geometric parameters based cubic PH curve interpolation and approximation algorithms are presented. The essential geometric parameters include the ratio ρ of the adjacent control polygon legs, the control polygon angle θ, the first control polygon leg L, the included angle δ between the first control polygon edge and the edge joining the origin O and the first control point, as well as the coefficient Dir of curve rotation. Furthermore the problem of PH curve approximation with endpoints interpolation to a cubic non-PH curve is studied, including the algorithms based on different geometric parameters input {δ, θ}, {ρ, θ} and {ρ, δ} respectively. © 2009 Binary Information Press.

关键词： Approximation algorithms

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Learning a nonlinear color distance metric for the identification of skin immunohistochemical staining

Learning a nonlinear color distance metric for the identific...

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2009 22nd IEEE International Symposium on computer-Based Medical Systems, CBMS 2009

作者： Sobieranski, Antonio Carlos Neto, Sylvio Luiz Mantelli Coser, Leandro Comunello, Eros Von Wangenheim, Aldo Cargnin-Ferreira, Eduardo Di Giunta, Gabriella LAPIX Laboratory of Image Processing and Computer Graphics UFSC Federal University of Santa Catarina Brazil CPTEC Center for Weather Forecasts and Environment Studies INPE - Brazilian Institute for Space Research Brazil EGC Knowledge Engineering Department UFSC - Federal University of Santa Catarina Brazil MCA Graduate Program in Applied Computer Science UNIVALI - Itajai Valley University Brazil Laboratory of Histological Markers Department of Biology Embriology and Genetics UFSC - Federal University of Santa Catarina Brazil Pathology Service UFSC - Federal University of Santa Catarina Brazil

ISBN: (纸本)9781424448784

This paper presents a semiautomatic method for the identification of immunohistochemical (IHC) staining in digitized samples. The user trains the system by selecting on a sample image some typical positive stained regions that will be used as a reference for the construction of a distance metric. In this learning process, the global optimum is obtained by induction employing higher polynomial terms of the Mahalanobis distance, extracting nonlinear features of the IHC pattern distributions. The results of the proposed method showed a high correlation to a pathologist's manual analysis, which was used as a golden standard, presenting a more robust discrimination between stained and non-stained areas with little bias. © 2009 IEEE.

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Free-Form Deformation with Rational DMS-Spline Volumes

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Journal of computer Science & Technology 2008年第5期23卷 862-873页

作者：徐岗汪国昭陈小雕 Institute of Computer Graphics and Image Processing Zhejiang University Department of Mathematics Zhejiang University College of Computer Science Hangzhou Dianzi University INRIA Nancy France

In this paper, we propose a novel free-form deformation （FFD） technique, RDMS-FFD （Rational DMS-FFD）, based on rational DMS-spline volumes. RDMS-FFD inherits some good properties of rational DMS-spline volumes and combines more deformation techniques than previous FFD methods in a consistent framework, such as local deformation, control lattice of arbitrary topology, smooth deformation, multiresolution deformation and direct manipulation of deformation. We first introduce the rational DMS-spline volume by directly generalizing the previous results related to DMS-splines. How to generate a tetrahedral domain that approximates the shape of the object to be deformed is also introduced in this paper. Unlike the traditional FFD techniques, we manipulate the vertices of the tetrahedral domain to achieve deformation results. Our system demonstrates that RDMS-FFD is powerful and intuitive in geometric modeling.

关键词： free-form deformation rational DMS-spline volume control lattice of arbitrary topology multiresolution deformation direct manipulation

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The structure of uniform B-spline curves with parameters

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Progress in Natural Science:Materials International 2008年第3期18卷 303-308页

作者： Juan Cao , Guozhao Wang institute of image processing and computer Graphic, department of mathematics, Zhejiang University, Hangzhou 310027, China Institute of Image Processing and Computer Graphic Department of Mathematics Zhejiang University Hangzhou 310027 China

The shape-adjustable curve constructed by uniform B-spline basis function with parameter is an extension of uniform B-spline curve. In this paper, we study the relation between the uniform B-spline basis functions with parameter and the B-spline basis functions. Based on the degree elevation of B-spline, we extend the uniform B-spline basis functions with parameter to ones with multiple parameters. Examples show that the proposed basis functions provide more flexibility for curve design.

关键词： Uniform B-spline Shape parameter Shape-adjustable curve Degree elevation

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Computational fluid flow simulation on body fitted mesh geometry with IBM cell broadband engine architecture

Computational fluid flow simulation on body fitted mesh geom...

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European Conference on Circuit Theory and Design, ECCTD

作者： Zoltan Nagy Andras Kiss Sandor Kocsardi Arpad Csik Computer and Automation Research Institute Hungarian Academy of Sciences Changzhou China Department Information Technology Pázmány Péter Catholic University Changzhou China Department Image Processing and Neurocomputing University of Pannonia Veszprem Hungary Department of Mathematics and Computational Sciences Széchenyi István University Gyor Hungary

The solutions of partial differential equations (PDEs) play a key role in today's real world simulations. Computational Fluid Dynamics (CFD) is an important part of this area, which involves the problem of gas or fluid flow over different obstacles, e.g., air flow around vehicles, buildings, or the flow of water in the oceans. In engineering applications the temporal evolution of non-ideal, compressible fluids is quite often modeled by the system of Navier-Stokes equations. They are a coupled set of nonlinear hyperbolic partial differential equations and form a relatively simple, yet efficient model of compressible fluid dynamics. In the paper the implementation of a CFD on Body Fitted Mesh geometry on the Cell Broadband Engine is described. An arbitrary surface can be more easily simulated on body fitted mesh than on rectangular computation domain.

关键词： Fluid flow Computational modeling Solid modeling Computational geometry Engines computer architecture Computational fluid dynamics Partial differential equations Marine vehicles Buildings

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ωB-splines

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Science in China(Series F) 2008年第8期51卷 1167-1176页

作者： FANG Mei'E WANG GuoZhao Institute of Computer and Image Processing and the Department of Mathematics Zhejiang University Hangzhou 310027 China College of Computer Hangzhou Dianzi University Hangzhou 310018 China

A new kind of spline with variable frequencies, called ωB-spline, is presented. It not only unifies B-splines, trigonometric and hyperbolic polynomial B-splines, but also produces more new types of splines, ωB-spline bases are defined in the space spanned by {coso） t, sino）t, ], t, ..., t^n, ...} with the sequence of frequencies m where n is an arbitrary nonnegative integer, ωB-splines persist all desirable properties of B-splines. Furthermore, they have some special properties advantageous for modeling free form curves and surfaces.

关键词： ωB-splines frequencies B-splines trigonometric polynomial B-splines hyperbolic polynomial B-splines

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Extended Cubic Uniform B-spline and α-B-spline

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自动化学报 2008年第8期34卷 980-983页

作者： XU Gang WANG Guo-Zhao Institute of Computer Graphics and Image Processing Department of Mathematics Zhejiang University Hangzhou 310027 P. R. China

花键曲线和表面在 CAD 和计算机图形起一个重要作用。在这份报纸，我们建议立方的一致 B 花键的几延期。然后，我们在场插入内推的延期 -B-spline 基于新 B 花键和单个相配技术。延期的优点是他们有全球、本地的形状参数。而且，我们也... 详细信息

花键曲线和表面在 CAD 和计算机图形起一个重要作用。在这份报纸，我们建议立方的一致 B 花键的几延期。然后，我们在场插入内推的延期 -B-spline 基于新 B 花键和单个相配技术。延期的优点是他们有全球、本地的形状参数。而且，我们也在数据插值和多角形的形状变丑调查他们的应用。

关键词：计算机技术 CAD 图象处理技术几何图形

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