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A subdivision algorithm FOR AXISYMMETRIC SECTIONS

COMPUTER-AIDED DESIGN 1984年第6期16卷 329-334页

作者： TAN, ST CHAN, KC Department of Mechanical Engineering University of Hong Kong Pokfulam Road Hong Kong

In the generation of curved surfaces through a subdivision process, Sabin and Doo applied and extended Chaikin's algorithm to three dimensions by using linear combinations of the vertices of a polyhedron. A similar smoothing subdivision algorithm was brought out by Catmull and Clark. This paper describes an alternative algorithm which uses a similar approach but applies to sections of axisymmetric objects. It shows that axisymmetric free-formed surfaces can be generated easily and effeciently.

关键词： subdivision algorithm curved surface generation axisymmetric sections

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subdivision algorithm for optimal control

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2013年第8期23卷 932-944页

作者： Taraba, Peter Slovak Univ Technol Bratislava Fac Elect Engn & Informat Technol Inst Control & Ind Informat Bratislava Slovakia

We present a novel algorithm for optimal control of nonlinear systems based on a subdivision algorithm. The algorithm presented in this paper is an alternative to a set-oriented approach for optimal feedback stabilization. We compare the proposed algorithm to the set-oriented approach, contrast these two approaches, and use examples to show that the new algorithm produces comparable results. Also, we demonstrate by example that we receive a precomputed optimal solution. The main contribution of the paper is understanding how cost function improves with further subdivision of state space and smaller memory footprint of the final solution in comparison with set-oriented approach. Copyright (c) 2012 John Wiley & Sons, Ltd.

关键词： optimal control region of convergence subdivision algorithm attractors of dynamical systems genetic algorithms shooting algorithm

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subdivision algorithm of Quartic Q-Ball Curves with Shape Parameters 3

Subdivision Algorithm of Quartic Q-Ball Curves with Shape Pa...

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3rd IEEE International Conference on Image, Vision and Computing (ICIVC)

作者： Qin, Xinqiang Lv, Dan Hu, Gang Wu, Junli Xian Univ Technol Sch Sci Xian Shaanxi Peoples R China

ISBN: (纸本)9781538649916

With the aim to tackle the problems of the local shape adjustment and shape control of quartic Q-Ball curves, we propose two direct subdivision algorithms for quartic QBall curves, which include coefficient subdivision and tangent subdivision. According to the two subdivision algorithms, the corresponding modeling examples are respectively given. Studies show that the sub-curves are independent and have no influence on other sub-curves in shape adjustment, which realize the local shape adjustment of the quartic Q-Ball curves and maintain the geometric meaning of shape parameters. The modeling examples show that the proposed subdivision algorithms are effective and easy to implement, which greatly improve the abilities to express complex curves in shape design by adjusting the position and shape of quartic Q-Ball curves.

关键词： quartic Q-Ball curves shape parameters subdivision algorithm shape design

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A Real-time Parallel Catmull-Clark subdivision algorithm on GPU

A Real-time Parallel Catmull-Clark Subdivision Algorithm on ...

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9th International Conference for Young Computer Scientists

作者： Zhang, Jingqiao Ji, Zhuoer Shanghai Univ Sch Comp Engn & Sci Shanghai 200072 Peoples R China

ISBN: (纸本)9781424441983

A novel real time Catmull-Clark subdivision algorithm on GPU is proposed. The algorithm divides a complicated 3D model into several kinds of simple fragments, and the subdivision masks of these simple fragments can be predefined. After the division of 3D models, these fragments are independent each other, thus can he subdivided in parallel in GPU. The proposed algorithm combines subdivision algorithm with programmable GPU and fully takes advantage of SPs' (stream processors) great ability of computation and parallel process. So the algorithm is more efficient.

关键词： Programmable GPU subdivision algorithm parallel stream processor

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Research on the subdivision algorithm about the approximate development of the undevelopable surfaces 3

Research on the subdivision algorithm about the approximate ...

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3rd International Conference on Advanced Engineering Materials and Architecture Science (ICAEMAS)

作者： Jiang, Fen Luo, Zhenhua Wuhan Univ Technol Huaxia Coll Wuhan 430223 Peoples R China

ISBN: (纸本)9783038352679

Modern industrial manufacturing contains different kinds of surface modeling, which is processed by planar materials. For the principle of the most efficient materials using, how to optimize subdivision undevelopable surface before development becomes an important topic in CAM design and manufacturing industries. The paper transforms the basic parameters of surface before subdivision, and gives the standards of subdivision surfaces. We proved the feasibility and the existence of triangle subdivision algorithm. By introducing double parameters MObius transformation, the subdivision surface is more uniform. At last, numerical examples prove that the algorithm about the approximate development of the undevelopable surfaces is effective and practical.

关键词： Undevelopable Surface subdivision algorithm MObius Transformation Triangle subdivision

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subdivision algorithm of Quartic λ-Bézier Curves with Shape Parameters

Subdivision Algorithm of Quartic λ-Bézier Curves with Shap...

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International Conference on Image, Vision and Computing (ICIVC)

作者： Xin Sun Yu Qiao Huinan Li School of Art and Design Xi’an University of Technology Xi’an China School of Science Xi’an University of Technology Xi’an China

ISBN: (纸本)9781728123264

This paper proposes a subdivision algorithm for quartic λ-Bézier curves with shape parameter. Firstly, the quartic λ-Bézier curves are converted to quartic traditional Bezier curves, then we solve the control points of the sub-curved curve after the subdivision by using the traditional Bezier curves so that it can remain shape unchanged before and after subdivision, that is, the expression of the curve is the same. Finally, it can be converted to the explicit combination expression of quartic λ-Bézier curves control points. The examples show that the proposed method is effective and easy to implement, which greatly enhances the ability to constructing complex surface by using quartic generalized λ-Bézier curves.

关键词： Quartic λ-Bezier curves Shape parameter subdivision algorithm Curves design shape parameter Quartic Curves subdivisions control point

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A subdivision algorithm for phase equilibrium calculations at high pressures

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BRAZILIAN JOURNAL OF CHEMICAL ENGINEERING 2007年第4期24卷 611-622页

作者： Corazza, M. L. Corazza, F. C. Cardozo Filho, L. Dariva, C. Univ Reg Integrada Alto Uruguai & Missoes Dept Food Engn BR-99700000 Erechim RS Brazil Univ Estadual Maringa Dept Chem Engn BR-87020900 Maringa Parana Brazil Univ Tiradentes Inst Res & Technol BR-49031490 Aracaju Brazil

Phase equilibrium calculations at high pressures have been a continuous challenge for scientists and engineers. Traditionally, this task has been performed by solving a system of nonlinear algebraic equations originating from isofugacity equations. The reliability and accuracy of the Solutions are strongly dependent oil the initial guess, especially due to the fact that the phase equilibrium problems frequently have multiple roots. This work is focused on the application of a subdivision algorithm for thermodynamic calculations at high pressures. The subdivision algorithm consists in the application of successive subdivisions at a given initial interval (rectangle) of variables and a systematic test to verily the existence of roots in each subinterval. If the interval checked passes in the test, then it is retained;otherwise it is discharged. The algorithm was applied for vapor-liquid, solid-fluid and solid-vapor-liquid equilibrium as well as for phase stability calculations for binary and multicomponent systems. The results show that the proposed algorithm was capable of finding all roots of all high-pressure thermodynamic problems investigated. independent of the initial guess used.

关键词： subdivision algorithm phase equilibrium phase stability thermodynamic modeling

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A Real-time Parallel Catmull-Clark subdivision algorithm on GPU

A Real-time Parallel Catmull-Clark Subdivision Algorithm on ...

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The 9th International Conference for Young Computer Scientists(第九届国际青年计算机大会)

作者： Jingqiao Zhang Zhuoer Ji School of Computer Engineering and Science Shanghai University Shanghai 200072 P.R. China

A novel real time Catmull-Clark subdivision algorithm on GPU is proposed. The algorithm divides a complicated 3D model into several kinds of simple fragments, and the subdivision masks of these simple fragments can be predefined. After the division of 3D models, these fragments are independent each other, thus can be subdivided in parallel in GPU. The proposed algorithm combines subdivision algorithm with programmable GPU and fully takes advantage of SPs' (stream processors) great ability of computation and parallel process. So the algorithm is more efficient.

关键词： Programmable GPU subdivision algorithm parallel stream processor.

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Solving two point boundary value problems by interpolatory subdivision algorithms

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 1996年第3-4期60卷 279-294页

作者： Qu, RB Agarwal, RP [a] Department of Mathematics National University of Singapore Singapore

Smooth interpolatory subdivision algorithms for the generation of curves are used to solve two point boundary value problems. A method of collocation is formulated for linear second order two point boundary value problems. It is proved that the algorithms produce smooth continuous solutions provided the algorithms are chosen appropriately. Error estimates for uniform partitions are also investigated. Finally, some numerical examples are given to show the convergence of the algorithms.

关键词： boundary value problems approximation method of collocation interpolation subdivision algorithm

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Smooth surface interpolation to scattered data using interpolatory subdivision algorithms

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 1996年第3期32卷 93-110页

作者： Qu, R Agarwal, RP Department of Mathematics National University of Singapore Singapore 119260 Singapore

In this paper, a smooth interpolatory subdivision algorithm for the generation of interpolatory surfaces (GC(1)) over arbitrary triangulations is constructed and its convergence properties over nonuniform triangulations studied. An immediate application of this algorithm to surface interpolation to scattered data in R(n), n greater than or equal to 3 is also studied. For uniform data, this method is a generalization of the analyses for univariate subdivision algorithms, and for nonuniform data, an extraordinary point analysis is proposed and a local subdivision matrix analysis presented. (-)It is proved that the subdivision algorithm produces smooth surfaces over arbitrary networks provided the shape parameters of the algorithm are kept within an appropriate range. Some error estimates for both uniform and nonuniform triangulations are also investigated. Finally, three graphical examples of surface interpolations over nonuniform data are given to show the smoothing interpolating process of the algorithm.

关键词： triangulation approximation surface interpolation scattered data interpolation subdivision algorithm

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