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研究生:鄭百盛
研究生(外文):Bai Cheng Zeng
論文名稱:用小波模式所產生之曲面網格
論文名稱(外文):The surface grid generation using wavelet modeling
指導教授:張桂芳張桂芳引用關係楊建成楊建成引用關係
學位類別:碩士
校院名稱:逢甲大學
系所名稱:應用數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2000
畢業學年度:88
語文別:英文
論文頁數:32
中文關鍵詞:網格生成系統小波
外文關鍵詞:Grid Generation SystemWavelet
相關次數:
  • 被引用被引用:1
  • 點閱點閱:214
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本論文以wavelet modeling中的DLG scheme 先產生構成曲面的基本曲線,然後在每個曲線所圍成的小cell 上以Transfinite Interpolation 產生其中的網格點,藉以構成整個曲面的基本曲面網格。如此所產生的曲面網格可做為各種不同大小網格及不同點分佈網格的根源。在以基本曲面網格為根本來產生各式各樣的網格過程中,必須將不同點分佈網格點內插入基本曲面網格中,本論文係先在計算域中求得網格點所對應的分佈點做為新的原始資料點,再依要求將所需的網格點內插入原來之網格中,重新建立新的曲面網格。
In this thesis, DLG scheme, a method of recursive (uniform) subdivision, is used to derive the basic smooth curves that form the basic surface grid and pass through the original surface points. This approach provides a new method of constructing a curve/surface grid. The linear transfinite interpolation is used to generate the grid in the cell and is good enough to satisfy the requirement of smooth grid generation. The curve approximation/interpolating is derived by the recursive subdivision scheme with linear-time complexity. The DLG scheme and the transfinite interpolation are combined into a scheme to generate grid.
Table OF CONTENT
LIST OF FIGURE
Chapter I INTRODUCTION
1.1 Background and Literature Review
1.2 Motivation
Chapter II THEORETICAL DEVELOPMENT
2.1 Grid Generation
2.2 Wavelets
2.3 Subdivision and DLG scheme
2.4 Transfinite Interpolation
2.4.1 Linear Transfinite Interpolation
2.4.2 Lagrange Transfinite Interpolation
Chapter III STRUCTURED GRID GENERATION
3.1 2D/3D Parametric Curve
3.1.1 The Algorithm of DLG
3.2 3D Grid Surface
3.3 Distribution Mesh and Geometric Catch Scheme
3.3.1 Geometric Catch Scheme
Chapter IV APPLICATIONS AND FUTURE WORK
4.1 Applications
4.2 Future Work
REFERENCES
[1] Thompson, J.F., Warsi, Z. U. A. and Mastin, C. W., : Numerical Grid Generation Foundations and Applications (North-Holland, 1985).
[2] Soni, B. K., “Grid Generation for Internal Flow Configuration”, Journal of Computers math. Application, Vol. 24,No.5/6,pp.191-201,1992
[3] Soni, B. K., “ GENIE: Generation of Computational Geometry-Grids for Internal Flow Configuration “, Proceedings of Numerical Grid Generation incomputational Fluid Mechanics ’88,Miami,FL, 1988.
[4] Schultz, Martin H., Spline Analysis, prentice-Hall, Series in Automatic Computation, Englewood Cliffs, New Jersey, USA,1973.
[5] Bezier P., The Mathematical Basis of the UNISURF CAD System, Butterworks, London,1986.
[6] Boehm W., Cubic B-spline curve s and surfaces in computeraided geometric design Computing, 19(1):29-34,1997.
[7] Roberts, A., “Automatic Topology Generation and Generalized B-spline Mapping “, Numerical Grid Generation, Ed. Joe F. Thompson, North-Holland, 465,1982.
[8] Chen Tzung Ching. “The Structured Grid Generation Using Beta-spline Curve /Surface Modeling”, master thesis, 1996.
[9] Eiseman, Peter R., and Smith, Robert, “Mesh Generation Using Algebraic Techniques”, Numerical Grid Generation Techniques, Ed. Robert E. Smith, NASA CP-2166,1980.
[10] Eric J. Stollnitz, Tony D. DeRose, David H. Salesin, “Wavelet for computer Graphics Theory and Application”, Morgan Kaufmann Publishes, Inc. 1996.
[11] G. Deslauriers, S. Dubuc, and D. Lemire, Derivees de l’interpolation
iterative de Lagrange et les ondelettes b-adiques de Cohen-Daubechies-Feauveau, Rapport technique EPM/RT-97/28, Departement de mathematique appliqués et de genie industriel, Ecole Ploytechnique de Momtreal, arrival 1997.
[12] 單維彰, “凌波初步 First concepts of wavelets’’.中央大學 數學系.
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