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研究生： 胡家維
CHIA-WEI HU
論文名稱： 曲面融合及相關技術之研究
Study of surface blending and related technique
指導教授： 賴景義
CHING-YI LAI
口試委員:
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
畢業學年度： 91
語文別： 中文
論文頁數： 127
中文關鍵詞： 剪切曲面 、連續性 、曲面交線 、融合曲面 、曲面偏移
外文關鍵詞： blending surface, trimmed surface, continuity, intersection curve of surfaces, surface offset
相關次數： 點閱：12  下載：0 
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    • 逆向工程(Reverse engineering)主要的目的在於由實體模型重建曲面模型，而曲面接合技術在重建曲面模型的過程中佔有舉足輕重的地位，在複雜度高且表面不規則的自由曲面(Free-form surface)接合處理上較難以傳統方式來完成，因此藉由數學模型將傳統模型數值化(Digitization)的方法來處理會比較準確且有效率，並且以CAD系統處理曲面的編修、設計及分析比傳統方式容易且有效率。
    本文以建構兩曲面之等半徑融合曲面為主軸，研究建構融合曲面過程所需技術及理論以及融合曲面與原始曲面之剪切關係，並且以剪切曲面形式處理經過剪裁曲面，透過融合曲面與原始曲面接合處位置及斜率之連續性分析融合曲面之品質。其中包含曲面偏移、曲面交線等演算方法，並討論各演算法使用時機及處理的適用性。

    The main purpose of Reverse engineering is reconstructing surface model from the real object. However, in the process of reconstructing surface model, surface connecting technique plays a decisive role, and it is hard to merge Free-from surface in traditional way, especially in complexity and irregular one. For the reason, made the traditional model Digitization by using Mathematics model is more exact and efficient, and comparing to traditional way, using CAD system to edit, design and analyze surface is easier and expeditious.
    This research focuses on constructing constant radius blending surface of two surfaces. It investigates the need of technique and theory in the process of constructing blending surface and the relation of trimming between blending surface and original surfaces. Trimmed surface represents the surface which has been trimmed, and then analyzing the quality of blending surface from the connecting position of blending surface and original surface and the continuity of slope. Such algorithms, including surface offset and intersection curve of surfaces and it also algorithms the timing and appropriateness of using each calculation.

    ABSTRACT I 摘要 II 誌謝 III 目錄 IV 圖目錄 VII 表目錄 XI 第一章 緒論 1 1.1 前言 1 1.2 文獻回顧 3 1.2.1 曲面偏移(Surface offset) 3 1.2.2 曲線/曲面 嵌合(Fitting)及插值(Interpolation) 4 1.2.3 曲面/曲面交線(Surface and Surface Intersection Curve) 5 1.2.4 融合曲面(Blending Surface) 5 1.2.5 剪切曲面(Trimmed Surface) 6 1.2.6 數值方法 7 1.3 研究目的與方法 7 1.4 論文架構 10 第二章 曲面偏移研究 12 2.1 前言 12 2.2 偏移曲面方法 13 2.3 標準型態曲面偏移 15 2.3.1 計算曲面之法向量 16 2.3.2 計算偏移距離 16 2.4 自由曲面偏移 17 2.4.1 自由曲面上採樣點的選擇 22 2.5 曲面嵌合(Surface fitting) 26 2.5.1 曲面嵌合方法 26 2.5.2 曲面嵌合運算流程 27 2.5.2 偏移後之採樣點與嵌合產生之曲面誤差分析 28 2.6 與其他商用軟體產生偏移曲面誤差分析 28 第三章 曲面交線理論 37 3.1 前言 37 3.2 曲面交線方法 37 3.2.1 曲面分割出矩形網格及三角形網格 39 3.2.2 直線與三角形交點 41 3.2.3 Powell數值方法 45 3.2.4 使用Powell由近似交點搜尋準確的交點 51 第四章 建立融合曲面 60 4.1 前言 60 4.2 建構圓錐曲線(Construct conic curve) 60 4.3 建構融合曲面 64 4.3.1插值法(Interpolation)建構融合曲面 66 4.3.2 曲面插值決定節點方法 66 4.4 實例 69 4.5 融合曲面品質檢驗 76 第五章 剪切曲面建立及應用 84 5.1 前言 84 5.2 剪切曲面之結構 84 5.3 融合曲面與原始曲面能建構的剪切曲面種類 86 5.4.1 判斷正確原始曲面經剪切後需保留的部分 88 5.4.2 剪切曲面2D邊界判定 90 5.5 融合曲面與原始曲面產生剪切曲面實例 94 第六章 剪切曲面建構融合曲面 99 6.1 前言 99 6.2 剪切曲面偏移 99 6.3 剪切曲面偏移實例與檢驗 103 6.4 曲線與曲線交點搜尋 106 6.5 剪切曲面交線組(有效區間判斷) 109 6.6 建構兩剪切曲面之融合曲面 115 第七章 結論及未來展望 123 7.1 結論 123 7.2 未來研究方向 123 參考文獻 125

    1. G.V.V. Ravi Kumar, K.G. Shastry, B.G. Prakash, “Computing non-self-intersecting of NURBS surfaces”, Computer-Aided Design, vol. 34, 2002, pp. 209-228.
    2. Les A. Piegl, Wayne Tiller, “Computing offsets of NURBS curves and surfaces1”, Computer-Aided Design, vol. 31, 1999, pp. 147-156.
    3. Malgorzata A. Kulczycka, Louis J. Nachman, “Qualitative and quantitative comparisons of B-spline offset surface approximation methods”, Computer-Aided Design, vol. 34, 2002, pp. 19-26.
    4. M. Alhanaty, M. Bercovier, “Shapes with offsets of nearly constant surface area”, Computer-Aided Design, vol. 31, 1999, pp. 287-296.
    5. WU-CHIH HU and HSIN-TENG SHEU, “Quadratic B-spline for Curve Fitting”, Proc. Natl. Sci. Counc. ROC(A), Vol. 24, No. 5, 2000. pp. 373-381.
    6. Karim Abdel-Malek and Harn-Jou Yeh, “On the determination of starting points for parametric surface intersection”, Computer-Aided Design, vol. 29, No.1 pp. 21-35, 1997.
    7. Hee-Seok Heo, Myung-Soo Kim, Gershon Elber, “The intersection of two ruled surfaces”, Computer-Aided Design, vol. 31, 1999, pp. 33-50.
    8. FUHUA CHENG, XUEFU WANG, B.A. BARSKY, “Quadratic B-Spline Curve Interpolation”, Computer and Mathematics with Applications, vol. 41, 2001, pp. 39-50.
    9. G. Pasko, A. Pasko, M. Ikeda, and T. Kunii, “Bounded Blending Operations”, Proceeding of the Shape Modeling International, 2002, (SMI’02)..4
    10. Kun Lung Hsu and Der Min Tsay, “Corner Blending of Free-Form N-sided Holes”, IEEE January/February, 1998.
    11. Markus Schichtel, “G2 Blend Surfaces and Filling of N-Sided Holes”, IEEE Computer Graphics & Applications, 1993.
    12. Erich Hartmann, “Numerical implicitization for intersection and Gn-continuous blending of surfaces”, Computer Aided Geometric Design, vol. 15, 1998, pp. 377-397.
    13. Johannes Wallner, Helmut Pottmann, “Rational blending surfaces between quadratics”, Computer Aided Geometric Design, vol. 14, 1997, pp. 407-419.
    14. Erich Hartmann, “Gn-blending with Rolling Ball Contact Curves”, IEEE Geometric Modeling and Processing, 2000, pp. 385.
    15. O.R?schel, “An Interpolation Subspline Scheme Related to B-Spline Techniques”, IEEE, 1997.
    16. 陳鵬任，逆向工程之曲面接合技術研究，國立中央大學機械工程所碩士論文，1998。
    17. 黃瑜玉，曲面量測資料之CAD模型重建及誤差分析，國立中央大學機械工程所碩士論文，1996。
    18. 翁文德，逆向工程之曲面模型重建技術發展，國立中央大學機械工程所博士論文，1999。
    19. 邱至意，3D曲面模型網格化之研究，國立中央大學機械工程所碩士論文，2002。
    20. Byoung K. Choi, Surface Modeling for CAD/CAM, ELSEVIER, 1991.
    21. Les Piegl, Wayne Tiller, The NURBS BOOK, Springer.
    22. William H. Press, Saul A. Teukolsky, William T. Vetterling, Brain P. Flannery, Numerical Recipes in C++ : The Art of Scientific Computing.
    23. Nathan Litke, Adi Levin, Peter Schr?der, “Trimming for subdivision surfaces”, Computer-Aided Design, vol. 18, 2001, pp. 463-481.
    24. WonJoon Chot, Nicholas M Patrikalakist and Jaime Peraire, ”Trimmed patches for surface tessellation”, Computer-Aided Design, vol. 30 No. 14, 1998, pp. 1077-1087.
    25. D.C.H. Yang, J.-J. Chuang, T.H. OuLee, ”Boundary-conformed toolpath generation for trimmed free-form surfaces”, Computer-Aided Design, vol. 35, 2003, pp. 127-139.

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