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研究生： 吳新逸
Wu, Hsin-I
論文名稱： 空間中具曲率連續的B-Spline封閉曲線建構
A Novel Method for G2 Continuity in 3D B-Spline Closed Curve Construction
指導教授： 許來興
Hsu, Lai-Hsing
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2004
畢業學年度： 92
語文別： 英文
論文頁數： 104
中文關鍵詞： 逆向工程 、曲線嵌合方法 、B-spline曲線 、G2平滑程度 、電腦輔助設計 、平滑封閉曲線
外文關鍵詞： reverse engineering, B-splines, curve interpolation, G2 continuity, smooth closed curves, CAD
相關次數： 點閱：107  下載：2 
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    • 　　近二十年來，隨著電腦硬體的快速強化，電腦輔助設計與製造(CAD/CAM)系統應聲演進，產品的設計程序也轉變為現今被廣泛使用的電腦輔助設計。曲面建構必須立基於良好的曲線設計，曲線建構的平滑程度可決定後續曲面建構的良莠。

    　　有時設計者得設計封閉曲線。以凸輪輪廓設計為例，使用者必須利用CAD軟體中的曲線建構方法，設計各個封閉曲線，進而通過各層曲線建立完整凸輪曲面。若是封閉曲線的平順程度不足，必定會造成凸輪模型表面的不平滑。

    　　本文提出三維空間中具有G2平滑程度封閉曲線的建構方法。此方法應用廣為CAD設計者所使用的B-spline曲線，利用曲線嵌合方法在三維空間中使得曲線依序通過設計者輸入的輪廓點，以設計封閉的剖面曲線。B-spline的運算使得建構出來的曲線與曲面資料具有檔案連結性；因為可轉換為標準的檔案格式如IGES和STEP，因此可進行後續的設計和製造。此方法不僅僅可應用在電腦輔助設計流程中，亦可應用於逆向工程中的剖面曲線建構。

    　　In the last two decades, the technology of computer-aided design and manufacturing (CAD/CAM) systems has evolved considerably due to the rapid growth in the development of computer hardware. Therefore, the design work changed from styling to CAD. The most complicated subject in CAD would be the design of surface and that is the reason why commercial CAD/CAM software vendors always emphasize the ability for constructing and editing surfaces. In general, a preferable surface is based on well-designed smooth curves.

    　　Sometimes a closed curve is needed. For example, when a designer designs the configuration of a cam wheel, closed curves are constructed and the cam wheel surface model passing through all curves is built. If unsmoothness occurs on curves, the surface would lose smoothness as well.

    　　In this study, a novel method that constructs smooth closed curves with G2 continuity is proposed. The method of B-spline curve interpolation is applied to construct the closed curve passing through the given points. Since B-splines are parts of graphics exchange standards such as IGES and STEP, so the curves and surfaces can be transmitted to commercial CAD/CAM systems for further engineering activities, e.g., analysis and manufacturing. The proposed algorithm can not only be employed in CAD systems but can also be employed in the reverse-engineering (RE) technique.

    Abstract I Abstract in Chinese II Table of Contents III List of Tables V List of Figures VI Notation IX Chapter 1 Introduction 1 1.1 Preface 1 1.2 Related Works Survey 2 1.3 Thesis Objective 6 1.4 Thesis Organization 7 Chapter 2 Fundamental Principles 9 2.1 Computer-Aided Geometric Design 9 2.1.1 Shape Design Process 10 2.1.2 Reverse Engineering Process 12 2.2 Curve and Surface Design 16 2.2.1 B-Spline Curves and Surfaces Construction 16 2.2.2 Interpolation of B-Spline Curves and Surfaces 19 2.2.3 Lofted Surface Construction 23 2.3 Definitions of Continuity 27 2.3.1 Geometric Continuity 27 2.3.2 Parametric Continuity 29 2.3.3 Continuity Verification of B-Spline Closed Curves and Surfaces 31 Chapter 3 The Construction of a Smooth B-Spline Closed Curve 44 3.1 2-D B-spline Closed Curve Establishment 45 3.1.1 Non-Smooth Closed Curve Interpolation 46 3.1.2 Planar Closed Curve Interpolation 47 3.2 3-D B-spline Closed Curve Establishment 59 3.2.1 Non-Planar Closed Curve Interpolation 59 3.2.2 General Equations and Solutions 61 3.2.3 Computer-Aided Operating Algorithms 69 3.2.4 Advanced Process for Curve Continuity Requirement 73 Chapter 4 Case Study 78 4.1 Operation Procedure of the Prototype System 78 4.2 Case 1- Computer Mouse Configuration Design 81 4.3 Case 2- Residual Limb Model Reconstruction 86 4.4 Case 3- Toy Model Reconstruction 90 Chapter 5 Conclusions and Future Work 95 5.1 Conclusions and Discussions 95 5.2 Recommendations for Future Work 98 References 99 Appendix A- The Solving and the Solution for Cx, Cy, and Cz obtained by using Mathematica 102 Appendix B- Prototype System Interface Functions 103

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