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研究生： 賴俊誠
Jiun-Cheng Lai
論文名稱： α-spline與NURBS雕塑曲面設計之研究
Studies on Sculpture Surface Design usingα-spline and NURBS Algorithms
指導教授： 歐石鏡
Shin-Ching Ou
口試委員:
學位類別： 碩士
Master
系所名稱： 資訊電機學院 - 電機工程學系
Department of Electrical Engineering
畢業學年度： 88
語文別： 中文
論文頁數： 64
中文關鍵詞： 雕塑曲面 、電腦輔助設計 、曲面
外文關鍵詞： NURBS, B-spline, α-spline, CAD
相關次數： 點閱：8  下載：0 
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    • 本論文探討α-spline與NURBS(Non-Uniform Rational B-spline)演算法的數學模式與特性，並實際應用在個人電腦(PC)的電腦輔助繪圖系統上。
    本論文在AutoCAD電腦繪圖輔助系統內建構雕塑曲面介面發展系統，以Visual C++為主要程式建構交談介面及運算程式，以增加運算速度。
    使用者可以在現有軟體AutoCAD上加入本文的雕塑曲面介面，即可設計複雜的造型，而不必重新學習其他具有雕塑曲面設計功能的電腦軟體，進而提升設計的效率。

    In this thesis we study the mathematics and properties on α-spline and NURBS(Non-Uniform Rational B-spline), and then implement it on computer-aided design system in PC.
    In Order to increase the efficiency and calculation speed, we use Visual C++ Language to construct sculpture surfaces on AutoCAD 2000 in an interactive way. The user can design complex sculpture surfaces such as die design, shoe shape, aircraft body, ship hull, automobile body, etc. in AutoCAD 2000.

    摘要……………………………………………………………I 目錄…………………………………………………………III 圖例索引………………………………………………………V 第一章 緒論……………………………………………………1 1.1引言………………………………………………………1 1.2文獻回顧…………………………………………………3 1.3研究目標…………………………………………………5 1.4論文架構…………………………………………………5 第二章 基本理論架構…………………………………………7 2.1 Bezier的數學模式和特性討論…………………………7 2.1.1 Bezier 曲線的數學模式…………………………7 2.1.2 Bezier 曲面的數學模式…………………………9 2.1.3 Bezier 的特性…………………………………10 2.2 B-Spline 的數學模式和特性討論…………………12 2.2.1 B-Spline 曲線的數學模式………………………12 2.2.2 B-Spline 曲面的數學模式………………………14 2.2.3 B-Spline 的特性………………………………16 2.3 NURBS 的數學模式和特性討論……………………18 2.3.1 NURBS 曲線的數學模式…………………………18 2.3.2 NURBS 曲面的數學模式…………………………19 2.3.3 NURBS 的特性……………………………………20 2.4α-Spline的數學模式和特性討論…………………………23 2.4.1α-Spline 曲線的數學模式…………………………23 2.4.2α-Spline 曲面的數學模式…………………………26 2.4.3α-Spline 的特性…………………………………28 第三章 曲面的設計與修改……………………………………29 3.1 曲面的設計方法…………………………………………29 3.1.1 給定控制點………………………………………29 3.1.2 插值法……………………………………………30 3.2 曲面的修改方法……………………………………33 3.2.1 控制頂點的位置…………………………………33 3.2.2 相對權重…………………………………………34 3.2.3 張力………………………………………………35 3.2.4 節向量……………………………………………36 第四章 系統架構介紹……………………………………40 4.1 CAD系統介紹……………………………………………40 4.2 使用工具介紹……………………………………………41 4.3 設計流程圖………………………………………………44 4.3.1 NURBS曲線的設計流程………………………………45 4.3.2 NURBS曲面的設計流程………………………………46 4.3.3 α-spline曲面的設計流程…………………………47 4.3.4 改變NURBS、α-spline控制頂點的設計流程………48 4.3.5 改變圖形變數的設計流程……………………………49 4.4 系統功能介紹……………………………………………50 第五章 結果的探討、結論以及未來研究方向與展望………52 5.1 結果探討…………………………………………………52 5.2 結論………………………………………………………60 5.3 未來研究方向與展望……………………………………60 參考文獻…………………………………………………………62

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