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研究生： 陳守恒
Shou-Heng Chen
論文名稱： NURBS曲面編修與平滑化技術
NURBS Shape Modification and Fairing
指導教授： 賴景義
Jiing-Yih 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： 93
語文別： 中文
論文頁數： 111
中文關鍵詞： 曲面編修 、拘束最佳化 、曲面平滑 、自由曲面造型 、NURBS
外文關鍵詞： Constrained Optimization, NURBS, Free-Form Deformation, Shape Modification, Shape Fairing
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    • 在整個CAD模型的建構過程當中，自由曲面造型所佔的比例越來越重，同時，為了因應各種原因，去要求自由曲面的造型必需能夠局部的自由加以變更，使其符合各式設計需求，為目前熱門的討論主題。本論文的目的在於提出一套曲面自由編修(Free-form deformation)的演算法，並且能夠達到設計變更的目的，另外也探討曲面平滑(Fairing)的主題，以求在編修的同時，能夠得到較佳的曲面品質。
    首先基於NURBS的數學模型來作分析，將其在曲面變更時所求出的各式解之限制條件以及改善方法作一討論。接著配合最佳解演算法來做為曲面變更的核心，最後在以拘束條件的加入方法作為最後的步驟。經由以上所提出的演算法，將能夠提供一個曲面造型編修技術的基礎流程。

    In CAD modeling Systems, the proportion of Free-Form surface is heavier and heavier. Meanwhile, in order to solve various kinds of demands of designing, we have to change ordinary CAD model. The purpose of this research lies in proposing an algorithm and procedure of NURBS shape deformation, via various combination of constrain condition to control shape deformation. At first, we do analysis of NURBS mathematics model and construct various types of limiting conditions. Then three kinds of methods be proposed, for improve limiting conditions before shape operation. When we start to determine shape parameter of modification, this paper presents an optimization algorithm method. It is the core of whole procedure. Second step, we can not only use basic shape modification function but also combine the constrained condition. At the end step, further fairing methods were used to improve shape quality in shape modification process.Based on this discussion, provide a integrated procedure for shape modification method by means of which one can control shape arbitrarily.

    摘要.......................................... I 英文摘要..................................... II 致謝........................................ III 目錄......................................... IV 圖目錄........................................VI 表目錄..................................... VIII 第一章 緒論....................................1 1.1 前言.......................................1 1.2 文獻回顧...................................2 1.3 研究目的...................................6 1.4 論文架構...................................7 第二章 曲面自由造型編修方法流程................9 2.1 前言.......................................9 2.2 NURBS之曲面編修............................9 2.3 曲面編修流程..............................12 2.3.1 決定曲面UV值............................15 2.3.2 判斷限制條件............................15 2.3.3 改善限制條件............................20 第三章 曲面自由造型編修演算法.................26 3.1 前言......................................26 3.2 基本曲面編方法............................27 3.3 參數最佳化演算法..........................34 3.4 曲面編修方法推導與應用延伸................37 3.5 結論......................................41 第四章 曲面品質改善方法.......................42 4.1 前言......................................42 4.2 各式曲面品質量化介紹......................43 4.3 曲面品質量化於平滑化......................45 4.4 Lagrange 乘數法與曲面品質改善.............58 4.5 曲面編修與品質考量........................64 第五章 範例與應用說明.........................70 5.1 目前市面上軟體之曲面編修功能..............70 5.2 本研究之各式編修方法......................81 5.3 綜合比較與整理............................93 第六章 結論與未來展望.........................94 6.1 結論......................................94 6.2 未來展望..................................96 參考文獻......................................98

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