臺灣博碩士論文加值系統

隨著計算機科技的日益發達，電腦輔助相關軟體應用日漸頻繁。其中，電腦輔助設計在各大領域已到不可或缺的程度。例如在商用及軍事用途軟體中，CNC加工對電腦輔助設計有著高度的依賴。CNC加工刀具路徑的模擬過程中，與電腦輔助設計軟體中的曲面偏移這項功能有著密不可分的關聯。
本文將著重於曲面偏移的優化改良，結合採樣點曲面偏移法以及控制點曲面偏移法之優點。交互應用後準確地找出搜尋起始點並透過黃金分割搜尋法，得到圖形中特徵點位置，藉以提升曲面偏移的精準度。並透過邊界曲線偏移與基礎曲面偏移後經拓樸資料之整合，將此法延伸運用至剪切曲面偏移。

With the development of the computer science, computer aided software is applied in several areas. Especially, the computer aided design is applied on many industries. For example, the CNC machining is important in the manufacture of the product. In the progress of the NC tool path simulation, it should have the inseparable geometry association of offset curve and offset surface.
The research focuses on the improvement of the surface offset method, by combining the advantages of using the data point and the control point for the construction of the offset surface. After the mutually application, finding the start position of the critical point, and using the golden search for the optimum local maximum and minimum is the key achievement of the proposed thesis. From the topological structure of the boundary curve and the base surface, the proposed method can be extended to the offset of the trimmed surface.

致謝 i
摘要 iii
Abstract v
目錄 vii
圖目錄 x
表目錄 xiii
第一章 緒論 1
1.1 前言 1
1.2 研究動機 3
1.3 文獻回顧 4
1.4 研究內容 7
1.5 開發環境 9
1.6 論文架構 10
第二章 背景介紹 11
2.1 Bezier曲線與Bezier曲面 11
2.2 b-spline曲線與b-spline曲面 13
2.3 曲面特徵點搜尋 16
2.3.1 特徵點 16
2.3.2 曲面曲率 19
2.3.3 黃金分割搜尋 20
第三章 曲面偏移 23
3.1 曲面偏移介紹 23
3.2 藉採樣點之偏移法 24
3.2.1 採樣點數量計算 26
3.2.2 採樣點方式之不足 26
3.3 藉控制點之偏移法 27
3.3.1 控制點曲線偏移法 27
3.3.2 控制點法曲面偏移 29
3.3.3 投影點法控制點曲面偏移 30
3.4 採樣點偏移與控制點偏移之比較 31
3.5 綜合偏移流程 32
第四章 剪切曲面 33
4.1 剪切曲面結構 33
4.2 剪切曲面偏移 37
第五章 案例驗證 43
5.1 曲面偏移測試範例一 43
5.2 曲面偏移測試範例二 49
5.3 偏移結果討論 52
5.4 曲面偏移測試範例三 54
5.5 剪切曲面測試範例 59
5.5.1 剪切曲面類型一 59
5.5.2 剪切曲面類型二 61
5.5.3 剪切曲面類型三 63
第六章 結論與未來展望 65
6.1 結論 65
6.2 未來展望 66
參考文獻 67
附錄A 偏移曲面之微分幾何 70
作者簡歷 73

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