本研究建構一套電腦輔助立體服裝曲面二維展開系統，來協助服裝設計師快速獲得服裝曲面攤平後的平面資訊。首先應用高斯曲率分析將立體服裝曲面，區分為可展曲面與不可展曲面。可展曲面可利用數學方程式所推導出之轉換矩陣進行二維展開，而不可展曲面可依高斯曲率之不同，區分為具拋物線（高斯曲率＞0）或雙曲線特性（高斯曲率＜0）之曲面，再依不同曲面之特性，採用適當之二維展開矩陣，進行3D曲面之攤平。
三維曲面轉二維平面之基礎理論，乃是應用Orthogonal Properties of Rotation Matrices，將3D曲面上之每一單一三角網格攤平在XY平面上，並依三角網格相互連結關係與曲面邊界設定條件，將三維曲面攤平在XY平面上得到初始之攤平結果。然而初始攤平之結果，依3D曲面特性之不同，會發生平面網格裂開或重疊之情形。平面網格裂開若在合理且服裝設計師容許範圍內，則可視為最佳之攤平結果。反之，若是平面網格之裂縫並非在合理範圍內或有互相重疊之現象，則初始攤平結果，必須再利用本研究所推導出之智慧型褶子轉移法，自動將初始攤平結果，編修成較接近實際平面衣版之樣式。
褶子轉移法是將初始攤平結果區分為固定寬帶與非固定寬帶，然後根據平面衣版之特性，設定褶子轉移方向，再依褶子轉移角度切割非固定寬帶，切割之間距以固定寬帶網格間距為依據。切割後之非固定寬帶分別向所屬之固定寬帶進行褶子轉移，並獲得第二次攤平結果。此結果已成功地去除平面網格重疊部分與縮減網格裂縫之數目，以符合平面衣版之編修法則。
第二次攤平後，本系統仍提供服裝設計師可自行選取不同之褶子位置或不同之褶子轉移角度，以產生不同形式之平面衣版，而不同形式之平面衣版，反穿回人體模型時會產生不同之3D服裝式樣。最後依據服裝設計師選取之平面衣版與實際之平面衣版間總面積之變化量與總位能之變化量，來評估最後攤平結果之實際效益與系統之攤平效能。

The goal of this research is to develop a computer-aided system, which can help garment designers to obtain two-dimensional flatten patterns from three-dimensional fashion designs of apparels quickly and efficiently. The system not only generates the two-dimensional flatten patterns automatically, but also provides the options for garment designers to acquire different styles of designs by alternating the locations of darts and gussets.
The three-dimensional surfaces of garment designs are analyzed using Guassian curvature analysis and classified into two types of surfaces, one is developable surface and the other one is non-developable surface. The developable apparel surfaces can be flattened using exact solutions, which have been well developed by textbooks and previous works. However, the non-developable surfaces should be flattened according to the characteristic of each surface.
The fundamental theory of our flattening process is based on the Orthogonal Property of Rotation Matrices. The transformation matrices are developed to transform the non-developable surfaces on to the XY plane with a boundary constraint and a predetermined flattening direction. The results obtained from the first flattening process are not acceptable in general owing to the unreasonable cuts and overlapping areas of the two-dimensional flatten patterns. Therefore, the algorithm of “Reorientation of darts and gussets,” which includes determining the location of the darts and realigning the two-dimensional meshes, is developed to reduce the number of unreasonable cuts and to eliminate the overlapping areas of the flatten patterns.
The computer-aided system is successfully implemented and applied to unfold two different types of surfaces of revolution and a bodysuit of a woman model. In the future, the system will be extended to unfold different styles of apparels to improve the efficiency and quality of garment fashion designs process.

中文摘要 i
Abstract iii
誌謝 v
目錄 vi
圖目錄 xi
表目錄 xvii

第1章 緒論 1
1.1 研究動機 1
1.2 研究目的 2
1.3 研究目標 3
1.4 研究架構與說明 3

第2章 相關研究探討 6
2.1 可展曲面與不可展曲面 6
2.2 曲面攤平的應用領域 7
2.3 曲面攤平的相關研究 7

第3章 研究之理論架構 16
3.1 高斯曲率 16
3.2 Bezier Spline 17
3.3 旋轉曲面建構 18
3.4 空間矩陣運算 19
3.4.1 平移矩陣 19
3.4.2 旋轉矩陣 19
3.5 快速直線交點演算法 20

第4章 研究步驟與方法 22
4.1 人台結構與服裝式樣定義 22
4.2 傳統衣版與服裝式樣相關性探討 23
4.2.1 傳統褶子轉移法 23
4.2.2 傳統褶子轉移法與相對應之服裝式樣 25
4.3 空間Transformation矩陣之推導 27
4.4 三維立體曲面對應到二維平面演算法之推導 31
4.5 褶子轉移演算法推導 32
4.5.1 網格切割 32
4.5.2 網格轉移 35
4.6 旋轉曲面建構 36
4.6.1 Bezier Spline建構旋轉曲面輪廓 36
4.6.2 旋轉曲面經線方向與緯線方向定義 36
4.7 旋轉曲面之攤平 39
4.7.1 旋轉曲面經線方向之攤平 39
4.7.2 旋轉曲面緯線方向攤平 40
4.8 旋轉曲面攤平結果與曲面特性關係之研究 41
4.9 旋轉曲面褶子轉移結果與曲面攤平關係之研究 41
4.9.1 經線方向之攤平與褶子轉移演算法 42
4.9.2 緯線方向之攤平與褶子轉移演算法 44
4.10 立體服裝曲面二維展開 46
4.11 人台攤平結果與曲面特性相對應關係之研究 49
4.12 人台攤平結果褶子轉移演算法 49
4.13 立體服裝曲面建構原型衣版模式之建立 49

第5章 系統程式建構及操作介面設計 50
5.1 Visual C++、MFC與OpenGL 50
5.1.1 Visual C++ 50
5.1.2 MFC（Microsoft Foundation Classes）與OpenGL（Open Graphics Library） 51
5.2 系統架構說明 53
5.2.1 點資料儲存處理與向量運算類別 53
5.2.2 網格儲存與轉移類別 54
5.2.3 基礎攤平演算法架構 54
5.2.4 基礎褶子轉移演算法架構 54
5.2.5 旋轉曲面攤平模組架構 56
5.2.6 立體服裝曲面攤平模組架構 56
5.3 程式介面說明 59
5.3.1 旋轉曲面攤平模組程式介面說明 59
5.3.2 立體服裝曲面攤平模組程式介面說明 64

第6章 結果與討論 69
6.1 攤平演算法與褶子轉移演算法應用於旋轉曲面之結果 69
6.1.1 旋轉曲面緯線方向攤平與褶子轉移結果 70
6.1.2 旋轉曲面經線方向攤平與褶子轉移結果 74
6.2 不同網格密度之人台攤平與褶子轉移結果比較 76
6.2.1 不同網格密度之人台初始攤平結果 79
6.2.2 不同網格密度之人台褶子轉移結果 81
6.3 人台原型衣版產生模式之建立 84
6.3.1 高網格密度之上衣前片原型衣版產生結果 87
6.3.2 中網格密度之上衣前片原型衣版產生結果 90
6.3.3 低網格密度之上衣前片原型衣版產生結果 93
6.4 編修後人台曲面上衣前片原型衣版之建構 95

第7章 結論與建議 101
7.1 結論 101
7.2 後續研究與建議 102

參考文獻 103

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