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.

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