本篇論文提出一種以網格為基礎的曲面展開法，針對龐大網格數目的參數曲面做快速的攤平展開處理，並保持網格間位置關係。展開的過程經由平面網格重建、網格攤平與靠攏等步驟，取得曲面的初始平面對映網格，並將結果應用於電腦輔助三維服飾設計的平面衣版製作上。
為了讓展開的網格能有正確的外形，攤平的演算法必須確保各個網格在所有的攤平步驟中不會發生互相重疊的現象，再設法減少網格之間的縫隙，以逼近合理的二維外形。此外可依不同的攤平需求在靠攏過程中設定個別的拘束條件，對攤平的網格外形加以限制。
不可展曲面攤平後可透過視覺化的誤差分佈圖來觀察局部區域因縫隙造成的誤差量，在誤差量較大的區域可以使用局部靠攏的方法裂開相鄰的網格來減少誤差，如同衣版上褶子的功能。
攤平後的網格可配合二維影像對原始的曲面做貼圖，本論文發展即時互動的貼圖介面方便使用者進行貼圖的工作，提高圖案與曲面匹配的效率，可應用於虛擬服裝中布紋與花色的預覽。

This paper presents a polygon-based flattening method, which can efficiently deal with parametric surfaces with enormous amount of polygons. Meanwhile, the consequent relationships among these polygons remain. The process of flatten contains the co-plane lattices reconstruction, lattices extension and lattices alignment, which can finally form the initial map of pattern. The flattening result can be applied to pattern manufacture of computer-aided 3D garment design.
In order to form the most proper shape, the flattening algorithm has to ensure that every lattice wouldn’t overlap with each other during flatten procedures. To approach the reasonable flattening shape, hereby, is to reduce the gaps between these lattices. In addition, for the purpose of fitting in diverse requirements, it provides many different individual constrains in alignment procedure to form the flattening pattern.
To develop an undevelopable surface could produce plenty gaps. We can simply use the visible color distribution diagram to reveal the local distortion caused by the gaps. In the areas of high level distortion, we propose a local lattices alignment method, which would reduce the local distortion, similar to the pleats generated on a pattern.
The flattening result can be applied to map corresponding texture to its original surface. In this research we employ a real-time interactive texture mapping technique based on polygon-based flattening method. It would enhance the matching performance between image and surface. Finally, virtual design garment can be previewed.

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