可展開性曲面(Developable Surface)為一種特殊的規則曲面(Ruled Surface)，可被還原成平面而不造成材料的扭曲或撕裂，此類曲面大量運用於電腦圖學以及CAD/CAM領域，例如衣服鞋類的造型、航太汽車零件設計，或是鈑金材料的彎曲變形等。本研究探討在各種不同目標函式最佳化的情況下，根據多片可展開性圓錐曲面內插空間中給定的兩條邊界曲線，藉以進行三維曲面之幾何設計。主要提出兩階段式創新性的演算法則，首先基於啟發式演算法根據三角與四角圓錐曲面自動排列成為Bézier複合曲面。接著根據目標函式，於局部區域先行決定較佳的曲面控制點，最後結合遺傳演算法(Genetic Algorithms)求得整體最佳化之曲面。與以往利用平面近似的方法相比較，不論是第一階段基於可展開性曲面局部最佳化或是經遺傳演算法產生的結果，其對應之目標函式值皆較佳。研究結果大幅改善電腦輔助幾何設計之可行性，進而提供三維造型的可製造性，亦可應用於三維形狀的電腦輔助物理模擬(Physical Modeling)。本研究成功地將提出之演算法則運用於實際的鞋類設計與製造，結果顯示其正確性與實用價值。

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