本研究主要探討由兩條邊界曲線所形成的可展開性曲面之幾何設計理論，以及如何應用該理論於三維產品設計與製造。首先利用可展開性條件配合Bézier與B-Spline曲線所對應之de Casteljau及de Boor演算法，推導出自由曲面具有可展開性時其控制點必須滿足的明確限制條件，並且證明在設計此類曲面時，無論曲面的階數為何，若其中一條邊界曲線被指定後，另一條邊界曲線的設計自由度將只剩下五個。對於m個可展開性塊面(patch)相接而成的可展開性複合曲面(composite surface)而言，若其中一條邊界曲線決定後，在G0、G1及G2連續性下時其可運用的設計自由度分別為(2m + 3)、(m + 4)及5；在C1及C2連續性下，對應的自由度分別為5及(7 - 2m)。本研究將上述推導之理論結果應用於三維產品造形設計上，實際利用Bézier複合式可展開性曲面模擬一船體的造型，並將設計出之船體外型實際攤平驗證之。在製造應用上，則利用可展開性曲面任一直紋線(Ruling)具有單一切平面的性質，提出一套全新的方法避免五軸刀柄銑削規則曲面所發生的區域性刀具干涉，並利用可展開性曲面的控制點自由度，產生相接的可展開性塊面逼近加工曲面，使用者可指定最大切削誤差值來控制此近似過程。藉此成功地將五軸銑削的路徑規劃問題轉換為幾何模擬之計算，結果並透過切削實驗加以驗證。本研究除了討論以二階Bézier曲面近似規則曲面的演算法外，並提出進階的曲面調整，以及重新參數法等兩項方式來改善近似法則的誤差。
未來研究重點在於將設計理論擴展至可展開性NURBS曲面，此外應用較高階的數學式產生更為接近加工形狀的可展開性複合曲面，並將建置互動式的曲面設計系統，使用者可自行設計符合其加工需求的可展開性曲面，自動產生刀具五軸側銑路徑。

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