以圓錐可展曲面擬合網格之演算法

Abstract

可展曲面可以應用於衣服或紙模型的設計。可展曲面具有易於生產，無扭曲等優點，但通常需要有經驗的專家才能設計可展曲面。舊有的可展曲面擬合演算法通常只能擬合近似可展之網格[3, 6, 8]，或限制擬合曲面為受限的可展曲面面[5, 7, 9]。我們在論文中，提出了更通用的演算法，能利用圓錐可展曲面來擬合網格。我們的演算法為一反覆擬合之架構，在每一次迴圈中，我們執行區域擴張並最佳化擬合之圓錐可展曲面。不同於舊有的方法利用單一的圓錐曲面，我們利用多段的圓錐曲面擬合網格以降低誤差，並保證同一區塊內，圓錐之間的C0連續性，因此我們的演算法可以利用較少的區塊，來更精確的擬合網格。

Developable surfaces have various applications like clothes or paper craft models design. They have many advantages like simple to construct and no distortion. Designing developable surfaces is not trivial though, so various developable surfaces approximation methods have been proposed. Previous developable surfaces approximation methods either only approximate near developable surfaces [3, 6, 8] or only use restrictive surfaces [5, 7, 9] as approximation surfaces. We propose a more general method that use cone spline surfaces as approximation surfaces. Our method is a iterative approach, in each iteration, our algorithm executes region growing and approximation surface optimization. Unlike previous approaches that use a single conic as proxy surface in the optimization phase, our method use multiple segments of conic to further reduce the error and guarantee C0 continuity between the conics in the same cone spline surface. As a result, our algorithm is more accurate and usually generates fewer patches than previous methods.