利用五元細分割的一致性網格參數化技術

Abstract

為多個物體建立對應關係的演算法在電腦圖學及幾何處理的領域裡非常的有用。然而，建立的過程中所需要大量人為設定的切割方式及很多特徵點對應。 因此，我們提出一個有系統的方法叫做``遞迴五元細分割''在不需要大量人為設定的情形之下進而求得一個共同的切割方式。 五元細分割是遞迴地將一個參數化之後會高度延展的曲塊細切成五個新的小曲塊。這個演算法可以延伸至多個物體，而且將使用者額外所指定的特徵對應點也列入考慮來得到一個共同的切割方式。 以這個切割方式為基礎，對原來物體的幾何資料做規則性或適應性重新取樣再產生``半正規網格''表示法的物體。 還有細部的幾何資訊也可以重新取樣再透過Normal map的表示法儲存下來。我們以二個或二個以上的網格物體在三度空間中或是小波空間中計算而產生變形動畫(Morphing)來當作本演算法的效果展示。

The correspondences establishment among multiple objects is a versatile algorithm in computer graphics and geometry processing, which in general takes as input the specification of a common dissection together with a set of feature points. We propose a systematic method called recursive quinary subdivision to find a dissection for an object with little user interventions. The quinary subdivision is a process that recursively dissects an highly stretched patch into five new patches. The process can be extended to multiple objects, taking into account the alignment of extra feature points and derive a common dissection. Based on the dissection, uniform or adaptive remeshig can be performed to yield a set of semi-regular meshes. Moveover, geometric details can be resampled and stored as normal maps. We also demonstrate the mesh morphing application between two or more objects in both spatial and wavelet domain based on the correspondence established by the common dissection and remeshing.