渐进插值的LOOP曲面细分

LOOP subdivision surface of progressive interpolation

目前很多细分方法都存在不能用同一种方法处理封闭网格和开放网格的问题。对此,一种新的基于插值技术的LOOP曲面细分方法,其主要思想就是给定一个初始三角网格M,反复生成新的顶点,新顶点是通过其相邻顶点的约束求解得到的,从而构造一个新的控制网格M,在取极限的情况下,可以证明插值过程是收敛的;因为生成新顶点使用的是与其相连顶点的约束求解得到的,本质上是一种局部方法,所以,该方法很容易定义。它在本地方法和全局方法中都有优势,能处理任意顶点数量和任意拓扑结构的网格,从而产生一个光滑的曲面并忠实于给定曲面的形状,其控制网格可以是封闭的或者开放的。

Subdivision surfaces can not deal with the open and closed mesh with the same method.This paper presented a new method based on interpolating LOOP subdivision surfaces.Gave a triangular mesh M,the main idea was to iteratively upgrade the vertices of M to generate a new control mesh such that limit surface of would interpolate M.The new vertex was bound through the constraint solving of its adjacent vertices.It could be shown that the iterative process was convergent for LOOP subdivision surfaces.As new vertex was generated by constraint solving of its adjacent vertices,essentially it was a local method.Hence,the method was well-defined.The new method has the advantages of both a local method and a global method,it can handle meshes of any size and any topology while generating smooth interpolating subdivision surfaces that faithfully resemble the shape of the given meshes.The meshes considered here can be open or closed.