用逼近型3^(1/2)细分方法构造闭三角网格的插值曲面  

Interpolating Closed Triangular Meshes by Approximation 3^(1/2) Subdivision Scheme

作　　者：邓重阳[1,2] 

机构地区：[1]杭州电子科技大学应用数学与工程计算研究所,杭州310018 [2]浙江大学CAD＆CG国家重点实验室,杭州310058

出　　处：《计算机辅助设计与图形学学报》2010年第2期312-317,326,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60673032,60904070);杭州电子科技大学校科研启动基金(KYS075608073)

摘　　要：为了避免用逼近型3^(1/2)细分方法构造插值曲面过程中出现的烦琐运算,利用3细分方法极限点计算公式,提出一种用逼近型3^(1/2)细分方法构造闭三角网格插值曲面的方法.给定待插值的闭三角网格,先用一个新的几何规则与原3^(1/2)细分方法的拓扑规则细分一次得到一个初始网格,用3^(1/2)细分方法细分该初始网格得到插值曲面;新几何规则根据极限点公式确定,保证了初始网格的极限曲面插值待插值的三角网格.由于初始网格的顶点仅与待插值顶点2邻域内的点相关,所以插值曲面具有良好的局部性,即改变一个待插值点的位置时,只影响插值曲面在其附近的形状.该方法中只有确定初始网格顶点的几何规则与原3细分方法不同,故易于整合到原有的细分系统中.实验结果表明,该方法具有计算简单、有充分的自由度调整插值曲面的形状等特点,使得利用3^(1/2)细分方法构造三角网格的插值曲面变得极其简单.To avoid the complex computation in the process of interpolating triangular mesh by subdivision scheme, we propose a simple and efficient algorithm for interpolating closed triangular meshes by √3 subdivision scheme using the limit point formula of √3 subdivision scheme. Given the interpolated triangular mesh, by subdividing it with a new geometric rule and the topology rules of,√3 subdivision scheme we obtain an initial mesh, whose limit surface of √3 subdivision scheme is the interpolation surface; the new geometric rule is determined by the limit point formula of √3 subdivision scheme, and assure that the limit surface of initial mesh interpolate the given triangular mesh. The new points of initial mesh are defined by the interpolated vertices and their 2-neighborhood vertices, so the interpolation method is local, i.e. the perturbation of a given vertex only influences the surface shape near this vertex. The geometric and topology rules of our interpolation method are the same as those of the √3 subdivision scheme except the first geometric rule of obtaining the initial mesh, so it is very easy to incorporate our method to the origin subdivision system. Numerical examples show that the new interpolation method has many advantageous properties, such as simplification, having enough freedoms to adjust the shape of the interpolation surfaces, and so on. These features make surface interpolation using,√3 subdivision scheme very simple.

关 键 词：细分曲面 逼近型细分方法 √3细分方法 曲面插值 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]