用参数样条插值挖补方法进行大规模散乱数据曲面造型

Surface Construction Over Large Scale Scattered Data Using Parametric Spline Interpolation and Hole Filling Approach

利用矩形域中带连续边界条件的多元散乱数据最优插值方法,结合张量积型参数样条插值,从挖补的思想得到启发,提出一种适合大规模散乱数据曲面造型的参数样条插值挖补方法.用该方法构造的参数曲面内部Cm,n连续,挖补的矩形边界分别为Cm-1,0和C0,n-1连续.最后就常见的m=n=2时的双三次样条给出一些数值例子,说明该算法简单易行,效果良好.

Using multivariate optimal interpolation to scattered data with uniform rectangular partition and continuous boundary conditions, applying the paradigm of tensor product parametric spline surface interpolation, and hole filling technique, a novel approach to construct smooth surface over massive scattered data is presented. The resulting surface is C^m,n in the interior, and across the boundaries of hole filling region are C^m- 1,0 and C^0,n- 1 respectively. Numerical examples for m = n = 2 bi-cubic surface show that the method is easy and applicable.