几种基于散乱数据拟合的局部插值方法

本文首先针对散乱数据拟合的Shepard方法,结合截断多项式、B样条基函数和指数函数来构造其权函数,使新的权函数具有更高的光滑度和更好的衰减性,并且其光滑性和衰减性可以根据实际需要自由调节,从而提高了曲面的拟合质量．同时还给出一种类似的局部插值方法．另外,本文还基于多重二次插值,结合多元样条的思想,给出了两个局部插值算法．该算法较好地继承了多重二次插值曲面的性质,从而保证了拟合曲面具有好地光顺性和拟合精度．曲面整体也具有较高的光滑性．

Some Local Methods for Scattered Data Interpolation

With regard to the Shepard method, in this paper, we use the truncated polynomial, the B-spline basis function and exponential function to construct the weight functions. They are of better property of smoothness and decay, which can be adjusted freely. And so the surface can be fitted better by the improved method, we also present a new local method, which performs better than the local Shepard method does. Moreover, we use the idea of multivariate spline to give out two local methods of the multiquadric interpolation. These methods perform almost as good as the global multiquard method does.