基于紧支撑径向基函数与共轭梯度法的大规模散乱数据快速曲面插值

于秋则; 曹矩; 柳健; 田金文

基于紧支撑径向基函数与共轭梯度法的大规模散乱数据快速曲面插值

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出版历程
- 收稿日期: 2003-10-09
- 修回日期: 2004-02-16
- 刊出日期: 2005-02-19

Rapid Surface Interpolation from Massive Scattered Data Using Compactly Supported Radial Basis Functions and Conjugate Gradient Method

摘要

摘要: 该文提出一种快速大规模散乱数据的曲面插值算法。在此算法中,首先采用紧支撑径向基函数(CSRBF)作为插值基函数,采用CSRBF的优点是保证构成的系数方程组是对称正定而且系数是稀疏的。这样可保证系数方程组一定可解而且可以减少内存的开销。其次采用共轭梯度法求解大规模系数方程组。该算法在系数方程组的系数矩阵A:NN是对称正定的情况下,最多迭代N步就可以求得方程组的解,实验结果表明该算法的快速性,特别适合大规模散乱数据的曲面的插值。
- 散乱数据曲面插值; 紧支撑径向基函数; 约束点; 系数方程组; 共轭梯度法
Abstract: A novel algorithm for rapid surface interpolation from massive scattered data using Compactly Supported Radial Basis Functions (CSRBF) and conjugate gradient method is presented in this paper, CSRBF is used because it can make the coefficient equations symmetric positive definite (spd), and very sparse. So there must be a solver and a smat 1 storage memory are needed. In solving the system equations, iterative method is used. The conjugate gradient method is used to solve the system equations, because the method converges in at most N steps for a symmetric positive definite N by TV matrix. Experimental results using massive scattered points demonstrate the algorithm is fast. The proposed algorithm is very appropriate for surface interpolation from massive scattered points.

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