基于B样条函数的散乱数据曲面拟合和数据压缩  

Surface fitting and scattered data compressing with B-spline smoothing function

作　　者：李波涛[1] 杨长春[1] 陈雨红[1,2] 孙福利[1] 喻岳钰[1] 

机构地区：[1]中国科学院地质与地球物理研究所油气资源研究重点实验室,北京100029 [2]中国科学院兰州地质研究所,兰州730000

出　　处：《地球物理学进展》2009年第3期936-943,共8页Progress in Geophysics

基　　金：国家重点基础研究发展计划(2005CB422104)资助.

摘　　要：针对大规模散乱数据,本文提出一种基于B样条函数的曲面拟合和数据压缩方法.在此方法中,构建最小平面矩形区域覆盖所有的散乱数据点,根据二维情况下的B样条函数的线性插值公式,利用最小二乘法拟合规则网格控制点的数值,存储有限规则网格控制点的数值,并通过插值可以得到任意点的数值,从而达到曲面拟合和数据压缩的目的.通过算例验证了此方法的可行性以及使用三次B样条函数曲面拟合的优越性.由于此方法具有局部误差小、计算高效的特征,可以适用于数据梯度较小的二维系统数据的曲面拟合和数据压缩,如地形高程数据和射线追踪走时表.A rapid algorithm based on B-spline function for large scale scattered data interpolation, surface fitting, approximation,and data compressing is presented in this paper. In this method,we construct a smallest rectangular area with regular grids to cover all the scattered data first, According to the liner interpolation method of 2-D B-spline smoothing function,the values of all the regular grids can be calculated using the least square method. Through storing these finite values of the regular grids, the value of every point from the original data area can be estimated. In this way, we achieve the aim of surface fitting and data compressing. This method is practiced successfully in several models and the cubic B spline function is the best basal fitting function for interpolation. Because this method has smaller local relative errors and fast calculation efficiency, it is applicable for 2-D data with low gradient such as hypsography data and ray tracing time tables.

关 键 词：散乱数据 样条插值 B样条函数 最小二乘法 曲面拟合 数据压缩 

分 类 号：P631[天文地球—地质矿产勘探]