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《Progress in Geophysics》 2009-03
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Surface fitting and scattered data compressing with B-spline smoothing function

LI Bo-tao~1 , YANG Chang-chun~(1,*), CHEN Yu-hong~(1,2), SUN Fu-li`1 , YU Yue-yu~1(1. Key Laboratory of Petroleum Resources Research , Institute of Geology and Geophysics , Chinese Academyof Sciences , Beijing 100029, China; 2. Lanzhou Institute of Geology , Chinese Academy of Sciences , Lanzhou 730000, China)  
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.
【Fund】: 国家重点基础研究发展计划(2005CB422104)资助.
【CateGory Index】: P229
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