移动格林基函数样条二维插值算法研究

针对用于插值的已知点较多时，插值计算需要解算大规模矩阵、计算耗时长甚至无法解算的问题，引入移动曲面的思想，取插值点周边最邻近k个已知点进行格林基函数二维样条移动插值，实例计算结果表示，该方法的插值精度高于Shepard插值法与多项式拟合法的精度。插值范围大及测点数量众多时，该方法仍可用，无需数据分区与光滑接边，与整体插值相比可大大降低计算时间。

STUDY ON TWO-DIMENSIONAL SPLINE INTERPOLATION BASED ON MOVING GREEN FUNCTION

When the data coverage is dense, some algorithms need to solve large size matrix, thus the computation time is proportional approximately to the cube of the number of data constraints,it makes the process very slow. Focusing on this problem, the moving curvature is introduced in interpolation. Only the nearest data points are chosen for interpolating by two dimensional spline based on the moving Green’s function. The examples show that the interpolation accuracy of the proposed method is higher than that of two other methods. No matter how many data points there are, this method can be implemented fast. It is not necessary to split the data into subsets which can be modeled individually, or to blend the subsets together into a final model. Comparing with the global solution, this algorithm can greatly reduce the computation time.