Moving Surface Spline Interpolation Based on Green’s Function |
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| Authors: | Xingsheng Deng Zhong-an Tang |
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| Institution: | (1) Department of Geology & Geophysics, School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, 1680 East-West Road, Honolulu, Hawaii, 96822 |
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| Abstract: | Some commonly used interpolation algorithms are analyzed briefly in this paper. Among all of the methods, biharmonic spline
interpolation, which is based on Green’s function and proposed by Sandwell, has become the mainstream method for its high
precision, simplicity and flexibility. However, the minimum curvature method has two flaws. First, it suffers from undesirable
oscillations between data points, which is solved by interpolation with splines in tension. Second, the computation time is
approximately proportional to the cube of the number of data constraints, making the method slow for situations with dense
data coverage. Focusing on the second problem, this paper introduces the moving surface spline interpolation method based
on Green’s function, and the interpolation error equations are deduced. Because the proposed method only chooses the nearest
data points by using the merge sort algorithm for interpolating, the computation time is greatly decreased. The optimal number
of the nearest points can be determined by using the interpolation error estimation equation. No matter how many data points
there are, this method can be implemented without difficulty. Examples show that the proposed method can obtain high interpolation
precision and high computation speed at the same time. |
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