• 学术论文 •

### 似大地水准面格网双二次多项式插值方法

• 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2009-02-25 发布日期:2009-02-25

### Quasigeoid Grid Network Biquadratic Interpolation Method

• Received:1900-01-01 Revised:1900-01-01 Online:2009-02-25 Published:2009-02-25

Abstract:

It is difficult for a mathematical model to express a big area surface with complex structure. As for a national or provincial quasigeoid, the common method is firstly to build a regular quasigeoid grid network, and then to interpolate the height anomaly based on the quasigeoid grid network. The distance weighted interpolation and bilinear interpolation, which are the common methods used in China, are discussed in this paper. It is pointed out that the distance weighted interpolation method could cause serious problems, such as surface distortion, unsmooth and discontinuity, while the bilinear model would bring the surface with “spire point” and “folding marks”. However, the quasigeoid is a continual and smooth surface obviously. Aiming at solving all these issues, this paper suggests the biquadratic interpolation method, which depends on the point's location relating to corners and edges of the grid network, only the nearest nine points are needed for each point's interpolation. But the biquadratic interpolation will cause surface distortion problem under the circumstance of inflexion, so this paper proposes a correction method to deal with it. The renewed biquadratic interpolation method could obtain a continual and smooth surface in the whole area. Therefore, its interpolation precision is enhanced. For these advantages, it is suggested that the renewed biquadratic interpolation method should be used universally for quasigeoid grid network interpolation.