数字地形数据的二维三次卷积插值

Two Dimensional Cubic Convolution Interpolation for Digital Map Data

由于数字地形数据库是以网格的形式给出网格点上的地形高度信息，在低空突防轨迹优化过程中，往往需要非网格点地形的高度信息和地形曲面的导数，这些都是离散的地形数据库所无法提供的。对二维的地形数据进行插值是解决问题的有效手段。本文提出一种二维离散数据的插值方法——二维三次卷积插值。该插值函数是地形曲面的三次逼近，具有连续的三阶导数，可以非常好地满足低空突防轨迹优化的需要。仿真结果表明，它具有比双线性插值和双立方Ｈｅｒｍｉｔｅ插值更好的插值效果。

Because the digital map data base gives terrain heights for a discrete grid of (x, y) values, in the course of the optimization of the low altitude penetration path, the terrain height values as well as the derivative of terrain surface are all needed. The discrete digital map data base can not give these information. One method for estimating unknown data is to interpolate two dimensional terrain data. This paper presents two dimensional cubic convolution interpolation function. The interpolation function is a third order approximation for terrain surface with a continuous third derivative. Therefore, it can satisfy the requirements of the optimization of the flight path. The simulation results show that this method has a better result than the bilinear interpolation and the bicubic Hermite interpolation.