Higher-order interpolation of regular grid digital elevation models

The fundamental aim of a digital elevation model (DEM) is to represent a surface accurately, such that elevations can be estimated for any given location. It is, therefore, necessary to have efficient and precise algorithms for the computation of surface elevations between given points. The hypothesis presented here, is that higher-order interpolation techniques will always be more accurate than the likes of the popular bilinear algorithm. This hypothesis will be evaluated through an assessment of the accuracy with which DEMs can be interpolated to higher spatial resolutions. A variety of interpolation techniques are assessed, ranging from the one-term level plane to the 36-term biquintic polynomial. In general, techniques that take account of the local terrain neighbourhood are more consistent and accurate, reducing the rms. error by up to 20% of the bilinear interpolant.