Abstract
An efficient algorithm was developed for generating horizons for each point in a digital elevaton grid in order N iterations. In two dimensional case, however, the algorithm has been suffered from the ambiguity in the definition of horizons. In this paper, we prove some important theorems based on a formal definition of the horizon which is applicable to two dimensional situation. For actual calculation, rotation and interpolation of the DEM are considered. We adopt a parametric cubic convolution familly of functions for the interpolation, which can control smoothness and sharpness of the converted DEM. The sampling interval is analyzed with regard not only to computational efficiency but also to estimation error.
