Terrain modeling: a constrained fractal model

Abstract

We present an algorithm mainly designed to reconstruct Digital Elevation Maps (DEM). Our approach relays on a fast and highly controllable fractal-based algorithm, we are able to create DEMs according to given constraints. Thus, these constraints can be given as scattered dataset of elevations obtained by satellite, our method supersamples this data and creates the according smooth terrain surface. Moreover, as a painter can make a sketch of his model, the final user can give or edit the main characteristics, local details and morphology, of his wanted DEM instantaneously obtaining the resulting terrain surface. Note that there is no limitation on the number of local constraints (that could vary from 0 to the number of points of the final DEM). Thus, the method we propose gives the ability to modify the global aspect (the surface behavior) as well as to constrain any local detail of the final terrain model. This paper presents the algorithm and reconstruction examples. Using a Root Mean Square Error computation between an original model and its downsampled-then-reconstructed version, the results confirm the method good behavior and show its efficiency. Other various terrain models and alternative applications are presented.