C¹-continuous Terrain Reconstruction from Sparse Contours

Abstract

Contour lines from topographic maps are still the most common form of elevation data for the Earth’s surface and in the case of historical landscapes, they often are the only available source of information. In this paper we present a new contour interpolation method that solves this bivariate problem by considering univariate curve interpolation along the approximate gradient directions of the unknown surface. For a point between two contours the height value is computed with Hermite interpolation based on the shortest distances to the contours and height and derivative information at the contours. The surfaces generated are C¹ except at terrain characteristics such as ridges and valleys which are reconstructed as sharp features. The method also faithfully reconstructs summits, pits, and saddles and is especially well-suited for sparse sets of contours. The approach allows for an efficient numerical implementation as we demonstrate with a number of examples.