An algorithm, Determination of Earth Surface Structures (DEST), is presented to reconstruct digital terrain models of complex landforms from topographic data, such as contour lines and spot heights. The algorithm provides a triangular irregular network (TIN) of the source data, based on a modified Delaunay approach. Delaunay triangulation can introduce artificial terraces from a nonrandom distribution of input points such as a sampled contour line. The algorithm proposed here constructs the three-dimensional principal skeletons of these artificial flat areas, eliminating the unwanted effects of contour lines. The algorithm can also be applied to topographic data from a variety of mixed sources such as photogrammetric information, radar altimetry measurements, and traditional contour lines. The sparse fine-surface structures present in the source data are preserved, allowing accurate morphological evaluations, tectonic lineament extraction, and volume estimation. A methodology (D-DEST) to easily derive, from a TIN computed by DEST, the drainage path and the catchment areas is also presented. A comparison of DEST with other methodologies is performed. It results that our approach does not introduce sensible biased effects in slopes, aspects, drainage network, and catchment areas. The evolution of the upper cone of Vesuvius volcano (Italy) during the last century, as derived from historical cartography, is presented as an application of DEST. The algorithm implemented in C can be requested at DEST_pareschi@pi.ingv.it.