Comparison of existing triangulation methods for regularly and irregularly spaced height fields

Over the last two decades, the Delaunay triangulation has been the only choice for most geographical information system (GIS) users and researchers to build triangulated irregular networks (TINs). The classical Delaunay triangulation for creating TINs only considers the 2D distribution of data points. Recent research efforts have been devoted to generating data-dependent triangulation which incorporate information on both distribution and values of input data in the triangulation process. This paper compares the traditional Delaunay triangulations with several variant data-dependent triangulations based on Lawson's local optimization procedure (LOP). Two USGS digital elevation models (DEMs) are used in the comparison. It is clear from the experiments that the quality of TINs not only depends on the vertex placement but also on the vertex connection. Traditonal two step processes for TIN construction, which separate point selection from the triangulation, generate far worse results than the methods which iteratively select points during the triangulation process. A pure data-dependent triangulation contains a large amount of slivers and steep triangles, which greatly affect the quality of TINs constructed. Among the triangulation methods tested, the classical Delaunay triangulation is still the most successful technique for constructing TINs for approximating natural terrain surfaces.