Using vertices of a triangular irregular network to calculate slope and aspect

Terrain derivative calculations from triangulated irregular network (TIN)-based digital elevation models (DEMs) have been extensively explored in geomorphometry. However, most calculation methods focus on the triangulation facets of TIN-based DEMs and ignore the vertices. In fact, these vertices are the original sampling points from the terrain surface and serve as the basis for triangulation. In this study, we argue that terrain derivative calculations using TIN-based DEMs should focus on the vertices. Employing examples with slope and aspect, we applied the TIN vertex-based method to a mathematical surface and a real topography using TIN-based DEMs with a range of sampling point densities. We performed a comparative analysis of the TIN vertex-based, TIN facet-based, and grid-based methods. Assessments on the mathematical surface showed that the TIN vertex-based method achieved the highest accuracy among the three methods. Error analysis for the real landform case indicated that the TIN vertex-based method performed slightly better than the grid-based method for slope calculation and slightly worse than the grid-based method for aspect calculation. Among the three methods, the TIN facet-based method was most sensitive to error. The TIN vertex-based method can provide a reference for the slope and aspect calculation based on point clouds.