Vector algebra for Steep Slope Model analysis

Geographic Information Systems offer many algorithms that allow analysis of digital elevation models. They work with both GRID and TIN data, but they are limited to 2.5D models, where one planar (X,Y) position refers to only one vertical (Z) value. In mountainous regions, however, many steep, vertical and even overhung parts of rock walls and slopes occur. GRID and TIN models in a standard projection are not capable to deal with such a relief as they are not able to capture all complexity of steep slopes that can be observed from the terrestrial perspective. Such a perspective can be introduced into GIS via computer graphics software that allows 3D surface modelling by means of mesh, e.g. 3D triangular network. The paper presents a concept that implements 3D mesh in GIS and utilizes vector algebra to analyze such a surface. The idea is based on using normal vectors to compute slope and aspect of each triangle in a mesh. The computed values are saved as their attributes. Complete procedures are written in Python programming language and implemented into popular GIS software to work as a plug-in tool.