Semi-automated construction of fully three-dimensional terrain models

Abstract

Extending the current 2.5 dimensional (2.5D) terrain model is a necessary development in Geographical Information System (GIS) because it cannot be handled adequately and displayed in 3D with holes and bridges. This paper examines the limitations of traditional modelling of a terrain surface for handing holes, bridges and buildings, and suggests a simple data structure and topological model for constructing complex structures on terrain. The concept of surface modelling, as practiced in Digital Terrain Model (DTM) triangulation models (Triangulated Irregular Networks - TINs), and in Computer Aided Design (CAD) systems are discussed. The concept of the exterior surface of a solid, the orientable manifold, and the embedding of a graph on this manifold are also examined. The basic concept of CAD design is examined, in particular surface based-representation methods, and the concept of Euler Operators, which guarantee and preserve the connectivity of the model. TINs, and CAD-type operators for creating TINs, are discussed. Several data structures for construction and maintenance are examined, and the choice of the Quad-Edge data structure is explained, along with details of its implementation in an object-oriented system. Quad-Edge pointer - navigation, and construction operators are discussed. Two parts of the implementations are shown. Firstly Euler Operators are implemented by using the Quad-Edge data structure and secondly the implementation of the TIN operators using the Euler Operators. However, phrasing this model in terms of Euler Operators allows the addition of one CAD type Euler Operator to permit the addition of bridges and tunnels to the TIN model - the objective of this research. In conclusion, there is a demonstration of the validity of this approach by constructing a complex city model using some real Hong Kong data.