Delaunay Triangulation Based Surface Modelling and Three-Dimensional Visualisation of Landforms

Surface modelling and its three-dimensional visualisation are important problems in a variety of disciplines including geographic data processing, computer vision, computer graphics and computer aided design. The different types of approaches used in surface representation/modelling are overviewed. The data structure and related primitives to manipulate it used for implementing a particular algorithm play an important role in determining its run-time complexity. This paper describes the underlying data structure and operators used in implementing an efficient divide-and-conquer based Delaunay triangulation scheme for surface modelling. Subsequently it briefly describes a method for three-dimensional (3-D) visualisation of landforms/topographic surfaces given a set of irregularly spaced points with elevation information on a topographic surface. The timing analysis of the triangulation method and some 3-D visualisation results on a real-world data set are presented and discussed.