A discussion of a method that has been used with success in terrain modelling to estimate the height at any point on the land surface from irregularly distributed samples. The special requirements of terrain modelling are discussed as well as a detailed description of the algorithm and an example of its application.

The representation by computer of 3 dimensional forms is normally restricted to the projection onto a plane, namely the 2 dimensional computer screen or hardcopy device. The following is a procedure that transforms points in 3 dimensional space to screen coordinates given a particular coordinate system, camera and projection plane models. This discussion describes the mathematics required for a perspective projection including clipping to the projection pyramid with a front and back cutting plane. It assumes the projection plane to be perpendicular to the view direction vector and thus it does not allow for oblique projections. Included in the appendices is source code (written in the C programming language) implementing all the processes described.

Triangle is a C program for two-dimensional mesh generation and construction of Delaunay triangulations, constrained Delaunay triangulations, and Voronoļ diagrams. Triangle is fast, memory-efficient, and robust; it computes Delaunay triangulations and constrained Delaunay triangulations exactly. Guaranteed-quality meshes (having no small angles) are generated using Ruppert's Delaunay refinement algorithm. Features include user-specified constraints on angles and triangle areas, user-specified holes and concavities, and the economical use of exact arithmetic to improve robustness. Triangle is freely available on the Web at ``http://www.cs.cmu.edu/~quake/triangle.html'' and from Netlib. This paper discusses many of the key implementation decisions, including the choice of triangulation algorithms and data structures, the steps taken to create and refine a mesh, a number of issues that arise in Ruppert's algorithm, and the use of exact arithmetic.