## ABSTRACT

Triangles are as old as geometry. They were of interest to the ancient Greeks, and in fact the roots of trigonometry can be found in their study. Triangles also became an indispensable tool in computer graphics and advanced disciplines such as finite element analysis. In graphics, objects are broken down into triangular facets for display purposes; in the finite element method, 2D shapes are broken down into triangles in order to facilitate complicated algorithms. For both applications, reducing the geometry to linear or piecewise planar makes computations more tractable. In this chapter we introduce barycentric coordinates again. We review some basic calculation of triangle geometry, such as the incenter. We introduce 2D triangulations and a basic data structure. A point location application demonstrates how barycentric coordinates can be used to optimize this problem. Then 3D triangulations are discussed briefly. Sketches and figures illustrate the concepts.