Chapter 5 Geometry

Section 5.3 All about Triangles

5.3.1 Introduction

Technical structures such as trusses and some bridges are built from triangles as design elements (see figure below).

Conversely, the question arises how an arbitrary surface can be subdivided into triangles. For many geometrical calculations this question is useful. Some examples are given in Section 5.4.
Furthermore, the problem of partitioning arbitrary surfaces into simple "basic elements" results in constructive answers in applications that are relevant far beyond simple geometric considerations. A first impression of such relevance gives us the integral calculus described in chapter 8 together with its application to the calculation of surface areas. There, the first approximation to the integral is a partition of the area into rectangles (each consisting of two triangles, to stay on topic). For the three-dimensional computer aided modelling of surfaces, for example in the manufacturing of car bodies, partitions into triangles (triangulations) are the basis of many calculations and deceptively realistic looking virtual animations.