Three-Dimensional Transformations

Abstract

Geometric transformations play an important part in the visualisation of three-dimensional scenes. The ability to rotate, translate and scale an object is fundamental to the understanding of its shape. This can easily be demonstrated by picking up a relatively complex and unfamiliar object. In an effort to understand its shape one rotates the object and looks at it from close or at arms length. In the generation of different views of a given scene with the computer, transformations are used to achieve the effect of different viewing positions and directions.

The techniques we shall develop in this chapter for expressing 3D transformations will be an extension of the 2D techniques that we have developed in the chapter concerning 2D transformations.