Introduction

Abstract

In computer graphics transforms are used to modify the position and orientation of an object or a virtual camera. Such transforms generally comprise: scale, translation and rotation. The first two transforms are relatively easy to visualise, but rotations can cause problems – due to the need to construct a rotation transform from individual rotations about the x-, y- and z-axes. Although such transforms work, they are far from perfect. What really is required, is a technique that is intuitive, simple and accurate. Over the years, rotation transforms have embraced direction cosines, Euler angles, Euler-Rodrigues parameterisation, quaternions and multivectors. The last two techniques are the most recent, and are historically related. However, the subject of this book is quaternions, and how they can be used within computer graphics.