Quaternion calculus as a basic tool in computer graphics

It is shown that quaternions, although up to now solely used for animation purposes, can be used successfully in the field of modelling and rendering and it is proved that the rendering algorithm can be sped up by using quaternion.

Abstract

Quaternions, although not well known, provide a fundamental and solid base to describe the orientation of an object or a vector. They are efficient and well suited to solve rotation and orientation problems in computer graphics and animation. This paper describes two new methods for splining quaternions so that they can be used within a keyframe animation system. We also show that quaternions, although up to now solely used for animation purposes, can be used successfully in the field of modelling and rendering and we prove that we can speed up the rendering algorithm by using quaternions.