Quaternions and their applications in computer graphics

Sammanfattning

In this thesis we will define quaternions and explore how they are used for rotations in three dimensions. We assume that the reader has read linear algebra and basic group theory. In the first part of the thesis we start by defining quaternions and the unit quaternions. We then build the foundation of the thesis by defining related groups, such as the special unitary group of degree two, and prove the group structure of quaternions. Finally, we define rotations in three dimensions and reveal the mathematical engine of rotations with the unit quaternions. In the second part of the thesis we will finally explore how the unit quaternions are used for rotations in the domain of computer graphics. Here, we will go over how we can interpolate between two unit quaternions and how they are applied in computer animations.