Abstract

The discovery of quaternions by Sir Hamilton in 1843 was motivated by the hope to creat a type of hipercomplex numbers related the three dimensional space like complex numbers are related to the plane.
Nowadays, quaternions are used as a tool for modelling problems in almost all applied sciences: computer vision, robotics, navigation, virtual reality, etc.
In this thesis we present the fundamental concepts and properties of quarternions and describe how quartenions can provide a unique and powerful tool for characterizing 3D rotations.
The computational contributions of this work are:

1. QuatCalc: a MATHLAB calculator for quaternions, wich was design to perform quaternion arithmetic.

2. QuatRot: a MATLAB qui for visualizing 3D rotations with quaternions.

3. A collection of MATLAB routines for 3D general rotations.