Building Solids Using Quaternions

This paper presents two ways to make solid modelling, defining the solid surface as a trajectory of a particle. The first one implements an existing method, where the trajectory of a particle is seen as a rational Bezier curve, so a dual quaternionic parametrization of mentioned trajectory is done. In the second one an original method based on a quaternionic representation of a Simple Harmonic Motion is presented. Then the main idea is to pick a surface given by regularly distributed data and be able to reproduce it carving it in some material.