Kinematics of the 2D and 3D Spaces

This chapter presents the geometric algebra framework for dealing with 3D kinematics. The reader will see the usefulness of this mathematical approach for applications in computer vision and kinematics. We start with an introduction to 4D geometric algebra for 3D kinematics. Then we reformulate, using 3D and 4D geometric algebras, the classic model for the 3D motion of vectors. Finally, we compare both models, that is, the one using 3D Euclidean geometric algebra and our model, which uses 4D motor algebra.