Complex Numbers and Quaternions – A unified view on representations and metrics for rotations
In Proceedings of the RIC Project Day "Framework & Standardization" and "Manipulation & Control", 19.6.2014, Selbstverlag, Bremen, series DFKI Documents, volume 14-03 , number 14-03, pages 120-121, Jun/2014. DFKI GmbH. ISBN: ISSN 0946-0098.
On this poster, a novel view on complex numbers and quaternions is motivated by introducing a five dimensional complex space which is defined as the union of the complex plane C with the quaternion space
H. For rotations with a fixed rotation axis, the complex 5-space can be visualized by R3 and by R2. In these visualizations, the representations of a rotation via a complex number, quaternions, and a rotation matrix
appear in an elementary-geometric setup generalizing the unit circle. The definition of the complex 5-space is based on an explicit distinction of four different imaginary units. The poster illustrates one usage of these
novel concepts with a comparison of distance measures for rotational displacements.