Quaternions In Three Dimensions

TL;DR

This paper presents a geometric construction of quaternion algebra in three dimensions, offering new methods for rotation implementation, interpolation, and topological understanding.

Contribution

It introduces a novel geometric approach to constructing quaternions in three dimensions, enhancing rotation methods and topological insights.

Findings

New geometric construction of quaternions in 3D

Improved methods for rotation implementation and interpolation

Enhanced understanding of quaternion topology

Abstract

We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three dimensions involves the addition of one term. The construction leads to novel methods for implementing and interpolating rotations and understanding their topology.