Applications of dual quaternions to 2D geometry: Difference between revisions

Revision as of 11:37, 30 September 2019

Revision as of 06:45, 3 October 2019

Line 77:

A principled construction of the dual-complex numbers can be found by first noticing that they're a subset of the [[Dual quaternion|dual-quaternions]].

There are two geometric interpretations of the 'dual-quaternions', both of which can be used to derive the action of the dual-complex numbers on the plane:

* As a way to represent [[Dual quaternion|rigid body motions in 3D space]]. The dual-complex numbers can then be seen to represent a subset of those rigid-body motions. This requires some familiarity with the way the dual quaternions act on Euclidean space. We won't describe this approach here as it's [[Dual quaternion|adequately done elsewhere]].