Applications of dual quaternions to 2D geometry information
Four-dimensional algebra over the real numbers
Planar quaternion multiplication
In this article, we discuss certain applications of the dual quaternion algebra to 2D geometry. At this present time, the article is focused on a 4-dimensional subalgebra of the dual quaternions which we will call the planar quaternions.
The planar quaternions make up a four-dimensional algebra over the real numbers.[1][2] Their primary application is in representing rigid body motions in 2D space.
Unlike multiplication of dual numbers or of complex numbers, that of planar quaternions is non-commutative.
^Matsuda, Genki; Kaji, Shizuo; Ochiai, Hiroyuki (2014), Anjyo, Ken (ed.), "Anti-commutative Dual Complex Numbers and 2D Rigid Transformation", Mathematical Progress in Expressive Image Synthesis I: Extended and Selected Results from the Symposium MEIS2013, Mathematics for Industry, Springer Japan, pp. 131–138, arXiv:1601.01754, doi:10.1007/978-4-431-55007-5_17, ISBN 9784431550075, S2CID 2173557
^Gunn C. (2011) On the Homogeneous Model of Euclidean Geometry. In: Dorst L., Lasenby J. (eds) Guide to Geometric Algebra in Practice. Springer, London
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