Dual complex numbers gives an efficient alternative to matrices for manipulating the rigid motions in 2D ( i.e., the group of 2D Euclidean transformations ).
- G. Matsuda, S. Kaji, and H. Ochiai, "Anti-commutative Dual Complex Numbers and 2D Rigid Transformation" in Mathematical Progress in Expressive Image Synthesis I, Springer-Japan, 2014. http://arxiv.org/abs/1601.01754