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About: Applications of dual quaternions to 2D geometry     Goto   Sponge   NotDistinct   Permalink

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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. 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.