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

Revision as of 15:49, 30 June 2022

Revision as of 15:49, 30 June 2022

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== Representing rigid body motions ==

Let <math display="block">q = A + Bi + C\varepsilon j + D\varepsilon k</math> be a unit-length dual-complex numberquaternion, i.e. we must have that <math display="block">|q| = \sqrt{A^2 + B^2} = 1.</math>

The Euclidean plane can be represented by the set <math display="inline">\Pi = \{i + x \varepsilon j + y \varepsilon k \mid x \in \Reals, y \in \Reals\}</math>.