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Double Conformal Geometric Algebra

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Abstract

This paper introduces the Double Conformal/Darboux Cyclide Geometric Algebra (DCGA), based in the \(\mathcal {G}_{8, 2}\) Clifford geometric algebra. DCGA is an extension of CGA and has entities representing points and general (quartic) Darboux cyclide surfaces in Euclidean 3D space, including circular tori and all quadrics, and all surfaces formed by their inversions in spheres. Dupin cyclides are quartic surfaces formed by inversions in spheres of torus, cylinder, and cone surfaces. Parabolic cyclides are cubic surfaces formed by inversions in spheres that are centered on points of other surfaces. All DCGA entities can be transformed by versors, and reflected in spheres and planes.

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Acknowledgements

We thank the organizers of the CGI 2016 conference in Heraklion, Crete, Greece, and in particular the organizers of the GACSE 2016 workshop day at CGI 2016. We further deeply thank the anonymous reviewers for their time consuming detailed study of our manuscript and very many suggestions for improvement.

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Correspondence to Eckhard Hitzer.

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Easter, R.B., Hitzer, E. Double Conformal Geometric Algebra. Adv. Appl. Clifford Algebras 27, 2175–2199 (2017). https://doi.org/10.1007/s00006-017-0784-0

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