# Double Conformal Geometric Algebra

Double Conformal Geometric Algebra This paper introduces the Double Conformal/Darboux Cyclide Geometric Algebra (DCGA), based in the $$\mathcal {G}_{8, 2}$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Applied Clifford Algebras Springer Journals

# Double Conformal Geometric Algebra

, Volume 27 (3) – Apr 20, 2017
25 pages

/lp/springer_journal/double-conformal-geometric-algebra-XMjLjuw9GX
Publisher
Springer International Publishing
Subject
Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics; Physics, general
ISSN
0188-7009
eISSN
1661-4909
D.O.I.
10.1007/s00006-017-0784-0
Publisher site
See Article on Publisher Site

### Abstract

This paper introduces the Double Conformal/Darboux Cyclide Geometric Algebra (DCGA), based in the $$\mathcal {G}_{8, 2}$$ 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.

### Journal

Advances in Applied Clifford AlgebrasSpringer Journals

Published: Apr 20, 2017

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