Algebra

1705 Submissions

[1] viXra:1705.0019 [pdf] submitted on 2017-05-02 04:07:01

Double Conformal Geometric Algebra (long CGI2016/GACSE2016 paper in SI of AACA)

Authors: Robert B. Easter, Eckhard Hitzer
Comments: 25 Pages. Published online First in AACA, 20th April 2017. DOI: 10.1007/s00006-017-0784-0. 2 tables, 26 references.

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. Keywords: Conformal geometric algebra, Darboux Dupin cyclide, Quadric surface Math. Subj. Class.: 15A66, 53A30, 14J26, 53A05, 51N20, 51K05
Category: Algebra