## G8,2 Geometric Algebra, DCGA

**Authors:** Robert B. Easter

This paper introduces the Double Conformal / Darboux Cyclide Geometric Algebra (DCGA), based in the G8,2 Clifford geometric algebra. DCGA is an extension of CGA and has entities representing points and general Darboux cyclide surfaces in Euclidean 3D space. The general Darboux cyclide is a quartic surface. Darboux cyclides include circular tori and all quadrics, and also all surfaces formed by their inversions in spheres. Dupin cyclide surfaces can be formed as inversions in spheres of circular toroid, cylinder, and cone surfaces. Parabolic cyclides are cubic surfaces formed by inversion spheres centered on other surfaces. All DCGA entities can be conformally transformed in 3D space by rotors, dilators, translators, and motors, which are all types of versors. All entities can be inversed in general spheres and reflected in general planes. Entities representing the intersections of surfaces can be created by wedge products. All entities can be intersected with spheres, planes, lines, and circles. DCGA provides a higher-level algebra for working with 3D geometry in an object/entity-oriented system of mathematics above the level of the underlying implicit surface equations of algebraic geometry. DCGA could be used in the study of geometry in 3D, and also for some applications.

**Comments:** 62 Pages.

**Download:** **PDF**

### Submission history

[v1] 2015-08-11 10:39:32

[v2] 2015-08-13 13:34:52

[v3] 2015-08-17 10:53:51

[v4] 2015-08-21 22:21:34

[v5] 2015-09-02 15:26:57

[v6] 2015-09-20 08:27:38

[v7] 2015-09-24 13:06:54

[v8] 2015-09-29 11:45:47

[v9] 2015-09-30 22:19:24

[vA] 2015-10-01 17:57:21

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