Conic and Cyclidic Sections in the G8,2 Geometric Algebra, DCGA

Authors: Robert B. Easter

The G(8,2) Geometric Algebra, also called the Double Conformal / Darboux Cyclide Geometric Algebra (DCGA), has entities that represent conic sections. DCGA also has entities that represent planar sections of Darboux cyclides, which are called cyclidic sections in this paper. This paper presents these entities and many operations on them. Operations include reflection, projection, rejection, and intersection with respect to spheres and planes. Other operations include rotation, translation, and dilation. Possible applications are introduced that include orthographic and perspective projections of conic sections onto view planes, which may be of interest in computer graphics or other computational geometry subjects.

Comments: 16 Pages.

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Submission history

[v1] 2015-11-19 20:01:11
[v2] 2016-07-22 09:22:40

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