Conic and cyclidic sections in double conformal geometric algebra G8,2 with computing and visualization using Gaalop

Abstract

The 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, in terms of algebraic expressions, computer code, and many examples of computer‐generated graphics. Operations include reflection, projection, rejection, and intersection with respect to spheres and planes. Other operations include rotation, translation, and dilation. Possible applications are introduced, which include orthographic and perspective projections of conic sections onto view planes, which may be of interest in computer graphics or other computational geometry subjects