Geometric Algebra for Conics

Abstract

We present a particular geometric algebra together with such an embedding of two–dimensional Euclidean space that the algebra elements may be in the most efficient way interpreted as arbitrary conic sections. Consequently, in this setting we provide full description of the conic sections analysis, classification and their transformations. Examples that show the functionality and consistency are provided in Maple together with the source code.

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Correspondence to Jaroslav Hrdina.

Additional information

This article is part of the Topical Collection on Proceedings ICCA 11, Ghent, 2017, edited by Hennie De Schepper, Fred Brackx, Joris van der Jeugt, Frank Sommen, and Hendrik De Bie

The research was supported by the Czech Science Foundation under Grant no.: 17-21360S.

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Hrdina, J., Návrat, A. & Vašík, P. Geometric Algebra for Conics. Adv. Appl. Clifford Algebras 28, 66 (2018). https://doi.org/10.1007/s00006-018-0879-2

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Keywords

  • Conformal geometric algebra
  • Geometric algebra
  • Clifford algebra
  • Conic section

Mathematics Subject Classification

  • Primary 15A66
  • Secondary 51N25