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Intersection of Conic Sections Using Geometric Algebra

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Advances in Computer Graphics (CGI 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14498))

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Abstract

Conic sections are extensively encountered in a wide range of disciplines, including optics, physics, and various other fields. Consequently, the geometric algebra community is actively engaged in developing frameworks that enable efficient support and manipulation of conic sections. Conic-conic intersection objects are known and supported by algebras specialized in conic sections representation, but there is yet no elegant formula to extract the intersection points from them. This paper proposes a method for point extraction from an conic intersection through the concept of pencils. It will be based on QC2GA, the 2D version of QCGA (Quadric Conformal Geometric Algebra), that we also prove to be equivalent to GAC (Geometric Algebra for Conics).

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Author information

Authors and Affiliations

  1. LIGM, Univ Gustave Eiffel, CNRS, Marne-la-Vallée, France

    Clément Chomicki, Venceslas Biri & Vincent Nozick

  2. LAMA, Univ Savoie Mont-Blanc, CNRS, Annecy, France

    Stéphane Breuils

Authors
  1. Clément Chomicki
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  2. Stéphane Breuils
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  3. Venceslas Biri
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  4. Vincent Nozick
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Corresponding author

Correspondence to Clément Chomicki .

Editor information

Editors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Bin Sheng

  2. Shanghai Jiao Tong University, Shanghai, China

    Lei Bi

  3. University of Sydney, Sydney, NSW, Australia

    Jinman Kim

  4. MIRALab-CUI, University of Geneve, Carouge, Geneve, Switzerland

    Nadia Magnenat-Thalmann

  5. Swiss federal Institute of Technology, Lausanne, Switzerland

    Daniel Thalmann

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Chomicki, C., Breuils, S., Biri, V., Nozick, V. (2024). Intersection of Conic Sections Using Geometric Algebra. In: Sheng, B., Bi, L., Kim, J., Magnenat-Thalmann, N., Thalmann, D. (eds) Advances in Computer Graphics. CGI 2023. Lecture Notes in Computer Science, vol 14498. Springer, Cham. https://doi.org/10.1007/978-3-031-50078-7_14

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  • DOI: https://doi.org/10.1007/978-3-031-50078-7_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-50077-0

  • Online ISBN: 978-3-031-50078-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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