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Advances in Applied Clifford Algebras

, Volume 27, Issue 3, pp 2795–2803 | Cite as

Intersection of a Double Cone and a Line in the Split-Quaternions Context

  • R. Serôdio
  • P. D. Beites
  • José Vitória
Article

Abstract

This is a work on an application of the real split-quaternions to Spatial Analytic Geometry. Concretely, the intersection of a double cone and a line, which can be the empty set, a point, two points or a line, is studied in the real split-quaternions setting.

Keywords

Double cone Line Intersection Split-quaternion Event Direction 

Mathematics Subject Classification

15A66 51P05 83A05 

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References

  1. 1.
    Cychosz, J.M., Waggenspack, W.N., Jr.: Intersecting a ray with a cylinder. In: Heckbert, P. (ed.) Graphics Gems IV pp. 356–365. AP Professional, San Diego (1994)Google Scholar
  2. 2.
    Goldblatt, R.: Orthogonality and Spacetime Geometry. Springer, New York (1987)CrossRefzbMATHGoogle Scholar
  3. 3.
    Jacobson, N.: Composition algebras and their automorphisms. Rendiconti del Circolo Matematico di Palermo 7, 55–80 (1958)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Lam, T.Y.: The Algebraic Theory of Quadratic Forms. W. A. Benjamin, Reading (1973)zbMATHGoogle Scholar
  5. 5.
    Ratcliffe, J.: Foundations of Hyperbolic Manifolds. Springer, New York (2006)zbMATHGoogle Scholar
  6. 6.
    Shene, C.-K.: Computing the Intersection of a Line and a Cone. In: Paeth, A. (ed.) Graphics Gems V pp. 227–231. AP Professional, London (1995)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Centro de Matemática e Aplicações (CMA-UBI) and Departamento de MatemáticaUniversidade da Beira InteriorCovilhãPortugal
  2. 2.Departamento de MatemáticaUniversidade de CoimbraCoimbraPortugal

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