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Invariant-Based Characterization of the Relative Position of Two Projective Conics

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Nonlinear Computational Geometry

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 151))

Abstract

In this paper, we give predicates of bidegree at most (6, 6) in the input for characterizing the relative position of two projective conics. By relative position we mean the morphology of the intersection, the rigid isotopy class and which conic is inside the other when applicable. The predicates are derived by analyzing the algebraic invariant theory of pencils of conics and related constructions.

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Author information

Authors and Affiliations

  1. LORIA-INRIA, Campus scientifique, BP 239, 54506, Vandœuvre-lès-Nancy cedex, France

    Sylvain Petitjean

Authors
  1. Sylvain Petitjean
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Correspondence to Sylvain Petitjean .

Editor information

Editors and Affiliations

  1. Dept. Informatics & Telecommunications, National University of Athens, Panepistimiopolis, Athens, 157 84, Greece

    Ioannis Z. Emiris

  2. Dept. Mathematics, Texas A & M University, Blocker Hall 608K, College Station, 77843, U.S.A.

    Frank Sottile

  3. Zentrum Mathematik (M10), TU München, Boltzmannstr. 3, Garching, 85748, Germany

    Thorsten Theobald

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Petitjean, S. (2009). Invariant-Based Characterization of the Relative Position of Two Projective Conics. In: Emiris, I., Sottile, F., Theobald, T. (eds) Nonlinear Computational Geometry. The IMA Volumes in Mathematics and its Applications, vol 151. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0999-2_8

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