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Some Covariants Related to Steiner Surfaces

In: Geometric Modeling and Algebraic Geometry

Author

Listed:
  • Franck Aries

    (INRA Biométrie)

  • Emmanuel Briand

    (Universidad de Cantabria)

  • Claude Bruchou

    (INRA Biométrie)

Abstract

A Steiner surface is the generic case of a quadratically parameterizable quartic surface used in geometric modeling. This paper studies quadratic parameterizations of surfaces under the angle of Classical Invariant Theory. Precisely, it exhibits a collection of covariants associated to projective quadratic parameterizations of surfaces, under the actions of linear reparameterization and linear transformations of the target space. Each of these covariants comes with a simple geometric interpretation. As an application, some of these covariants are used to produce explicit equations and inequalities defining the orbits of projective quadratic parameterizations of quartic surfaces.

Suggested Citation

  • Franck Aries & Emmanuel Briand & Claude Bruchou, 2008. "Some Covariants Related to Steiner Surfaces," Springer Books, in: Bert Jüttler & Ragni Piene (ed.), Geometric Modeling and Algebraic Geometry, chapter 2, pages 31-46, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-72185-7_2
    DOI: 10.1007/978-3-540-72185-7_2
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