Some Covariants Related to Steiner Surfaces

Franck Aries (), Emmanuel Briand () and Claude Bruchou ()
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Franck Aries: INRA Biométrie
Emmanuel Briand: Universidad de Cantabria
Claude Bruchou: INRA Biométrie

Chapter 2 in Geometric Modeling and Algebraic Geometry, 2008, pp 31-46 from Springer

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.

Keywords: Triple Point; Tangent Plane; Geometric Object; Zero Locus; Zariski Closure (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-72185-7_2

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DOI: 10.1007/978-3-540-72185-7_2

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