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Moving Curve Ideals of Rational Plane Parametrizations

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Computer Algebra and Polynomials

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8942))

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Abstract

In the nineties, several methods for dealing in a more efficient way with the implicitization of rational parametrizations were explored in the Computer Aided Geometric Design Community. The analysis of the validity of these techniques has been a fruitful ground for Commutative Algebraists and Algebraic Geometers, and several results have been obtained so far. Yet, a lot of research is still being done currently around this topic. In this note we present these methods, show their mathematical formulation, and survey current results and open questions.

Partially supported by the Research Project MTM2010–20279 from the Ministerio de Ciencia e Innovación, Spain.

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Acknowledgments

I am grateful to Laurent Busé, Eduardo Casas-Alvero and Teresa Cortadellas Benitez for their careful reading of a preliminary version of this manuscript, and very helpful comments. Also, I thank the anonymous referee for her further comments and suggestions for improvements, and to Marta Narváez Clauss for her help with the computations of some examples. All the plots in this text have been done with Mathematica 8.0 [Wol10].

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  1. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain

    Carlos D’Andrea

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  1. Carlos D’Andrea
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Correspondence to Carlos D’Andrea .

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  1. University of Cantabria, Santander, Spain

    Jaime Gutierrez

  2. Ricam Linz, Linz, Austria

    Josef Schicho

  3. University of Caen, Caen, France

    Martin Weimann

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D’Andrea, C. (2015). Moving Curve Ideals of Rational Plane Parametrizations. In: Gutierrez, J., Schicho, J., Weimann, M. (eds) Computer Algebra and Polynomials. Lecture Notes in Computer Science(), vol 8942. Springer, Cham. https://doi.org/10.1007/978-3-319-15081-9_2

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  • DOI: https://doi.org/10.1007/978-3-319-15081-9_2

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