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Computing the Topology of an Arrangement of Implicit and Parametric Curves Given by Values

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Book cover Computer Algebra in Scientific Computing (CASC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8660))

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Abstract

Curve arrangement studying is a subject of great interest in Computational Geometry and CAGD. In our paper, a new method for computing the topology of an arrangement of algebraic plane curves, defined by implicit and parametric equations, is presented. The polynomials appearing in the equations are given in the Lagrange basis, with respect to a suitable set of nodes. Our method is of sweep-line class, and its novelty consists in applying algebra by values for solving systems of two bivariate polynomial equations. Moreover, at our best knowledge, previous works on arrangements of curves consider only implicitly defined curves.

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Author information

Authors and Affiliations

  1. Universidad Complutense de Madrid, Spain

    Jorge Caravantes

  2. Universidad de Cantabria, Spain

    Mario Fioravanti & Laureano Gonzalez–Vega

  3. Universidad de Sevilla, Spain

    Ioana Necula

Authors
  1. Jorge Caravantes
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  2. Mario Fioravanti
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  3. Laureano Gonzalez–Vega
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  4. Ioana Necula
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Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research, 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Institut für Mathematik, Universität Kassel, 34132, Kassel, Germany

    Werner M. Seiler

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Caravantes, J., Fioravanti, M., Gonzalez–Vega, L., Necula, I. (2014). Computing the Topology of an Arrangement of Implicit and Parametric Curves Given by Values. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2014. Lecture Notes in Computer Science, vol 8660. Springer, Cham. https://doi.org/10.1007/978-3-319-10515-4_5

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  • DOI: https://doi.org/10.1007/978-3-319-10515-4_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10514-7

  • Online ISBN: 978-3-319-10515-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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