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Numerical Implicitization of Parametric Hypersurfaces with Linear Algebra

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Artificial Intelligence and Symbolic Computation (AISC 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1930))

Abstract

We present a new method for implicitization of parametric curves, surfaces and hypersurfaces usingessen tially numerical linear algebra. The method is applicable for polynomial, rational as well as trigonometric parametric representations. The method can also handle monoparametric families of parametric curves, surfaces and hypersurfaces with a small additional amount of human interaction. We illustrate the method with a number of examples. The efficiency of the method compares well with the other available methods for implicitization.

Work supported by the Ontario Research Centre for Computer Algebra the Ontario Research and Development Challenge Fund and the Natural Sciences and Engineering Re search Council of Canada.

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Author information

Authors and Affiliations

  1. Canada Ontario Research Centre for Computer Algebra, University of Western Ontario, London, Ontario, N6A 5B9

    Robert M. Corless, Mark W. Giesbrecht, Ilias S. Kotsireas & Stephen M. Watt

Authors
  1. Robert M. Corless
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  2. Mark W. Giesbrecht
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  3. Ilias S. Kotsireas
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  4. Stephen M. Watt
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Editor information

Editors and Affiliations

  1. University College London, Gower Street, WC1E 6BT, London, UK

    John A. Campbell

  2. Dept. Algebra, Fac. Educación, Universidad Complutense de Madrid, c/Rector Royo Villanova s/n, 28040, Madrid, Spain

    Eugenio Roanes-Lozano

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© 2001 Springer-Verlag Berlin Heidelberg

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Corless, R.M., Giesbrecht, M.W., Kotsireas, I.S., Watt, S.M. (2001). Numerical Implicitization of Parametric Hypersurfaces with Linear Algebra. In: Campbell, J.A., Roanes-Lozano, E. (eds) Artificial Intelligence and Symbolic Computation. AISC 2000. Lecture Notes in Computer Science(), vol 1930. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44990-6_13

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  • DOI: https://doi.org/10.1007/3-540-44990-6_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42071-2

  • Online ISBN: 978-3-540-44990-4

  • eBook Packages: Springer Book Archive

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