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Computing the Orthogonal Projection of Rational Curves onto Rational Parameterized Surface by Symbolic Methods

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Mathematical Software – ICMS 2014 (ICMS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8592))

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Abstract

This paper presents three algorithms to compute orthogonal projection of rational curves onto rational parameterized surface. One of them, based on regular systems, is able to compute the exact parametric loci of projection. The one based on Gröbner basis can compute the minimal variety that contains the parametric loci. The rest one computes a variety that contains the parametric loci via resultant. Examples show that our algorithms are efficient and valuable.

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Author information

Authors and Affiliations

  1. School of Mathematics and System Science, Beihang University, Beijing, China

    Zhiwang Gan & Meng Zhou

Authors
  1. Zhiwang Gan
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  2. Meng Zhou
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Editor information

Editors and Affiliations

  1. Department of Mathematics, North Carolina State University, Box 8205, 27695, Raleigh, NC, USA

    Hoon Hong

  2. Courant Institute, Dept. of Computer Science, New York Institute, 251 Mercer Street, 10012, New York, NY, USA

    Chee Yap

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Gan, Z., Zhou, M. (2014). Computing the Orthogonal Projection of Rational Curves onto Rational Parameterized Surface by Symbolic Methods. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_41

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  • DOI: https://doi.org/10.1007/978-3-662-44199-2_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44198-5

  • Online ISBN: 978-3-662-44199-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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