extended-abstract

Parametrization of ε-rational curves: extended abstract

Authors:

Sonia Peréz-Díaz,

J. Rafael Sendra,

Sonia L. Rueda,

Juana SendraAuthors Info & Claims

SNC '09: Proceedings of the 2009 conference on Symbolic numeric computation

Pages 199 - 200

https://doi.org/10.1145/1577190.1577221

Published: 03 August 2009 Publication History

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Abstract

In this talk we deal with the problem of parametrizing approximately a perturbed rational affine plane curve implicitly given. We present some of our recent results (see [3], [4], [5], [6]) and we describe our on going research in this context. More precisely, we focus on our approximate parametrization algorithm in [6], and we present an empirical analysis that shows that the input and output curves of the algorithm are close in practice.

References

[1]

Corless R. M., Giesbrecht M. W., Kotsireas I. S., van Hoeij M., Watt S.M., (2001). Towards Factoring Bivariate ApproximatePolynomials. Proc. ISSAC 2001, London, Bernard Mourrain, ed. pp85--92.

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[2]

Kaltofen E., May J. P., Yang Z., Zhi L., (2008). Approximate Factorization of Multivariate Polynomials Using Singular Value Decomposition. J. Symbolic Computation. Vol.43/5.pp.359--376.

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[3]

P&#233;rez-D&#237;az, S., Sendra, J., Sendra, J. R., (2004). Parametrizations by Lines of Approximate Algebraic Curves. Theoretical Computer Science on Algebraic-Numeric Algorithms, 315/2-3, pp. 627--650.

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[4]

P&#233;rez-D&#237;az, S., Sendra, J., Sendra, J. R., (2005). Parametrizations by Lines of Approximate Algebraic Surfaces. Computer Aided Geometric Design, 22/2, pp. 147--181.

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[5]

P&#233;rez-D&#237;az, S., Sendra, J., Sendra, J. R., (2006). Distance Bounds of &#949;-Points on Hypersurfaces. Theoretical Computer Science, 359/1-3. pp. 344--368.

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[6]

P&#233;rez-D&#237;az, S., Rueda S. L., Sendra, J., Sendra, J. R., (2009). Approximate Parametrization of Plane Algebraic Curves by Linear Systems of Curves. arXiv: 0901.0320v1.

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[7]

Sasaki T., Terui A., (2002). A Formula for Separating Small Roots of a Polynomial. ACM, SIGSAM Bulletin, Vol.36, N.3. pp. 19--23.

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[8]

Sendra J. R., Winkler J. R., P&#233;rez-D&#237;az S. (2007). Rational Algebraic Curves: A Computer Algebra Approach. Springer-Verlag Heidelberg, in series Algorithms and Computation in Mathematics. Vol. 22.

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Index Terms

Parametrization of ε-rational curves: extended abstract
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms

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Published In

SNC '09: Proceedings of the 2009 conference on Symbolic numeric computation

August 2009

210 pages

ISBN:9781605586649

DOI:10.1145/1577190

Editors:
Hiroshi Kai
Ehime University, Japan
,
Hiroshi Sekigawa
NTT Communication Science Laboratories, Japan
,
General Chairs:
Tateaki Sasaki
University of Tsukuba, Japan
,
Kiyoshi Shirayanagi
Tokai University, Japan
,
Program Chair:
Ilias Kotsireas
Wilfrid Laurier University, Canada

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

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Published: 03 August 2009

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SNC '09: Symbolic Numeric Computation

August 3 - 5, 2009

Kyoto, Japan

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Rational parametrization of conchoids to algebraic curves

Rational Pythagorean-hodograph space curves

Curves with rational chord-length parametrization

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