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ISSAC 2019 software presentations communicated by Yue Ren: a package to compute implicit equations for rational curves and surfaces

Published: 08 November 2019 Publication History

Abstract

Implicit is a package for implicitizing rational planar curves and rational tensor product surfaces, developed on Maplesoft based on the state-of-the-art implicitization techniques. The main functions ImpCurve and ImpSurface return the implicit equation of a rational planar curve or a rational tensor product surface. Other popularly used functions, such as ImpDegree, ImpMatrix and ImpRuled that are used for deciding the implicit degree and the implicit matrix of a general rational surface, and computing the implicit equation of a rational ruled surface in a more efficient way, are also proposed.

References

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Falai Chen and Wenping Wang. The μ-basis of a planar rational curve¡aproperties and computation. Graphical Models, 64(6):368--381, 2002.
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Eng-Wee Chionh, Ming Zhang, and Ronald N. Goldman. Implicitization by dixon A-resultants. In Proceedings of the Geometric Modeling and Processing 2000, GMP '00, pages 310--317, Washington, DC, USA, 2000. IEEE Computer Society.
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Thomas W. Sederberg and Falai Chen. Implicitization using moving curves and surfaces. In Proceedings of the 22Nd Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH'95, pages 301--308, New York, NY, USA, 1995. ACM.
[4]
Li-Yong Shen and Ron Goldman. Implicitizing rational tensor product surfaces using the resultant of three moving planes. ACM Transactions on Graphics, 36(5):167:1--167:14, August 2017.
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Li-Yong Shen and Ron Goldman. Strong μ-bases for rational tensor product surfaces and extraneous factors associated to bad base points and anomalies at infinity. SIAM Journal on Applied Algebra and Geometry, 1(1):328--351, 2017.
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Li-Yong Shen and Ron Goldman. Combining complementary methods for implicitizing rational tensor product surfaces. Computer-Aided Design, 104:100 -- 112, 2018.
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Chunming Yuan. Li-Yong Shen. Implicitization using univariate resultants. Journal of Systems Science and Complexity, 23(4):804--814, 2010.
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David A. Cox, John B. Little, and Donal O'Shea. Using algebraic geometry. Graduate texts in mathematics. Springer, New York, 1998.
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Angelos Mantzaflaris and Elias Tsigaridas. Resultants and discriminants for bivariate tensor-product polynomials. In Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '17, pages 309--316, New York, NY, USA, 2017. ACM.

Cited By

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  • (2023)Bounds for degrees of syzygies of polynomials defining a grade two idealJournal of Symbolic Computation10.1016/j.jsc.2022.08.004115(124-141)Online publication date: Mar-2023

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Published In

cover image ACM Communications in Computer Algebra
ACM Communications in Computer Algebra  Volume 53, Issue 2
June 2019
45 pages
ISSN:1932-2232
EISSN:1932-2240
DOI:10.1145/3371991
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 08 November 2019
Published in SIGSAM-CCA Volume 53, Issue 2

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Author Tags

  1. implicitization
  2. rational curve
  3. rational surface

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View all
  • (2023)Bounds for degrees of syzygies of polynomials defining a grade two idealJournal of Symbolic Computation10.1016/j.jsc.2022.08.004115(124-141)Online publication date: Mar-2023

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