An Implicitization Algorithm for Rational Surfaces with no Base Points

We present an implicitization algorithm which is free of extraneous factors if the rational parametric surface has no base points. This algorithm is based on the method of Sylvester for computing the resultant of three homogeneous polynomials in three variables. Some examples and computations illust...

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Vydáno v:Journal of symbolic computation Ročník 31; číslo 4; s. 357 - 365
Hlavní autoři: Aries, Franck, Senoussi, Rachid
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.04.2001
ISSN:0747-7171, 1095-855X
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Abstract We present an implicitization algorithm which is free of extraneous factors if the rational parametric surface has no base points. This algorithm is based on the method of Sylvester for computing the resultant of three homogeneous polynomials in three variables. Some examples and computations illustrate the efficiency and limits of this method.
AbstractList We present an implicitization algorithm which is free of extraneous factors if the rational parametric surface has no base points. This algorithm is based on the method of Sylvester for computing the resultant of three homogeneous polynomials in three variables. Some examples and computations illustrate the efficiency and limits of this method.
Author Senoussi, Rachid
Aries, Franck
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Cites_doi 10.1016/0167-8396(92)90051-P
10.1112/plms/s2-21.1.14
10.1016/0167-8396(92)90009-E
10.1016/0167-8396(95)00026-7
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References Manocha, Canny (RF10) 1992; 9
G. Salmon
Dixon (RF6) 1908; 7
Gelfand, Kapranov, Zelevinsky (RF7) 1994
Chionh, Goldman (RF3) 1992; 9
Aries, Senoussi (RF1) 1997; 12
Kapur, Saxena (RF8) 1995
Becker, Weispfenning (RF2) 1993
Sturmfels (RF13) 1998
Sederberg, Chen (RF12) 1995; 18
Cox, Little, O’Shea (RF5) 1998
Coffman, Schwartz, Stanton (RF4) 1996; 13
Macauley (RF9) 1923; 21C1408
Kapur (10.1006/jsco.1999.0436_RF8) 1995
10.1006/jsco.1999.0436_RF11
Dixon (10.1006/jsco.1999.0436_RF6) 1908; 7
Sturmfels (10.1006/jsco.1999.0436_RF13) 1998
Aries (10.1006/jsco.1999.0436_RF1) 1997; 12
Chionh (10.1006/jsco.1999.0436_RF3) 1992; 9
Cox (10.1006/jsco.1999.0436_RF5) 1998
Coffman (10.1006/jsco.1999.0436_RF4) 1996; 13
Gelfand (10.1006/jsco.1999.0436_RF7) 1994
Manocha (10.1006/jsco.1999.0436_RF10) 1992; 9
Becker (10.1006/jsco.1999.0436_RF2) 1993
Sederberg (10.1006/jsco.1999.0436_RF12) 1995; 18
Macauley (10.1006/jsco.1999.0436_RF9) 1923; 21C1408
References_xml – year: 1998
  ident: RF5
  publication-title: Using Algebraic Geometry
– volume: 9
  start-page: 93
  year: 1992
  end-page: 108
  ident: RF3
  article-title: Degree, multiplicity and inversion formulas for rational surfaces using u-resultants
  publication-title: Comput.-Aided Geom. Des.
– volume: 12
  start-page: 627
  year: 1997
  end-page: 645
  ident: RF1
  article-title: Approximation de surfaces paramétriques par des carreaux rationnels du second degré en lancer de rayons
  publication-title: Rev. Int. CFAO Inform. Graph.
– start-page: 25
  year: 1998
  end-page: 39
  ident: RF13
  article-title: Introduction to resultants
  publication-title: Applications of Computational Geometry
– reference: G. Salmon,
– year: 1994
  ident: RF7
  publication-title: Discriminants, Resultants and Mulitidimensional Determinants
– volume: 21C1408
  start-page: 14
  year: 1923
  end-page: 21
  ident: RF9
  article-title: Note on the resultant of a number of polynomials of the same degree
  publication-title: Proc. London Math. Soc.
– volume: 7
  start-page: 49
  year: 1908
  end-page: 69, (473–492)
  ident: RF6
  article-title: The eliminant of three quantics in two independant variables
  publication-title: Proc. London Math. Soc.
– volume: 18
  start-page: 301
  year: 1995
  end-page: 308
  ident: RF12
  article-title: Implicitization using curves and surfaces
  publication-title: Comput. Graph. Siggraph 1995
– volume: 9
  start-page: 25
  year: 1992
  end-page: 50
  ident: RF10
  article-title: Algorithm for implicitizing rational parametric surfaces
  publication-title: Comput.-Aided Geom. Des.
– year: 1995
  ident: RF8
  article-title: Comparison of various multivariate resultant formulations
  publication-title: Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC’95)
– year: 1993
  ident: RF2
  publication-title: Gröbner Bases: A Computational Approach to Commutative Algebra
– volume: 13
  start-page: 257
  year: 1996
  end-page: 286
  ident: RF4
  article-title: The algebra and geometry of steiner and other quadratically parametrizable surfaces
  publication-title: Comput.-Aided Geom. Des.
– year: 1995
  ident: 10.1006/jsco.1999.0436_RF8
  article-title: Comparison of various multivariate resultant formulations
– volume: 9
  start-page: 25
  year: 1992
  ident: 10.1006/jsco.1999.0436_RF10
  article-title: Algorithm for implicitizing rational parametric surfaces
  publication-title: Comput.-Aided Geom. Des.
  doi: 10.1016/0167-8396(92)90051-P
– volume: 18
  start-page: 301
  year: 1995
  ident: 10.1006/jsco.1999.0436_RF12
  article-title: Implicitization using curves and surfaces
  publication-title: Comput. Graph. Siggraph 1995
– volume: 21C1408
  start-page: 14
  year: 1923
  ident: 10.1006/jsco.1999.0436_RF9
  article-title: Note on the resultant of a number of polynomials of the same degree
  publication-title: Proc. London Math. Soc.
  doi: 10.1112/plms/s2-21.1.14
– volume: 12
  start-page: 627
  year: 1997
  ident: 10.1006/jsco.1999.0436_RF1
  article-title: Approximation de surfaces paramétriques par des carreaux rationnels du second degré en lancer de rayons
  publication-title: Rev. Int. CFAO Inform. Graph.
– volume: 9
  start-page: 93
  year: 1992
  ident: 10.1006/jsco.1999.0436_RF3
  article-title: Degree, multiplicity and inversion formulas for rational surfaces using u-resultants
  publication-title: Comput.-Aided Geom. Des.
  doi: 10.1016/0167-8396(92)90009-E
– year: 1998
  ident: 10.1006/jsco.1999.0436_RF5
– start-page: 25
  year: 1998
  ident: 10.1006/jsco.1999.0436_RF13
  article-title: Introduction to resultants
– volume: 13
  start-page: 257
  year: 1996
  ident: 10.1006/jsco.1999.0436_RF4
  article-title: The algebra and geometry of steiner and other quadratically parametrizable surfaces
  publication-title: Comput.-Aided Geom. Des.
  doi: 10.1016/0167-8396(95)00026-7
– year: 1993
  ident: 10.1006/jsco.1999.0436_RF2
– year: 1994
  ident: 10.1006/jsco.1999.0436_RF7
– ident: 10.1006/jsco.1999.0436_RF11
– volume: 7
  start-page: 49
  year: 1908
  ident: 10.1006/jsco.1999.0436_RF6
  article-title: The eliminant of three quantics in two independant variables
  publication-title: Proc. London Math. Soc.
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