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Topics in Algebraic Geometry and Geometric Modeling
 
Edited by: Ron Goldman Rice University, Houston, TX
Rimvydas Krasauskas Vilnius University, Vilnius, Lithuania
Topics in Algebraic Geometry and Geometric Modeling
eBook ISBN:  978-0-8218-7924-5
Product Code:  CONM/334.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Topics in Algebraic Geometry and Geometric Modeling
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Topics in Algebraic Geometry and Geometric Modeling
Edited by: Ron Goldman Rice University, Houston, TX
Rimvydas Krasauskas Vilnius University, Vilnius, Lithuania
eBook ISBN:  978-0-8218-7924-5
Product Code:  CONM/334.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 3342003; 366 pp
    MSC: Primary 14; 52; 65; 68; Secondary 13; 41; 58;

    Algebraic geometry and geometric modeling both deal with curves and surfaces generated by polynomial equations. Algebraic geometry investigates the theoretical properties of polynomial curves and surfaces; geometric modeling uses polynomial, piecewise polynomial, and rational curves and surfaces to build computer models of mechanical components and assemblies for industrial design and manufacture.

    The NSF sponsored the four-day “Vilnius Workshop on Algebraic Geometry and Geometric Modeling”, which brought together some of the top experts in the two research communities to examine a wide range of topics of interest to both fields. This volume is an outgrowth of that workshop. Included are surveys, tutorials, and research papers. In addition, the editors have included a translation of Minding's 1841 paper, “On the determination of the degree of an equation obtained by elimination”, which foreshadows the modern application of mixed volumes in algebraic geometry.

    The volume is suitable for mathematicians, computer scientists, and engineers interested in applications of algebraic geometry to geometric modeling.

    Readership

    Graduate students, research mathematicians, computer scientists, and engineers interested in applications of algebraic geometry to geometric modeling.

  • Table of Contents
     
     
    • Modeling Curves and Surfaces [ MR 2046835 ]
    • Ron Goldman — Polar forms in geometric modeling and algebraic geometry [ MR 2039963 ]
    • Wenping Wang and Rimvydas Krasauskas — Interference analysis of conics and quadrics [ MR 2039964 ]
    • Raimundas Vidūnas — Geometrically continuous octahedron [ MR 2039965 ]
    • Multisided Patches [ MR 2046835 ]
    • Jörg Peters — Smoothness, fairness and the need for better multi-sided patches [ MR 2039966 ]
    • Rimvydas Krasauskas and Ron Goldman — Toric Bézier patches with depth [ MR 2039967 ]
    • Joe Warren — On the uniqueness of barycentric coordinates [ MR 2039968 ]
    • Kȩstutis Karčiauskas — Rational $M$-patches and tensor-border patches [ MR 2039969 ]
    • Implicitization and Parametrization [ MR 2046835 ]
    • David Cox — Curves, surfaces, and syzygies [ MR 2039970 ]
    • Jianmin Zheng, Thomas W. Sederberg, Eng-Wee Chionh and David A. Cox — Implicitizing rational surfaces with base points using the method of moving surfaces [ MR 2039971 ]
    • Tor Dokken and Jan Brede Thomassen — Overview of approximate implicitization [ MR 2039972 ]
    • Josef Schicho — Algorithms for rational surfaces [ MR 2039973 ]
    • Tonic Varieties [ MR 2046835 ]
    • David Cox — What is a toric variety? [ MR 2039974 ]
    • Frank Sottile — Toric ideals, real toric varieties, and the moment map [ MR 2039975 ]
    • David Cox, Rimvydas Krasauskas and Mircea Mustaţǎ — Universal rational parametrizations and toric varieties [ MR 2039976 ]
    • Claire Delaunay — Real structures on smooth compact toric surfaces [ MR 2039977 ]
    • Mixed Volume and Resultants [ MR 2046835 ]
    • J. Maurice Rojas — Why polyhedra matter in non-linear equation solving [ MR 2039978 ]
    • Laurent Busé, Mohamed Elkadi and Bernard Mourrain — Using projection operators in computer aided geometric design [ MR 2039979 ]
    • Ivan Soprounov — On combinatorial coefficients and the Gelfond-Khovanskii residue formula [ MR 2039980 ]
    • Ferdinand Minding — On the determination of the degree of an equation obtained by elimination [ MR 2039981 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 3342003; 366 pp
MSC: Primary 14; 52; 65; 68; Secondary 13; 41; 58;

Algebraic geometry and geometric modeling both deal with curves and surfaces generated by polynomial equations. Algebraic geometry investigates the theoretical properties of polynomial curves and surfaces; geometric modeling uses polynomial, piecewise polynomial, and rational curves and surfaces to build computer models of mechanical components and assemblies for industrial design and manufacture.

The NSF sponsored the four-day “Vilnius Workshop on Algebraic Geometry and Geometric Modeling”, which brought together some of the top experts in the two research communities to examine a wide range of topics of interest to both fields. This volume is an outgrowth of that workshop. Included are surveys, tutorials, and research papers. In addition, the editors have included a translation of Minding's 1841 paper, “On the determination of the degree of an equation obtained by elimination”, which foreshadows the modern application of mixed volumes in algebraic geometry.

The volume is suitable for mathematicians, computer scientists, and engineers interested in applications of algebraic geometry to geometric modeling.

Readership

Graduate students, research mathematicians, computer scientists, and engineers interested in applications of algebraic geometry to geometric modeling.

  • Modeling Curves and Surfaces [ MR 2046835 ]
  • Ron Goldman — Polar forms in geometric modeling and algebraic geometry [ MR 2039963 ]
  • Wenping Wang and Rimvydas Krasauskas — Interference analysis of conics and quadrics [ MR 2039964 ]
  • Raimundas Vidūnas — Geometrically continuous octahedron [ MR 2039965 ]
  • Multisided Patches [ MR 2046835 ]
  • Jörg Peters — Smoothness, fairness and the need for better multi-sided patches [ MR 2039966 ]
  • Rimvydas Krasauskas and Ron Goldman — Toric Bézier patches with depth [ MR 2039967 ]
  • Joe Warren — On the uniqueness of barycentric coordinates [ MR 2039968 ]
  • Kȩstutis Karčiauskas — Rational $M$-patches and tensor-border patches [ MR 2039969 ]
  • Implicitization and Parametrization [ MR 2046835 ]
  • David Cox — Curves, surfaces, and syzygies [ MR 2039970 ]
  • Jianmin Zheng, Thomas W. Sederberg, Eng-Wee Chionh and David A. Cox — Implicitizing rational surfaces with base points using the method of moving surfaces [ MR 2039971 ]
  • Tor Dokken and Jan Brede Thomassen — Overview of approximate implicitization [ MR 2039972 ]
  • Josef Schicho — Algorithms for rational surfaces [ MR 2039973 ]
  • Tonic Varieties [ MR 2046835 ]
  • David Cox — What is a toric variety? [ MR 2039974 ]
  • Frank Sottile — Toric ideals, real toric varieties, and the moment map [ MR 2039975 ]
  • David Cox, Rimvydas Krasauskas and Mircea Mustaţǎ — Universal rational parametrizations and toric varieties [ MR 2039976 ]
  • Claire Delaunay — Real structures on smooth compact toric surfaces [ MR 2039977 ]
  • Mixed Volume and Resultants [ MR 2046835 ]
  • J. Maurice Rojas — Why polyhedra matter in non-linear equation solving [ MR 2039978 ]
  • Laurent Busé, Mohamed Elkadi and Bernard Mourrain — Using projection operators in computer aided geometric design [ MR 2039979 ]
  • Ivan Soprounov — On combinatorial coefficients and the Gelfond-Khovanskii residue formula [ MR 2039980 ]
  • Ferdinand Minding — On the determination of the degree of an equation obtained by elimination [ MR 2039981 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.