## Geometric Modeling and Algebraic Geometry (Google eBook)The two fields of Geometric Modeling and Algebraic Geometry, though closely related, are traditionally represented by two almost disjoint scientific communities. Both fields deal with objects defined by algebraic equations, but the objects are studied in different ways. This contributed book presents, in 12 chapters written by leading experts, recent results which rely on the interaction of both fields. Some of these results have been obtained in the frame of the European GAIA II project (IST 2001-35512) entitled “Intersection algorithms for geometry-based IT applications using approximate algebraic methods”. |

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Algebraic Geometry and Geometric Modeling Mohamed Elkadi,Bernard Mourrain,Ragni Piene Limited preview - 2006 |

### Contents

The GAIA Project on Intersection and Implicitization | 5 |

Some Covariants Related to Steiner Surfaces | 30 |

Real Line Arrangements and Surfaces with Many Real Nodes | 47 |

Monoid Hypersurfaces | 55 |

Canal Surfaces Deﬁned by Quadratic Families of Spheres | 79 |

General Classification of 12 Parametric Surfaces in ℙ³ | 93 |

Curve Parametrization over Optimal Field Extensions Exploiting the Newton Polygon | 118 |

Ridges and Umbilics of Polynomial Parametric Surfaces | 141 |

Intersecting Biquadratic Bézier Surface Patches | 161 |

Cube Decompositions by Eigenvectors of Quadratic Multivariate Splines | 181 |

Subdivision Methods for the Topology of 2d and 3d Implicit Curves | 198 |

Approximate Implicitization of Space Curves and of Surfaces of Revolution | 215 |

228 | |

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