Geometric Modeling and Algebraic Geometry (Google eBook)

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Springer Science & Business Media, Dec 24, 2007 - Computer graphics - 240 pages
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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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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
Index
228
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