Geometric Modeling and Algebraic Geometry

ISBN-13: 9783540721840 / Angielski / Twarda / 2007 / 231 str.

Opis

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. In 12 chapters written by leading experts, this book presents recent results which rely on the interaction of both fields. Some of these results have been obtained from a major European project in geometric modeling.

Spis treści

Table of Contents Part I Survey of the European project GAIA II 1 The GAIA Project on Intersection and Implicitization T Dokken Part II Some special algebraic surfaces 2 Some Covariants Related to Steiner Surfaces F Aries, E Briand, C Bruchou 3 Real Line Arrangements and Surfaces with Many Real Nodes S Breske, O Labs, D van Straten 4 Monoid Hypersurfaces P H Johansen, M Loeberg, R Piene 5 Canal Surfaces Defined by Quadratic Families of Spheres R Krasauskas, S Zube 6 General Classification of (1,2) Parametric Surfaces in P3 Thi-Ha Le, Andre Galligo Part III Algorithms for geometric computing 7 Curve Parametrization over Optimal Field Extensions Exploiting the Newton Polygon T Beck, J Schicho 8 Ridges and Umbilics of Polynomial Parametric Surfaces F Cazals, J C Faugere, M Pouget, F Rouillier 9 Intersecting Biquadratic Bezier Surface Patches S Chau, M Oberneder, A Galligo, B Juettler 10 Cube Decompositions by Eigenvectors of Quadratic Multivariate Splines I Ivrissimtzis, H-P Seidel 11 Subdivision Methods for the Topology of 2d and 3d Implicit Curves C Liang, B Mourrain, J P Pavone 12 Approximate Implicitization of Space Curves and of Surfaces of Revolution M Shalaby, B Juettler

O autorze

Bert Jüttler ist Professor am Institut für Angewandte Geometrie der Johannes-Kepler-Universität Linz und forscht dort u.a. in den Gebieten Geometrische Datenverarbeitung und Algebraische Geometrie.