Book arising from major European project in geometric modeling
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.
|The two ?elds of Geometric Modeling and Algebraic Geometry, though closely - lated, are traditionally represented by two almost disjoint scienti?c communities. Both ?elds deal with objects de?ned by algebraic equations, but the objects are studied in different ways. While algebraic geometry has developed impressive - sults for understanding the theoretical nature of these objects, geometric modeling focuses on practical applications of virtual shapes de?ned by algebraic equations. Recently, however, interaction between the two ?elds has stimulated new research. For instance, algorithms for solving intersection problems have bene?ted from c- tributions from the algebraic side. The workshop series on Algebraic Geometry and Geometric Modeling (Vilnius 1 2 2002 , Nice 2004 ) and on Computational Methods for Algebraic Spline Surfaces 3 (Kefermarkt 2003 , Oslo 2005) have provided a forum for the interaction between the two ?elds. The present volume presents revised papers which have grown out of the 2005 Oslo workshop, which was aligned with the ?nal review of the European project GAIA II, entitled Intersection algorithms for geometry based IT-applications 4 using approximate algebraic methods (IST 2001-35512) .
Table of Contents Part I Survey of the European project GAIA II 1 The GAIA Project on Intersection and ImplicitizationT DokkenPart II Some special algebraic surfaces 2 Some Covariants Related to Steiner SurfacesF Aries, E Briand, C Bruchou3 Real Line Arrangements and Surfaces with Many Real NodesS Breske, O Labs, D van Straten 4 Monoid HypersurfacesP H Johansen, M Loeberg, R Piene5 Canal Surfaces Defined by Quadratic Families of SpheresR Krasauskas, S Zube6 General Classification of (1,2) Parametric Surfaces in P3Thi-Ha Le, Andre GalligoPart III Algorithms for geometric computing 7 Curve Parametrization over Optimal Field Extensions Exploiting theNewton PolygonT Beck, J Schicho 8 Ridges and Umbilics of Polynomial Parametric SurfacesF Cazals, J C Faugere, M Pouget, F Rouillier 9 Intersecting Biquadratic Bezier Surface PatchesS Chau, M Oberneder, A Galligo, B Juettler 10 Cube Decompositions by Eigenvectors of Quadratic MultivariateSplinesI Ivrissimtzis, H-P Seidel 11 Subdivision Methods for the Topology of 2d and 3d Implicit CurvesC Liang, B Mourrain, J P Pavone 12 Approximate Implicitization of Space Curves and of Surfaces ofRevolutionM Shalaby, B Juettler
Survey of the European project GAIA II.- The GAIA Project on Intersection and Implicitization.- Some special algebraic surfaces.- Some Covariants Related to Steiner Surfaces.- Real Line Arrangements and Surfaces with Many Real Nodes.- Monoid Hypersurfaces.- Canal Surfaces Defined by Quadratic Families of Spheres.- General Classification of (1,2) Parametric Surfaces in ?3.- Algorithms for geometric computing.- Curve Parametrization over Optimal Field Extensions Exploiting the Newton Polygon.- Ridges and Umbilics of Polynomial Parametric Surfaces.- Intersecting Biquadratic Bézier Surface Patches.- Cube Decompositions by Eigenvectors of Quadratic Multivariate Splines.- Subdivision Methods for the Topology of 2d and 3d Implicit Curves.- Approximate Implicitization of Space Curves and of Surfaces of Revolution.
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.
Inhaltsverzeichnis
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
Klappentext
The two ?elds of Geometric Modeling and Algebraic Geometry, though closely - lated, are traditionally represented by two almost disjoint scienti?c communities. Both ?elds deal with objects de?ned by algebraic equations, but the objects are studied in different ways. While algebraic geometry has developed impressive - sults for understanding the theoretical nature of these objects, geometric modeling focuses on practical applications of virtual shapes de?ned by algebraic equations. Recently, however, interaction between the two ?elds has stimulated new research. For instance, algorithms for solving intersection problems have bene?ted from c- tributions from the algebraic side. The workshop series on Algebraic Geometry and Geometric Modeling (Vilnius 1 2 2002 , Nice 2004 ) and on Computational Methods for Algebraic Spline Surfaces 3 (Kefermarkt 2003 , Oslo 2005) have provided a forum for the interaction between the two ?elds. The present volume presents revised papers which have grown out of the 2005 Oslo workshop, which was aligned with the ?nal review of the European project GAIA II, entitled Intersection algorithms for geometry based IT-applications 4 using approximate algebraic methods (IST 2001-35512) .
Book arising from major European project in geometric modeling
n
Includes supplementary material: sn.pub/extras
n
