About this product

Product Identifiers

PublisherSpringer Berlin / Heidelberg

ISBN-103540721843

ISBN-139783540721840

eBay Product ID (ePID)60456946

Product Key Features

Number of PagesVIII, 231 Pages

Publication NameGeometric Modeling and Algebraic Geometry

LanguageEnglish

Publication Year2007

SubjectComputer Graphics, Geometry / General, Applied, Geometry / Algebraic

TypeTextbook

Subject AreaMathematics, Computers

AuthorRagni Piene

FormatHardcover

Dimensions

Item Weight18.7 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

Number of Volumes1 vol.

IllustratedYes

Table Of ContentSurvey 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.

SynopsisThe 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) ., 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) ., 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) ., 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) .

LC Classification NumberQA564-609