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Mathematics and Visualization Ser.: Algebraic Geometry and Geometric Modeling by Bernard Mourrain (2006, Hardcover)
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About this product
Product Identifiers
PublisherSpringer Berlin / Heidelberg
ISBN-10354033274X
ISBN-139783540332749
eBay Product ID (ePID)20038408234
Product Key Features
Number of PagesX, 252 Pages
Publication NameAlgebraic Geometry and Geometric Modeling
LanguageEnglish
Publication Year2006
SubjectEngineering (General), Applied, Geometry / Algebraic
TypeTextbook
Subject AreaMathematics, Technology & Engineering
AuthorBernard Mourrain
SeriesMathematics and Visualization Ser.
FormatHardcover
Dimensions
Item Height0.2 in
Item Weight21.6 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2006-929216
Number of Volumes1 vol.
IllustratedYes
Table Of ContentAlgebraic geometry and geometric modeling: insight and computation.- Implicitization using approximation complexes.- Piecewise approximate implicitization: experiments using industrial data.- Computing with parameterized varieties.- Implicitization and Distance Bounds.- Singularities and their deformations: how they change the shape and view of objects.- Overview of topological properties of real algebraic surfaces.- Illustrating the classification of real cubic surfaces.- Bézier patches on almost toric surfaces.- On parametric surfaces of low degree in P3(C).- On the intersection with revolution and canal surfaces.- A sampling algorithm computing self-intersections of parametric surfaces.- Elimination in generically rigid 3D geometric constraint systems.- Minkowski decomposition of convex lattice polygons.- Reducing the number of variables of a polynomial.
SynopsisThis book spans the distance between algebraic descriptions of geometric objects and the rendering of digital geometric shapes based on algebraic models. These contrasting points of view inspire a thorough analysis of the key challenges and how they are met. The articles focus on important classes of problems: implicitization, classification, and intersection. Combining illustrative graphics, computations and review articles this book helps the reader gain a firm practical grasp of these subjects., Algebraic Geometry provides an impressive theory targeting the understanding of geometric objects defined algebraically. Geometric Modeling uses every day, in order to solve practical and difficult problems, digital shapes based on algebraic models. In this book, we have collected articles bridging these two areas. The confrontation of the different points of view results in a better analysis of what the key challenges are and how they can be met. We focus on the following important classes of problems: implicitization, classification, and intersection. The combination of illustrative pictures, explicit computations and review articles will help the reader to handle these subjects.
LC Classification NumberQA564-609
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