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Algebraic Geometry and Geometric Modeling

Contributor(s): Elkadi, Mohamed [editor.1] | Mourrain, Bernard [editor.1] | Piene, Ragni [editor.2] | SpringerLink (Online service)0.
Material type: materialTypeLabelBookSeries: Mathematics and Visualization: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.Description: X, 252 p. 52 illus., 27 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540332756.Subject(s): Mathematics | Computer science -- Mathematics | Algebraic geometry | Mathematical models | Applied mathematics | Engineering mathematics.1 | Mathematics.2 | Algebraic Geometry.2 | Mathematical Modeling and Industrial Mathematics.2 | Math Applications in Computer Science.2 | Appl.Mathematics/Computational Methods of Engineering.1DDC classification: 516.35 Online resources: Click here to access online
Contents:
Algebraic 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 -- B�zier 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.
In: Springer eBooks0Summary: 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.
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Item type Current location Call number Status Date due Barcode Item holds
PK Kelkar Library, IIT Kanpur
Available EBK7903
Total holds: 0

Algebraic 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 -- B�zier 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.

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.

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