Algebraic Geometry and Geometric Modeling (Mathematics and Visualization)

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ISBN 10: 3642069932 / ISBN 13: 9783642069932

Editore: Springer, 2010

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252 pages. 9.21x5.98x0.71 inches. In Stock.

Codice articolo 3642069932

Dati bibliografici

• Titolo: Algebraic Geometry and Geometric Modeling (Mathematics and Visualization)
• Editore: Springer
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 3642069932
• ISBN 13: 9783642069932
• Rilegatura: Paperback
• Condizione: Brand New
• Peso: 0,36 chilogrammi

Descrizione articolo

Riassunto

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.

Contenuti

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.- 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.