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Algebraic Geometry and Geometric Modeling: Mathematics and Visualization

Editat de Mohamed Elkadi, Bernard Mourrain, Ragni Piene
en Limba Engleză Hardback – 19 sep 2006
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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Specificații

ISBN-13: 9783540332749
ISBN-10: 354033274X
Pagini: 262
Ilustrații: X, 252 p. 52 illus., 27 illus. in color.
Dimensiuni: 155 x 235 x 21 mm
Greutate: 0.49 kg
Ediția:2006
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Mathematics and Visualization

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

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.

Caracteristici

Includes supplementary material: sn.pub/extras