Algebraic Geometry and Geometric Modeling
Published on 19. November 2010
Book
Paperback/Softback
X, 252 pages
978-3-642-06993-2 (ISBN)
Description
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.
More details
Series
Edition
Softcover reprint of hardcover 1st ed. 2006
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
25 s/w Abbildungen, 27 farbige Abbildungen
X, 252 p. 52 illus., 27 illus. in color.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 15 mm
Weight
406 gr
ISBN-13
978-3-642-06993-2 (9783642069932)
DOI
10.1007/978-3-540-33275-6
Schweitzer Classification
Other editions
Additional editions
Mohamed Elkadi | Bernard Mourrain | Ragni Piene
Algebraic Geometry and Geometric Modeling
Book
09/2006
1st Edition
Springer
€192.59
Shipment within 10-15 days
Content
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.