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＜電子ブック＞
Algebraic Geometry and Geometric Modeling / edited by Mohamed Elkadi, Bernard Mourrain, Ragni Piene
(Mathematics and Visualization. ISSN:2197666X)

版	1st ed. 2006.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2006
本文言語	英語
大きさ	X, 252 p. 52 illus., 27 illus. in color : online resource
著者標目	Elkadi, Mohamed editor Mourrain, Bernard editor Piene, Ragni editor SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Mathematical models LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 FREE:Algebraic Geometry FREE:Mathematical Modeling and Industrial Mathematics FREE:Mathematical Applications in Computer Science FREE:Mathematical and Computational Engineering Applications
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-540-33275-6

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