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Algebraic Geometry and Geometric Modeling

Algebraic Geometry and Geometric Modeling

Series: Mathematics and Visualization
Elkadi, Mohamed; Mourrain, Bernard; Piene, Ragni (Eds.)
2006, X, 252 p. 52 illus., 27 in Color, Hardcover
ISBN: 978-3-540-33274-9
Book of the  conference AGGM, Nice, 27-29  Sep. 2004.

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.



Table of contents:

  • Algebraic geometry and geometric modeling: insight and computation, Ron Goldman.
  • Implicitization using approximation complexes, Marc Chardin.
  • Piecewise approximate implicitization: experiments usingindustrial data, Mohamed F. Shalaby, Jan B. Thomassen, Elmar M. Wurm,Tor Dokken, Bert Juttler.
  • Computing with parameterized varieties, Daniel Lazard.
  • Implicitization and Distance Bounds, Martin Aigner, Ibolya Szil´agyi, Bert Juttler, Josef Schicho.
  • Singularities and their deformations: how they change the shape and view of objects, Alexandru Dimc.
  • Overview of topological properties of real algebraic surfaces,Viatcheslav Kharlamov.
  • Illustrating the classification of real cubic surfaces, Stephan Holzer, Oliver Labs.
  • Bezier patches on almost toric surfaces,Rimvydas Krasauska.
  • On parametric surfaces of low degree in P3(C), Mohamed Elkadi, Andre Galligo, Thi Ha Le.
  • On the intersection with revolution and canal surfaces,Mario Fioravanti, Laureano Gonzalez Vega, Ioana Necula.
  • A sampling algorithm computing self-intersections of parametric surfaces, A. Galligo, J.P. Pavone.
  • Elimination in generically rigid 3D geometric constraintsystems, J¨org Peters, Meera Sitharam, Yong Zhou, JianHua Fan.
  • Minkowski decomposition of convex lattice polygons,Ioannis Z. Emiris, Elias P. Tsigaridas.
  • Reducing the number of variables of a polynomial, Enrico Carlini.



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