Algebraic geometry and geometric modeling

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.

Ron GoldmanMarc ChardinMohamed F. Shalaby and Jan B. Thomassen and Elmar M. Wurm and Tor Dokken and Bert JuttlerDaniel LazardMartin Aigner and Ibolya Szilagyi and Bert Juttler and Josef SchichoAlexandru DimcaViatcheslav KharlamovStephan Holzer and Oliver LabsRimvydas KrasauskasMohamed Elkadi and Andre Galligo and Thi Ha LeMario Fioravanti and Laureano Gonzalez-Vega and Ioana NeculaA. Galligo and J.P. PavoneJorg Peters and Meera Sitharam and Yong Zhou and JianHua FanIoannis Z. Emiris and Elias P. TsigaridasEnrico Carlini

Algebraic geometry and geometric modeling: insight and computation	p. 1
Implicitization using approximation complexes	p. 23
Piecewise approximate implicitization: experiments using industrial data	p. 37
Computing with parameterized varieties	p. 53
Implicitization and Distance Bounds	p. 71
Singularities and their deformations: how they change the shape and view of objects	p. 87
Overview of topological properties of real algebraic surfaces	p. 103
Illustrating the classification of real cubic surfaces	p. 119
Bezier patches on almost toric surfaces	p. 135
On parametric surfaces of low degree in P3(C)	p. 151
On the intersection with revolution and canal surfaces	p. 169
A sampling algorithm computing self-intersections of parametric surfaces	p. 185
Elimination in generically rigid 3D geometric constraint systems	p. 205
Minkowski decomposition of convex lattice polygons	p. 217
Reducing the number of variables of a polynomial	p. 237
Index	p. 249

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