Algebraic geometry and geometric modeling
著者
書誌事項
Algebraic geometry and geometric modeling
（Mathematics and visualization）
Springer, c2006
- : hd.
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注記
'This was the aim of the workshop entitled Algebraic Geometry and Geometric Modeling, held from September 27 to September 29, 2004, at theUniversity of Nice-Sophia Antipolis.' --Pref.
内容説明・目次
内容説明
This book spans the distance between algebraic descriptions of geometric objects and the rendering of digital geometric shapes based on algebraic models. These contrasting points of view inspire a thorough analysis of the key challenges and how they are met. The articles focus on important classes of problems: implicitization, classification, and intersection. Combining illustrative graphics, computations and review articles this book helps the reader gain a firm practical grasp of these subjects.
目次
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.- Bezier 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.
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