Algebraic Geometry and Geometric Modeling (Mathematics and Visualization)

✍ Scribed by Mohamed Elkadi (Editor), Bernard Mourrain (Editor), Ragni Piene (Editor)

• Year: 2006
• Tongue: English
• Leaves: 263
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Contents......Page 10
Algebraic geometry and geometric modeling: insight and computation......Page 12
Implicitization using approximation complexes......Page 34
Piecewise approximate implicitization: experiments using industrial data......Page 48
Computing with parameterized varieties......Page 64
Implicitization and Distance Bounds......Page 82
Singularities and their deformations:how they change the shape and view of objects......Page 98
Overview of topological properties of real algebraic surfaces......Page 115
Illustrating the classification of real cubic surfaces......Page 130
Bézier patches on almost toric surfaces......Page 146
On parametric surfaces of low degree in P3(C)......Page 162
On the intersection with revolution and canal surfaces......Page 180
A sampling algorithm computing self-intersections of parametric surfaces......Page 196
Elimination in generically rigid 3D geometric constraint systems......Page 216
Minkowski decomposition of convex lattice polygons......Page 228
Reducing the number of variables of a polynomial......Page 248
A-C......Page 260
C-L......Page 261
M-R......Page 262
S-Z......Page 263