This title outlines the foundations of non-linear computational geometry. It covers combinatorial data structures and algorithms, algebraic issues in geometric computing, approximation of curves and surfaces, and computational topology. Each chapter fully details and provides a tutorial introduction to important concepts and results. The focus is on methods which are both well founded mathematically and efficient in practice. Coverage includes references to open source software and discussion of potential applications of the presented techniques. This book can serve as a textbook on non-linear computational geometry. It will also be useful to engineers and researchers working in computational geometry or other fields, like structural biology, 3D medical imaging, CAD/CAM, robotics, and graphics.

Contains recent progress in the interaction of mathematics, computer graphics, and CAGD Includes supplementary material: sn.pub/extras

Inhalt

1 Arrangements - Efi Fogel, Dan Halperin, Lutz Kettner, Monique Teillaud, Ron Wein, Nicola Wolpert.- 2 Curved Voronoi Diagrams - Jean-Daniel Boissonnat, Camille Wormser, Mariette Yvinec.- 3 Algebraic Issues in Computational Geometry - Bernard Mourrain, Sylvain Pion, Susanne Schmitt, Jean-Pierre Técourt, Elias Tsigaridas, Nicola Wolpert.- 4 Differential Geometry on Discrete Surfaces - David Cohen-Steiner, Jean-Marie Morvan.- 5 Meshing of Surfaces - Jean-Daniel Boissonnat, David Cohen-Steiner, Bernard Mourrain, Günter Rote, Gert Vegter.- 6 Delaunay Triangulation Based Surface Reconstruction - Frédéric Cazals, Joachim Giesen.- 7 Computational Topology: An Introduction - Günter Rote, Gert Vegter.- 8 Appendix - Generic Programming and the Cgal Library - Efi Fogel, Monique Teillaud.- References.- Index.