Algorithmic Geometry

by Jean-Daniel Boissonnat , Mariette Yvinec , Translated by Herve Bronniman

• ISBN13: 9780521565295
• ISBN10: 0521565294
• Format: Paperback
• Copyright: 1998-03-13
• Publisher: Cambridge University Press

Summary

The design and analysis of geometric algorithms have seen remarkable growth in recent years, due to their application in, for example, computer vision, graphics, medical imaging and CAD. The goals of this book are twofold: first to provide a coherent and systematic treatment of the foundations; secondly to present algorithmic solutions that are amenable to rigorous analysis and are efficient in practical situations. When possible, the algorithms are presented in their most general d-dimensional setting. Specific developments are given for the 2- or 3-dimensional cases when this results in significant improvements. The presentation is confined to Euclidean affine geometry, though the authors indicate whenever the treatment can be extended to curves and surfaces. The prerequisites for using the book are few, which will make it ideal for teaching advanced undergraduate or beginning graduate courses in computational geometry.

Table of Contents

Preface

Part I. Algorithmic Tools: 1. Notions of complexity

2. Basic data structures

3. Deterministic methods used in geometry

4. Random sampling

5. Randomized algorithms

6. Dynamic randomized algorithms

Part II. Convex Hulls: 7. Polytopes

8. Incremental convex hulls

9. Convex hulls in 2 and 3 dimensions

10. Linear programming

Part III. Triangulations: 11. Complexes and triangulations

12 Triangulations in dimension 2

13. Triangulations in dimension 3

Part IV. Arrangements: 14. Arrangements of hyperplanes

15. Arrangements of line segments in the plane

16. Arrangements of triangles

Part V. Voronoi Diagrams: 17. Euclidean metrics

18. Non-Euclidean metrics

19. Diagrams in the plane

References

Notation

Index.