Algorithmic Geometry
Algorithmic Geometry
Mariette Yvinec, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt
Herve Bronniman
$87.99
USDThe 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.
- Systematic and coherent treatment
- Practical algorithmic approach
- Illustrated with simple but applicable examples
Reviews & endorsements
'The book is well written … covers a wealth of material, is copiously illustrated, and has a comprehensive bibliography. Especially in view of its modest price, the book would be a welcome addition to the shelves of anyone interested in algorithmic geometry.' Peter McMullen, Bull. London Mathematical Society
Product details
March 1998Paperback
9780521565295
544 pages
246 × 189 × 28 mm
0.96kg
160 b/w illus. 1 table 182 exercises
Available
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.
