Algorithmic Geometry

Algorithmic Geometry

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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 more

Product details

  • Online resource
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 160 b/w illus. 1 table 182 exercises
  • 1139172999
  • 9781139172998

Review quote

'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 Societyshow more

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; more

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