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Algorithmic Geometry

Algorithmic Geometry


  • Date Published: March 1998
  • availability: Available
  • format: Paperback
  • isbn: 9780521565295

£ 56.99

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About the Authors
  • 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.

    • Systematic and coherent treatment
    • Practical algorithmic approach
    • Illustrated with simple but applicable examples
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    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

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    Product details

    • Date Published: March 1998
    • format: Paperback
    • isbn: 9780521565295
    • length: 544 pages
    • dimensions: 246 x 189 x 28 mm
    • weight: 0.96kg
    • contains: 160 b/w illus. 1 table 182 exercises
    • availability: Available
  • Table of Contents

    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

  • Authors

    Jean-Daniel Boissonnat, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt

    Mariette Yvinec, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt


    Herve Bronniman

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