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  • Book
  • © 2014

A Short Course in Computational Geometry and Topology

  • Presents a short course in computational geometry and topology
  • Provides exercises at the end of each chapter
  • Written by an expert in the field
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Applied Sciences and Technology (BRIEFSAPPLSCIENCES)

Part of the book sub series: SpringerBriefs in Mathematical Methods (BRIEFSMATHMETH)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-ix
  2. Roots of Geometry and Topology

    • Herbert Edelsbrunner
    Pages 1-6
  3. Tessellations

    1. Front Matter

      Pages 7-7
    2. Voronoi and Delaunay Diagrams

      • Herbert Edelsbrunner
      Pages 9-15
    3. Weighted Diagrams

      • Herbert Edelsbrunner
      Pages 17-22
    4. Three Dimensions

      • Herbert Edelsbrunner
      Pages 23-27
  4. Back Matter

    Pages 29-29
  5. Complexes

    1. Front Matter

      Pages 31-31
    2. Alpha Complexes

      • Herbert Edelsbrunner
      Pages 33-39
    3. Holes

      • Herbert Edelsbrunner
      Pages 41-46
    4. Area Formulas

      • Herbert Edelsbrunner
      Pages 47-52
  6. Back Matter

    Pages 53-54
  7. Homology

    1. Front Matter

      Pages 55-55
    2. Topological Spaces

      • Herbert Edelsbrunner
      Pages 57-63
    3. Homology Groups

      • Herbert Edelsbrunner
      Pages 65-71
    4. Complex Construction

      • Herbert Edelsbrunner
      Pages 73-78
  8. Back Matter

    Pages 79-80
  9. Persistence

    1. Front Matter

      Pages 81-81
    2. Filtrations

      • Herbert Edelsbrunner
      Pages 83-89
    3. PL Functions

      • Herbert Edelsbrunner
      Pages 91-97

About this book

This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields.

Authors and Affiliations

  • Institute of Science and Technology Austria, Klosterneuburg, Austria

    Herbert Edelsbrunner

Bibliographic Information

Buy it now

Buying options

eBook USD 29.99 USD 59.99
50% discount Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.99 USD 79.99
50% discount Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access