Polyhedral and Algebraic Methods in Computational Geometry

  • Michael Joswig
  • Thorsten Theobald

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-X
  2. Michael Joswig, Thorsten Theobald
    Pages 1-6
  3. Linear Computational Geometry

    1. Front Matter
      Pages 7-7
    2. Michael Joswig, Thorsten Theobald
      Pages 9-17
    3. Michael Joswig, Thorsten Theobald
      Pages 19-46
    4. Michael Joswig, Thorsten Theobald
      Pages 47-64
    5. Michael Joswig, Thorsten Theobald
      Pages 65-79
    6. Michael Joswig, Thorsten Theobald
      Pages 81-98
    7. Michael Joswig, Thorsten Theobald
      Pages 99-116
  4. Non-linear Computational Geometry

    1. Front Matter
      Pages 117-117
    2. Michael Joswig, Thorsten Theobald
      Pages 119-136
    3. Michael Joswig, Thorsten Theobald
      Pages 137-156
    4. Michael Joswig, Thorsten Theobald
      Pages 157-177
  5. Applications

    1. Front Matter
      Pages 179-179
    2. Michael Joswig, Thorsten Theobald
      Pages 181-192
    3. Michael Joswig, Thorsten Theobald
      Pages 193-207
    4. Michael Joswig, Thorsten Theobald
      Pages 209-222
  6. Back Matter
    Pages 223-250

About this book

Introduction

Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry.  

The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations.  

The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics.  

Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. 

Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.

Keywords

Computational Geometry Convex Hull Polyhedron Polytope Voronoi diagram

Authors and affiliations

  • Michael Joswig
    • 1
  • Thorsten Theobald
    • 2
  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.FB 12 – Institut für MathematikGoethe-UniversitätFrankfurt am MainGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-4817-3
  • Copyright Information Springer-Verlag London 2013
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-4816-6
  • Online ISBN 978-1-4471-4817-3
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book