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  • © 2013

Polyhedral and Algebraic Methods in Computational Geometry

  • Provides a mathematical introduction to linear and non-linear (i.e. algebraic) computational geometry

  • Applies the theory to computer graphics, curve reconstruction and robotics

  • Establishes interconnections with other disciplines such as algebraic geometry, optimization and numerical mathematics

  • Includes supplementary material: sn.pub/extras

Part of the book series: Universitext (UTX)

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eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-1-4471-4817-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 84.99
Price excludes VAT (USA)

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-X
  2. Introduction and Overview

    • Michael Joswig, Thorsten Theobald
    Pages 1-6
  3. Linear Computational Geometry

    1. Front Matter

      Pages 7-7
    2. Geometric Fundamentals

      • Michael Joswig, Thorsten Theobald
      Pages 9-17
    3. Polytopes and Polyhedra

      • Michael Joswig, Thorsten Theobald
      Pages 19-46
    4. Linear Programming

      • Michael Joswig, Thorsten Theobald
      Pages 47-64
    5. Computation of Convex Hulls

      • Michael Joswig, Thorsten Theobald
      Pages 65-79
    6. Voronoi Diagrams

      • Michael Joswig, Thorsten Theobald
      Pages 81-98
    7. Delone Triangulations

      • Michael Joswig, Thorsten Theobald
      Pages 99-116
  4. Non-linear Computational Geometry

    1. Front Matter

      Pages 117-117
  5. Non-Linear Computational Geometry

    1. Algebraic and Geometric Foundations

      • Michael Joswig, Thorsten Theobald
      Pages 119-136
    2. Gröbner Bases and Buchberger’s Algorithm

      • Michael Joswig, Thorsten Theobald
      Pages 137-156
    3. Solving Systems of Polynomial Equations Using Gröbner Bases

      • Michael Joswig, Thorsten Theobald
      Pages 157-177
  6. Applications

    1. Front Matter

      Pages 179-179
    2. Reconstruction of Curves

      • Michael Joswig, Thorsten Theobald
      Pages 181-192
    3. Plücker Coordinates and Lines in Space

      • Michael Joswig, Thorsten Theobald
      Pages 193-207
    4. Applications of Non-linear Computational Geometry

      • Michael Joswig, Thorsten Theobald
      Pages 209-222
  7. Back Matter

    Pages 223-250

About this book

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

Reviews

From the reviews:

“The authors discuss in the book a selection of linear and non-linear topics in computational geometry. … The book’s audience is made up of mathematicians interested in applications of geometry and algebra as well as computer scientists and engineers with good mathematical background.” (Antonio Valdés Morales, The European Mathematical Society, September, 2013)

Authors and Affiliations

  • Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany

    Michael Joswig

  • FB 12 – Institut für Mathematik, Goethe-Universität, Frankfurt am Main, Germany

    Thorsten Theobald

Bibliographic Information

Buying options

eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-1-4471-4817-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 84.99
Price excludes VAT (USA)