Polyhedral and algebraic methods in computational geometry / Michael Joswig, Thorsten Theobald.

Format:

Book

Author/Creator:

Joswig, Michael, 1965-

Contributor:

Theobald, Thorsten, 1971-

Series:

Universitext

Standardized Title:

Algorithmische Geometrie. English

Language:

English

German

Subjects (All):

Geometry, Algebraic.

Geometry--Data processing.

Geometry.

Polyhedral functions.

Polyhedra.

Physical Description:

x, 250 pages : illustrations ; 24 cm.

Place of Publication:

London ; New York : Springer, [2013]

Summary:

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.

Contents:

1. Introduction and overview

2. Geometric fundamentals

3. Polytopes and polyhedra

4. Linear programming

5. Computation of convex hulls

6. Voronoi diagrams

7. Delone triangulations

8. Algebraic and geometric foundations

9. Gröbner bases and Buchberger's algorithm

10. Solving systems of polynomial equations using Gröbner bases

11. Reconstruction of curves

12. Plücker coordinates and lines in space

13. Applications of non-linear computational geometry

Appendix A. Algebraic structures

Appendix B. Separation theorems

Appendix C. Algorithms and complexity

Appendix D. Software

Appendix E. Notation.

Notes:

Originally published in the German language by Vieweg+Teubner, 65189 Wiesbaden, Germany as "Joswig, M.; Theobald, T.; Algorithmische Geometrie, © Vieweg+Teubner

Includes bibliographical references and index.

Other Format:

Print version: Joswig, Michael Polyhedral and Algebraic Methods in Computational Geometry

ISBN:

9781447148166

1447148169

OCLC:

813946900