Polyhedral and Algebraic Methods in Computational Geometry
Authors: Joswig, Michael, Theobald, Thorsten
Free Preview- 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
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- About this Textbook
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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.
- Reviews
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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)
- Table of contents (13 chapters)
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Introduction and Overview
Pages 1-6
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Geometric Fundamentals
Pages 9-17
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Polytopes and Polyhedra
Pages 19-46
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Linear Programming
Pages 47-64
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Computation of Convex Hulls
Pages 65-79
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Table of contents (13 chapters)
- Download Preface 1 PDF (77.2 KB)
- Download Sample pages 2 PDF (253.9 KB)
- Download Table of contents PDF (81.3 KB)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Polyhedral and Algebraic Methods in Computational Geometry
- Authors
-
- Michael Joswig
- Thorsten Theobald
- Series Title
- Universitext
- Copyright
- 2013
- Publisher
- Springer-Verlag London
- Copyright Holder
- Springer-Verlag London
- eBook ISBN
- 978-1-4471-4817-3
- DOI
- 10.1007/978-1-4471-4817-3
- Softcover ISBN
- 978-1-4471-4816-6
- Series ISSN
- 0172-5939
- Edition Number
- 1
- Number of Pages
- X, 250
- Number of Illustrations
- 50 b/w illustrations, 17 illustrations in colour
- Topics
