Authors:
- 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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Table of contents (13 chapters)
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Front Matter
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Linear Computational Geometry
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Front Matter
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Non-linear Computational Geometry
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Front Matter
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Non-Linear Computational Geometry
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Applications
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Front Matter
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Back Matter
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.
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
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Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany
Michael Joswig
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FB 12 – Institut für Mathematik, Goethe-Universität, Frankfurt am Main, Germany
Thorsten Theobald
Bibliographic Information
Book Title: Polyhedral and Algebraic Methods in Computational Geometry
Authors: Michael Joswig, Thorsten Theobald
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4471-4817-3
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London 2013
Softcover ISBN: 978-1-4471-4816-6Published: 04 January 2013
eBook ISBN: 978-1-4471-4817-3Published: 04 January 2013
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: X, 250
Number of Illustrations: 50 b/w illustrations, 17 illustrations in colour
Topics: Geometry, Convex and Discrete Geometry, Mathematical Applications in Computer Science, Mathematics of Computing, Symbolic and Algebraic Manipulation, Algorithms