Polyhedral and algebraic methods in computational geometry

Author(s): 
Michael Joswig, Thorsten Theobald
Publisher: 
Springer
Year: 
2013
ISBN: 
9781447148166
Price (tentative): 
€41.64
Short description: 

The authors discuss in the book a selection of linear and non-linear topics in computational geometry. The first part of the book is devoted to linear computational geometry problems while the second part of the book focuses on non-linear computational geometry techniques, being the main tool the use of Groebner bases. In the third part of the book a selection of applications is given.

URL for publisher, author, or book: 
http://www.springer.com/mathematics/geometry/book/978-1-4471-4816-6
MSC main category: 
68 Computer science
MSC category: 
68Q25
Other MSC categories: 
52B55, 13P10
Review: 

The authors discuss in the book a selection of linear and non-linear topics in computational geometry. The first part of the book, devoted to linear computational geometry, starts with an introduction to projective geometry to proceed to study polytopes, linear programming problemas, convex hulls, Voronoi diagrams and Delaunay triangulations. The software program polymake is used to illustrate and visualize the concepts that are discussed.

The second part of the book focuses on non-linear computational geometry techniques, being the main tool the use of Groebner bases to solve systems of polynomial equations. Examples are provided using software programs Maple and Singular.

Finally, the third part of the book is devoted to a selection of applications, including the reconstruction of curves using Delaunay triangulation as a tool and an application of Groebner bases to geolocalization using GPS satellites.

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.

Reviewer: 
Antonio Valdés Morales
Affiliation: 
Departamento de Geometría y Topología, Universidad Complutense de Madrid

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