Polyhedral and Algebraic Methods in Computational Geometry
By: by Michael Joswig, Thorsten Theobald
Contributors: Theobald, Thorsten; SpringerLink (Online service)
Series: Universitext
Publisher: Springer London; Imprint: Springer
Published: 2013
Place of publication: London
Language: eng
Format: [electronic resource] /
Number of pages: 250
ISBN-13: 9781447148173
Subjects: Mathematical Applications in Computer Science; Algebra; Geometry; Symbolic and Algebraic Manipulation; Mathematics; Discrete groups; Computer science; Data processing; Convex and Discrete Geometry; Algorithms; Mathematics of Computing
Description: <p><i>Polyhedral and Algebraic Methods in Computational Geometry</i> 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.  </p><p>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.  </p><p>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.  </p><p>Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. </p><p><i>Polyhedral and Algebraic Methods in Computational Geometry</i> 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.<i></p>
Table of contents: title: <p>Introduction and Overview; title: Geometric Fundamentals; title: Polytopes and Polyhedra; title: Linear Programming; title: Computation of Convex Hulls; title: Voronoi Diagrams; title: Delone Triangulations; title: Algebraic and Geometric Foundations; title: Gröbner Bases and Buchberger’s Algorithm; title: Solving Systems of Polynomial Equations Using Gröbner Bases; title: Reconstruction of Curves; title: Plücker Coordinates and Lines in Space; title: Applications of Non-Linear Computational Geometry; title: Algebraic Structures; title: Separation Theorems; title: Algorithms and Complexity; title: Software; title: Notation.</p>.