Polyhedral and Algebraic Methods in Computational Geometry

• Main Authors: Joswig, Michael. (Author), Theobald, Thorsten. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: London : Springer London : Imprint: Springer, 2013.
• Series: Universitext,
• Subjects: Mathematics.; Computer science.; Algebra > Data processing.; Algorithms.; Geometry.; Discrete groups.; Convex and Discrete Geometry.; Mathematical Applications in Computer Science.; Mathematics of Computing.; Symbolic and Algebraic Manipulation.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-4471-4817-3

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 problem...

Table of Contents:

• Introduction and Overview
• Geometric Fundamentals
• Polytopes and Polyhedra
• Linear Programming
• Computation of Convex Hulls
• Voronoi Diagrams
• Delone Triangulations
• Algebraic and Geometric Foundations
• Grb̲ner Bases and Buchberger<U+0019>s Algorithm
• Solving Systems of Polynomial Equations Using Grb̲ner Bases
• Reconstruction of Curves
• Pl<U+00fc>cker Coordinates and Lines in Space
• Applications of Non-Linear Computational Geometry
• Algebraic Structures
• Separation Theorems
• Algorithms and Complexity
• Software
• Notation.