Polyhedral and algebraic methods in computational geometry
Author(s)
Bibliographic Information
Polyhedral and algebraic methods in computational geometry
（Universitext）
Springer, c2013
- : [pbk.]
- Other Title
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Algorithmische Geometrie : polyedrische und algebraische Methoden
Available at / 22 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: [pbk.]JOS||9||1200026147562
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science数学
: [pbk.]/J 7992080322672
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Note
"Revised and updated translation of the German textbook Algorithmische Geometrie: polyedrische und algebraische Methoden, Vieweg, 2008"--Pref., p. vi
Includes bibliographical reference (p. 243-246) and index
Description and Table of Contents
Description
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 Groebner 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.
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.- Groebner Bases and Buchberger's Algorithm.- Solving Systems of Polynomial Equations Using Groebner Bases.- Reconstruction of Curves.- Plucker Coordinates and Lines in Space.- Applications of Non-Linear Computational Geometry.- Algebraic Structures.- Separation Theorems.- Algorithms and Complexity.- Software.- Notation.
by "Nielsen BookData"