Polyhedral and Algebraic Methods in Computational Geometry

By Michael Joswig

Subjects: Discrete groups, Algebra, Mathematics, Mathematical Applications in Computer Science, Geometry, Convex and Discrete Geometry, Computer science, Data processing, Algorithms, Symbolic and Algebraic Manipulation, 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>