Triangulations
Subtitle: structures for algorithms and applications
By: Jesús A. De Loera, Jörg Rambau, Francisco Santos
Contributors: Rambau, Jörg; Santos, Francisco, 1968-
Series: Algorithms and computation in mathematics -- v. 25; Algorithms and computation in mathematics -- v. 25.
Publisher: Springer
Published: 2010
Place of publication: Berlin; New York
Language: eng
Number of pages: 535
ISBN-13: 9783642129704
Subjects: Geometry; Triangularization (Mathematics); Combinatorial geometry; Data processing
Description: Triangulations appear everywhere, from volume computations and meshing to algebra and topology. This book studies the subdivisions and triangulations of polyhedral regions and point sets and presents the first comprehensive treatment of the theory of secondary polytopes and related topics. A central theme of the book is the use of the rich structure of the space of triangulations to solve computational problems (e.g., counting the number of triangulations or finding optimal triangulations with respect to various criteria), and to establish connections to applications in algebra, computer science, combinatorics, and optimization. With many examples and exercises, and with nearly five hundred illustrations, the book gently guides readers through the properties of the spaces of triangulations of "structured" (e.g., cubes, cyclic polytopes, lattice polytopes) and "pathological" (e.g., disconnected spaces of triangulations) situations using only elementary principles.
Notes: Includes bibliographical references (p. [513]-530) and index.
Table of contents: title: Triangulations in mathematics; title: Configuations, triangulations, subdivisions, and flips; title: Life in two dimensions; title: A tool box; title: Regular triangulations and secondary polytopes; title: Some interesting configurations; title: Some interesting triangulations; title: Algorithmic issues; title: Further topics.