Triangulations [electronic resource] : Structures for Algorithms and Applications / by Jesús A. De Loera, Jörg Rambau, Francisco Santos.
Contributor(s): Rambau, Jörg [author.] | Santos, Francisco [author.] | SpringerLink (Online service)Material type: TextSeries: Algorithms and Computation in Mathematics: 25Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010Description: X, 539 p. 496 illus., 281 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783642129711Subject(s): Mathematics | Computers | Computer science -- Mathematics | Algebraic geometry | Computer mathematics | Convex geometry | Discrete geometry | Discrete mathematics | Mathematics | Algebraic Geometry | Discrete Mathematics | Theory of Computation | Convex and Discrete Geometry | Mathematics of Computing | Computational Mathematics and Numerical AnalysisAdditional physical formats: Printed edition:: No titleDDC classification: 516.35 LOC classification: QA564-609Online resources: Click here to access online
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Triangulations in Mathematics -- Configurations, Triangulations, Subdivisions, and Flips -- Life in Two Dimensions -- A Tool Box -- Regular Triangulations and Secondary Polytopes -- Some Interesting Configurations -- Some Interesting Triangulations -- Algorithmic Issues -- Further Topics.
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.