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Triangulations : Structures for Algorithms and Applications - Jesus De Loera

Triangulations

Structures for Algorithms and Applications

By: Jesus De Loera, Joerg Rambau, Francisco Santos

eText | 16 August 2010

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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.
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Non-FictionComputing & I.T.Computer ScienceDatabasesData Capture & AnalysisComputer Programming & Software DevelopmentAlgorithms & Data StructuresMathematicsGeometryAnalytic GeometryCombinatorics & Graph TheoryAlgebraic Geometry

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