Triangulations
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Triangulations
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Author : Jesus De Loera
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-16
Triangulations written by Jesus De Loera and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-16 with Mathematics categories.
Triangulations presents the first comprehensive treatment of the theory of secondary polytopes and related topics. The text discusses the geometric structure behind the algorithms and shows new emerging applications, including hundreds of illustrations, examples, and exercises.
Triangulations And Applications
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Author : Øyvind Hjelle
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-19
Triangulations And Applications written by Øyvind Hjelle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-19 with Mathematics categories.
This book will serve as a valuable source of information about triangulations for the graduate student and researcher. With emphasis on computational issues, it presents the basic theory necessary to construct and manipulate triangulations. In particular, the book gives a tour through the theory behind the Delaunay triangulation, including algorithms and software issues. It also discusses various data structures used for the representation of triangulations.
Spline Functions On Triangulations
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Author : Ming-Jun Lai
language : en
Publisher: Cambridge University Press
Release Date : 2007-04-19
Spline Functions On Triangulations written by Ming-Jun Lai and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-19 with Mathematics categories.
Comprehensive graduate text offering a detailed mathematical treatment of polynomial splines on triangulations.
Triangulations Of Oriented Matroids
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Author : Francisco Santos
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Triangulations Of Oriented Matroids written by Francisco Santos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Matroids categories.
We consider the concept of triangulation of an oriented matroid. We provide a definition which generalizes the previous ones by Billera-Munson and by Anderson and which specializes to the usual notion of triangulation (or simplicial fan) in the realizable case. Then we study the relation existing between triangulations of an oriented matroid $\mathcal{M}$ and extensions of its dual $\mathcal{M}^*$, via the so-called lifting triangulations. We show that this duality behaves particularly well in the class of Lawrence matroid polytopes. In particular, that the extension space conjecture for realizable oriented matroids is equivalent to the restriction to Lawrence polytopes of the Generalized Baues problem for subdivisions of polytopes. We finish by showing examples and a characterization of lifting triangulations.
Triangulations And Simplicial Methods
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Author : Chuangyin Dang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Triangulations And Simplicial Methods written by Chuangyin Dang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
As a new type of technique, simplicial methods have yielded extremely important contributions toward solutions of a system of nonlinear equations. Theoretical investigations and numerical tests have shown that the performance of simplicial methods depends critically on the triangulations underlying them. This monograph describes some recent developments in triangulations and simplicial methods. It includes the D1-triangulation and its applications to simplicial methods. As a result, efficiency of simplicial methods has been improved significantly. Thus more effective simplicial methods have been developed.
Existence Of Unimodular Triangulations Positive Results
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Author : Christian Haase
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-21
Existence Of Unimodular Triangulations Positive Results written by Christian Haase and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-21 with Education categories.
Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review several classes of polytopes that do have unimodular triangulations and constructions that preserve their existence. We include, in particular, the first effective proof of the classical result by Knudsen-Mumford-Waterman stating that every lattice polytope has a dilation that admits a unimodular triangulation. Our proof yields an explicit (although doubly exponential) bound for the dilation factor.
A Course In Triangulations For Solving Equations With Deformations
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Author : B. C. Eaves
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Course In Triangulations For Solving Equations With Deformations written by B. C. Eaves and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
Voronoi Diagrams And Delaunay Triangulations
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Author : Franz Aurenhammer
language : en
Publisher: World Scientific Publishing Company
Release Date : 2013-06-26
Voronoi Diagrams And Delaunay Triangulations written by Franz Aurenhammer and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-26 with Computers categories.
Voronoi diagrams partition space according to the influence certain sites exert on their environment. Since the 17th century, such structures play an important role in many areas like Astronomy, Physics, Chemistry, Biology, Ecology, Economics, Mathematics and Computer Science. They help to describe zones of political influence, to determine the hospital nearest to an accident site, to compute collision-free paths for mobile robots, to reconstruct curves and surfaces from sample points, to refine triangular meshes, and to design location strategies for competing markets. This unique book offers a state-of-the-art view of Voronoi diagrams and their structure, and it provides efficient algorithms towards their computation. Readers with an entry-level background in algorithms can enjoy a guided tour of gently increasing difficulty through a fascinating area. Lecturers might find this volume a welcome source for their courses on computational geometry. Experts are offered a broader view, including many alternative solutions, and up-to-date references to the existing literature; they might benefit in their own research or application development.
Polycubes Triangulations And Polyhexes Over Zn
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Author : Raymond R. Fletcher III
language : en
Publisher: Xlibris Corporation
Release Date :
Polycubes Triangulations And Polyhexes Over Zn written by Raymond R. Fletcher III and has been published by Xlibris Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
A mathematical puzzle book that involves labeling points or edges on three types of graphs: (1) polycubes, which consist of cubes attached face-to-face, (2) polyhexes, which consist of regular hexagons joined edge to edge, and (3) triangulations, which consist of triangles attached edge to edge. For a polycube with n points, the puzzle consists of labeling each vertex with the full set of integers (mod n), (Zn) so that the four labels belonging to each face of every component cube have the same sum. For a polyhex with n points, the vertices are to be labeled with elements from Zn so that the six labels assigned to each component hexagon have the same sum. For puzzles involving triangulation, the edges, instead of the vertices, are to be labeled with elements of Zn. To solve the puzzle, a labeling must be found so that the edges of each component triangle have the same sum. Unlike sudoku, these puzzles have many solutions; the solutions provided in the back of the book are included just to show that a solution exists. Readers are encouraged to create and solve their own puzzles in any of the three genres. Questions of mathematical interest are provided throughout.
Computational Geometry
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Author : Mark de Berg
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-07
Computational Geometry written by Mark de Berg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-07 with Computers categories.
This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.