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Author: Jesus De Loera
Publisher: Springer Science & Business Media
ISBN: 3642129714
Category : Mathematics
Languages : en
Pages : 547
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Book Description
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.
Author: Jesus De Loera
Publisher: Springer Science & Business Media
ISBN: 3642129714
Category : Mathematics
Languages : en
Pages : 547
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Book Description
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.
Author: Øyvind Hjelle
Publisher: Springer Science & Business Media
ISBN: 3540332618
Category : Mathematics
Languages : en
Pages : 239
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Book Description
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.
Author: Chuangyin Dang
Publisher: Springer Science & Business Media
ISBN: 3642487750
Category : Business & Economics
Languages : en
Pages : 199
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Book Description
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.
Author: Ming-Jun Lai
Publisher: Cambridge University Press
ISBN: 0521875927
Category : Mathematics
Languages : en
Pages : 28
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Book Description
Comprehensive graduate text offering a detailed mathematical treatment of polynomial splines on triangulations.
Author: Siu-Wing Cheng
Publisher: CRC Press
ISBN: 1584887311
Category : Computers
Languages : en
Pages : 404
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Book Description
Written by authors at the forefront of modern algorithms research, Delaunay Mesh Generation demonstrates the power and versatility of Delaunay meshers in tackling complex geometric domains ranging from polyhedra with internal boundaries to piecewise smooth surfaces. Covering both volume and surface meshes, the authors fully explain how and why thes
Author: Sergey Fomin
Publisher: American Mathematical Soc.
ISBN: 1470429675
Category : Mathematics
Languages : en
Pages : 110
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Book Description
For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, the authors construct a geometric realization in terms of suitable decorated Teichmüller space of the surface. On the geometric side, this requires opening the surface at each interior marked point into an additional geodesic boundary component. On the algebraic side, it relies on the notion of a non-normalized cluster algebra and the machinery of tropical lambda lengths. The authors' model allows for an arbitrary choice of coefficients which translates into a choice of a family of integral laminations on the surface. It provides an intrinsic interpretation of cluster variables as renormalized lambda lengths of arcs on the surface. Exchange relations are written in terms of the shear coordinates of the laminations and are interpreted as generalized Ptolemy relations for lambda lengths. This approach gives alternative proofs for the main structural results from the authors' previous paper, removing unnecessary assumptions on the surface.
Author: Frank Dehne
Publisher: Springer Science & Business Media
ISBN: 3540405453
Category : Computers
Languages : en
Pages : 533
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Book Description
The papers in this volume were presented at the 8th Workshop on Algorithms and Data Structures (WADS 2003). The workshop took place July 30–August 1, 2003, at Carleton University in Ottawa, Canada. The workshop alternates with the Scandinavian Workshop on Algorithm Theory (SWAT), continuing the tradition of SWAT and WADS starting with SWAT’88 and WADS’89. In response to the call for papers, 126 papers were submitted. From these submissions, the program committee selected 40 papers for presentation at the workshop. In addition, invited lectures were given by the following distinguished researchers: Gilles Brassard, Dorothea Wagner, Daniel Spielman, and Michael Fellows. Atthisyear’sworkshop,WingT.Yan(NelliganO’BrienPayneLLP,Ottawa) gave a special presentation on “Protecting Your Intellectual Property.” On July 29, Hans-Georg Zimmermann (Siemens AG, Munc ̈ hen) gave a seminar on “N- ral Networks in System Identi?cation and Forecasting: Principles, Techniques, and Applications,” and on August 2 there was a workshop on “Fixed Parameter Tractability” organized by Frank Dehne, Michael Fellows, Mike Langston, and Fran Rosamond. On behalf of the program committee, we would like to express our apprec- tion to the invited speakers and to all authors who submitted papers.
Author: Francisco Santos
Publisher: American Mathematical Soc.
ISBN: 0821827693
Category : Mathematics
Languages : en
Pages : 95
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Book Description
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.
Author: Jan Ambjorn
Publisher: Springer Science & Business Media
ISBN: 3540694277
Category : Science
Languages : en
Pages : 207
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Book Description
The express purpose of these lecture notes is to go through some aspects of the simplicial quantum gravity model known as the dynamical triangula tions approach. Emphasis has been on laying the foundations of the theory and on illustrating its subtle and often unexplored connections with many distinct mathematical fields ranging from global Riemannian geometry, to moduli theory, number theory, and topology. Our exposition will concentrate on these points so that graduate students may find in these notes a useful exposition of some of the rigorous results one can -establish in this field and hopefully a source of inspiration for new exciting problems. We try as far as currently possible to expose the interplay between the analytical aspects of dynamical triangulations and the results of Monte Carlo simulations. The techniques described here are rather novel and allow us to address points of current interest in the subject of simplicial quantum gravity while requiring very little in the way of fancy field-theoretical arguments. As a consequence, these notes contain mostly original and until now unpublished material, which will hopefully be of interest both to the expert practitioner and to graduate students entering the field. Among the topics addressed here in considerable detail are the following. (i) An analytical discussion of the geometry of dynamical triangulations in dimensions n == 3 and n == 4.
Author: Franz Aurenhammer
Publisher: World Scientific Publishing Company
ISBN: 981444765X
Category : Computers
Languages : en
Pages : 346
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Book Description
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.
