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Triangulations and Applications by Øyvind Hjelle,Morten Dæhlen Pdf
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.
Triangulations by Jesus De Loera,Joerg Rambau,Francisco Santos Pdf
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 of Oriented Matroids by Francisco Santos Pdf
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 by Chuangyin Dang Pdf
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 by Christian Haase Pdf
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.
Voronoi Diagrams and Delaunay Triangulations by Franz Aurenhammer,Rolf Klein,Der-Tsai Lee Pdf
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 by Raymond R. Fletcher III Pdf
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.
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.
Algorithms and Data Structures by Frank Dehne,Jörg Rüdiger Sack,Michiel Smid Pdf
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.
Mathematics of Surfaces by Michael J. Wilson,Ralph R. Martin Pdf
This book constitutes the refereed proceedings of the 10th IMA International Conference on the Mathematics of Surfaces, held in Leeds, UK in September 2003. The 25 revised full papers presented were carefully reviewed and selected from numerous submissions. Among the topics addressed are triangulated surface parameterization, bifurcation structures, control vertex computation, polyhedral surfaces, watermarking 3D polygonal meshed, subdivision surfaces, surface reconstruction, vector transport, shape from shading, surface height recovery, algebraic surfaces, box splines, the Plateau-Bezier problem, spline geometry, generative geometry, manifold representation, affine arithmetic, and PDE surfaces.
Recent Advances in Nonsmooth Optimization by Ding-Zhu Du,Liqun Qi,Robert S Womersley Pdf
Nonsmooth optimization covers the minimization or maximization of functions which do not have the differentiability properties required by classical methods. The field of nonsmooth optimization is significant, not only because of the existence of nondifferentiable functions arising directly in applications, but also because several important methods for solving difficult smooth problems lead directly to the need to solve nonsmooth problems, which are either smaller in dimension or simpler in structure. This book contains twenty five papers written by forty six authors from twenty countries in five continents. It includes papers on theory, algorithms and applications for problems with first-order nondifferentiability (the usual sense of nonsmooth optimization) second-order nondifferentiability, nonsmooth equations, nonsmooth variational inequalities and other problems related to nonsmooth optimization. Contents:Hybrid Methods for Finding the Nearest Euclidean Distance Matrix (S Al-Homidan & R Fletcher)On Generalized Differentiability of Optimal Solutions and Its Application to an Algorithm for Solving Bilevel Optimization Problems (S Dempe)An Elementary Rate of Convergence Proof for the Deep Cut Ellipsoid Algorithm (J B G Frenk & J Gromicho)On Second-Order Directional Derivatives in Nonsmooth Optimization (L R Huang & K F Ng)Sensitivity of Solutions in Nonlinear Programming Problems with Nonunique Multipliers (A B Levy & R T Rockafellar)Necessary and Sufficient Conditions for Solution Stability of Parametric Nonsmooth Equations (J-S Pang)Characterizations of Optimality for Homogeneous Programming Problems with Applications (A M Rubinov & B M Glover)A Globally Convergent Newton Method for Solving Variational Inequality Problems with Inequality Constraints (K Taji & M Fukushima)A Successive Approximation Quasi-Newton Process for Nonlinear Complementarity Problem (S-Z Zhou et al.)and other papers Readership: Students, academics and industry professionals. keywords:
Surveys in Combinatorics 2003 by C. D. Wensley Pdf
The British Combinatorial Conference is held every two years and is a key event for mathematicians worldwide working in combinatorics. In June 2003 the conference was held at the University of Wales, Bangor. The papers contained here are surveys contributed by the invited speakers and are of the high quality that befits the event. There is also a tribute to Bill Tutte who had a long-standing association with the BCC. The papers cover topics currently attracting significant research interest as well as some less traditional areas such as the combinatorics of protecting digital content. They will form an excellent resource for established researchers as well as graduate students who will find much here to inspire future work.
