Advances In Discrete Differential Geometry

Author : Alexander I. Bobenko
Publisher : Springer
Page : 441 pages
File Size : 44,6 Mb
Release : 2016-08-12
Category : Mathematics
ISBN : 9783662504475

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Advances in Discrete Differential Geometry by Alexander I. Bobenko Pdf

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture. This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.

Author : Alexander I. Bobenko TU Berlin,Peter Schröder,John M. Sullivan,Günter M. Ziegler
Publisher : Springer Science & Business Media
Page : 341 pages
File Size : 44,5 Mb
Release : 2008-03-27
Category : Mathematics
ISBN : 9783764386214

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Discrete Differential Geometry by Alexander I. Bobenko TU Berlin,Peter Schröder,John M. Sullivan,Günter M. Ziegler Pdf

This is the first book on a newly emerging field of discrete differential geometry providing an excellent way to access this exciting area. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. The carefully edited collection of essays gives a lively, multi-facetted introduction to this emerging field.

Author : Alexander I. Bobenko,Yuri B. Suris
Publisher : American Mathematical Society
Page : 432 pages
File Size : 49,7 Mb
Release : 2023-09-14
Category : Mathematics
ISBN : 9781470474560

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Discrete Differential Geometry by Alexander I. Bobenko,Yuri B. Suris Pdf

An emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture, and numerics. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of integrable systems. One of the main goals of this book is to reveal this integrable structure of discrete differential geometry. For a given smooth geometry one can suggest many different discretizations. Which one is the best? This book answers this question by providing fundamental discretization principles and applying them to numerous concrete problems. It turns out that intelligent theoretical discretizations are distinguished also by their good performance in applications. The intended audience of this book is threefold. It is a textbook on discrete differential geometry and integrable systems suitable for a one semester graduate course. On the other hand, it is addressed to specialists in geometry and mathematical physics. It reflects the recent progress in discrete differential geometry and contains many original results. The third group of readers at which this book is targeted is formed by specialists in geometry processing, computer graphics, architectural design, numerical simulations, and animation. They may find here answers to the question “How do we discretize differential geometry?” arising in their specific field. Prerequisites for reading this book include standard undergraduate background (calculus and linear algebra). No knowledge of differential geometry is expected, although some familiarity with curves and surfaces can be helpful.

Author : American Mathematical Society. Short Course, Discrete Differential Geometry
Publisher : American Mathematical Soc.
Page : 140 pages
File Size : 55,9 Mb
Release : 2020-09-02
Category : Education
ISBN : 9781470446628

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An Excursion Through Discrete Differential Geometry by American Mathematical Society. Short Course, Discrete Differential Geometry Pdf

Discrete Differential Geometry (DDG) is an emerging discipline at the boundary between mathematics and computer science. It aims to translate concepts from classical differential geometry into a language that is purely finite and discrete, and can hence be used by algorithms to reason about geometric data. In contrast to standard numerical approximation, the central philosophy of DDG is to faithfully and exactly preserve key invariants of geometric objects at the discrete level. This process of translation from smooth to discrete helps to both illuminate the fundamental meaning behind geometric ideas and provide useful algorithmic guarantees. This volume is based on lectures delivered at the 2018 AMS Short Course ``Discrete Differential Geometry,'' held January 8-9, 2018, in San Diego, California. The papers in this volume illustrate the principles of DDG via several recent topics: discrete nets, discrete differential operators, discrete mappings, discrete conformal geometry, and discrete optimal transport.

Author : F Tricerri
Publisher : World Scientific
Page : 192 pages
File Size : 48,8 Mb
Release : 1990-11-20
Category : Electronic
ISBN : 9789814522144

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Advances in Differential Geometry and Topology by F Tricerri Pdf

The aim of this volume is to offer a set of high quality contributions on recent advances in Differential Geometry and Topology, with some emphasis on their application in physics. A broad range of themes is covered, including convex sets, Kaehler manifolds and moment map, combinatorial Morse theory and 3-manifolds, knot theory and statistical mechanics. Contents:Convex Sets and Kaehler Manifolds (M Gromov)Accessibilite En Geometrie Riemannienne Non-Holonome (T Hangan)Riemannian Manifolds with Homogeneous Geodesics (O Kowalski)Triangulations of Manifolds with Few Vertices (W Kühnel)Geometry and Symmetry (L Vanhecke)3-Manifolds and Orbifold Groups of Links (B Zimmermann)Knots, Braids, and Statistical Mechanics (V F R Jones) Readership: Pure mathematicians. keywords:Differential Geometry;Topology

Author : Li M. Chen
Publisher : Springer
Page : 322 pages
File Size : 53,9 Mb
Release : 2014-12-12
Category : Computers
ISBN : 9783319120997

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Digital and Discrete Geometry by Li M. Chen Pdf

This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData. The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms. The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and advanced topics. Chapters especially focus on the applications of these methods to other types of geometry, algebraic topology, image processing, computer vision and computer graphics. Digital and Discrete Geometry: Theory and Algorithms targets researchers and professionals working in digital image processing analysis, medical imaging (such as CT and MRI) and informatics, computer graphics, computer vision, biometrics, and information theory. Advanced-level students in electrical engineering, mathematics, and computer science will also find this book useful as a secondary text book or reference. Praise for this book: This book does present a large collection of important concepts, of mathematical, geometrical, or algorithmical nature, that are frequently used in computer graphics and image processing. These concepts range from graphs through manifolds to homology. Of particular value are the sections dealing with discrete versions of classic continuous notions. The reader finds compact definitions and concise explanations that often appeal to intuition, avoiding finer, but then necessarily more complicated, arguments... As a first introduction, or as a reference for professionals working in computer graphics or image processing, this book should be of considerable value." - Prof. Dr. Rolf Klein, University of Bonn.

Author : J. Szenthe
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401152761

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New Developments in Differential Geometry, Budapest 1996 by J. Szenthe Pdf

Proceedings of the Conference on Differential Geometry, Budapest, Hungary, July 27-30, 1996

Author : Maks A. Akivis,Vladislav V. Goldberg
Publisher : John Wiley & Sons
Page : 404 pages
File Size : 43,7 Mb
Release : 2011-09-20
Category : Mathematics
ISBN : 9781118030882

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Conformal Differential Geometry and Its Generalizations by Maks A. Akivis,Vladislav V. Goldberg Pdf

Comprehensive coverage of the foundations, applications, recent developments, and future of conformal differential geometry Conformal Differential Geometry and Its Generalizations is the first and only text that systematically presents the foundations and manifestations of conformal differential geometry. It offers the first unified presentation of the subject, which was established more than a century ago. The text is divided into seven chapters, each containing figures, formulas, and historical and bibliographical notes, while numerous examples elucidate the necessary theory. Clear, focused, and expertly synthesized, Conformal Differential Geometry and Its Generalizations * Develops the theory of hypersurfaces and submanifolds of any dimension of conformal and pseudoconformal spaces. * Investigates conformal and pseudoconformal structures on a manifold of arbitrary dimension, derives their structure equations, and explores their tensor of conformal curvature. * Analyzes the real theory of four-dimensional conformal structures of all possible signatures. * Considers the analytic and differential geometry of Grassmann and almost Grassmann structures. * Draws connections between almost Grassmann structures and web theory. Conformal differential geometry, a part of classical differential geometry, was founded at the turn of the century and gave rise to the study of conformal and almost Grassmann structures in later years. Until now, no book has offered a systematic presentation of the multidimensional conformal differential geometry and the conformal and almost Grassmann structures. After years of intense research at their respective universities and at the Soviet School of Differential Geometry, Maks A. Akivis and Vladislav V. Goldberg have written this well-conceived, expertly executed volume to fill a void in the literature. Dr. Akivis and Dr. Goldberg supply a deep foundation, applications, numerous examples, and recent developments in the field. Many of the findings that fill these pages are published here for the first time, and previously published results are reexamined in a unified context. The geometry and theory of conformal and pseudoconformal spaces of arbitrary dimension, as well as the theory of Grassmann and almost Grassmann structures, are discussed and analyzed in detail. The topics covered not only advance the subject itself, but pose important questions for future investigations. This exhaustive, groundbreaking text combines the classical results and recent developments and findings. This volume is intended for graduate students and researchers of differential geometry. It can be especially useful to those students and researchers who are interested in conformal and Grassmann differential geometry and their applications to theoretical physics.

Author : John K. Beem,Stamatis A. Dostoglou,Paul E. Ehrlich
Publisher : American Mathematical Soc.
Page : 140 pages
File Size : 53,6 Mb
Release : 2004-10-14
Category : Mathematics
ISBN : 0821856944

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Advances in Differential Geometry and General Relativity by John K. Beem,Stamatis A. Dostoglou,Paul E. Ehrlich Pdf

This volume consists of expanded versions of invited lectures given at The Beemfest: Advances in Differential Geometry and General Relativity (University of Missouri-Columbia) on the occasion of Professor John K. Beem's retirement. The articles address problems in differential geometry in general and in particular, global Lorentzian geometry, Finsler geometry, causal boundaries, Penrose's cosmic censorship hypothesis, the geometry of differential operators with variable coefficients on manifolds, and asymptotically de Sitter spacetimes satisfying Einstein's equations with positive cosmological constant. The book is suitable for graduate students and research mathematicians interested in differential geometry.

Author : Valentin Vasilʹevich Lychagin
Publisher : American Mathematical Soc.
Page : 308 pages
File Size : 47,7 Mb
Release : 1995
Category : Differential equations, Nonlinear
ISBN : 0821804286

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The Interplay between Differential Geometry and Differential Equations by Valentin Vasilʹevich Lychagin Pdf

Author : Toshiaki Adachi,Hideya Hashimoto,Milen J Hristov
Publisher : World Scientific
Page : 208 pages
File Size : 53,7 Mb
Release : 2011-09-01
Category : Mathematics
ISBN : 9789814458542

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Recent Progress in Differential Geometry and Its Related Fields by Toshiaki Adachi,Hideya Hashimoto,Milen J Hristov Pdf

This volume contains the contributions by the main participants of the 2nd International Colloquium on Differential Geometry and its Related Fields (ICDG2010), held in Veliko Tarnovo, Bulgaria to exchange information on current topics in differential geometry, information geometry and applications. These contributions from active specialists in differential geometry provide significant information for research which cover geometric structures, concrete Lie group theory and information geometry. This volume is invaluable not only for researchers in this special area but also for those who are interested in interdisciplinary areas in differential geometry, complex analysis, probability theory and mathematical physics. It also serves as a good guide to graduate students in the field of differential geometry. Contents:Homogeneous Einstein Metrics on Generalized Flag Manifolds Sp(n)/(U(p) x U(q) x Sp(n — p — q)) (Andreas Arvanitoyeorgos, Ioannis Chrysikos and Yusuke Sakane)On G2-Invariants of Curves in Purely Imaginary Octonions (Misa Ohashi)Magnetic Jacobi Fields for Kähler Magnetic Fields (Toshiaki Adachi)Geometry for q-Exponential Families (Hiroshi Matsuzoe and Atsumi Ohara)Sasakian Magnetic Fields on Homogeneous Real Hypersurfaces in a Complex Hyperbolic Space (Tuya Bao)TYZ Expansions for Some Rotation Invariant Kähler Metrics (Todor Gramchev and Andrea Loi)Kershner's Tilings of Type 6 by Congruent Pentagons are Not Dirichlet (Atsushi Kubota and Toshiaki Adachi)Eleven Classes of Almost Paracontact Manifolds with Semi-Riemannian Metric of (n + 1, n) (Galia Nakova and Simeon Zamkovoy)Notes on Geometry of q-Normal Distributions (Daiki Tanaya, Masaru Tanaka and Hiroshi Matsuzoe)A Remark on Complex Lagrangian Cones in Hn (Norio Ejiri and Kazumi Tsukada)Realizations of Subgroups of G2, Spin(7) and Their Applications (Hideya Hashimoto and Misa Ohashi)Bézier Type Almost Complex Structures on Quaternionic Hermitian Vector Spaces (Milen J Hristov) Readership: Professionals, researchers and graduate students in differential geometry, complex analysis, probability theory and mathematical physics. Keywords:Einstein Metrics;Complex Lagrangian Cones;Kaehler Manifolds;Statistical Manifolds;Exceptional Lie Groups;Magnetic Fields;Real HypersurfacesKey Features:Contains well-organized reports of recent progress of special tiesProvides articles which explain results with concrete examples

Author : David Xianfeng Gu,Emil Saucan
Publisher : CRC Press
Page : 690 pages
File Size : 44,5 Mb
Release : 2023-01-31
Category : Computers
ISBN : 9781000804461

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Classical and Discrete Differential Geometry by David Xianfeng Gu,Emil Saucan Pdf

This book introduces differential geometry and cutting-edge findings from the discipline by incorporating both classical approaches and modern discrete differential geometry across all facets and applications, including graphics and imaging, physics and networks. With curvature as the centerpiece, the authors present the development of differential geometry, from curves to surfaces, thence to higher dimensional manifolds; and from smooth structures to metric spaces, weighted manifolds and complexes, and to images, meshes and networks. The first part of the book is a differential geometric study of curves and surfaces in the Euclidean space, enhanced while the second part deals with higher dimensional manifolds centering on curvature by exploring the various ways of extending it to higher dimensional objects and more general structures and how to return to lower dimensional constructs. The third part focuses on computational algorithms in algebraic topology and conformal geometry, applicable for surface parameterization, shape registration and structured mesh generation. The volume will be a useful reference for students of mathematics and computer science, as well as researchers and engineering professionals who are interested in graphics and imaging, complex networks, differential geometry and curvature.

Author : Dominik Volland
Publisher : Springer
Page : 102 pages
File Size : 50,9 Mb
Release : 2017-12-01
Category : Mathematics
ISBN : 9783658204570

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A Discrete Hilbert Transform with Circle Packings by Dominik Volland Pdf

Dominik Volland studies the construction of a discrete counterpart to the Hilbert transform in the realm of a nonlinear discrete complex analysis given by circle packings. The Hilbert transform is closely related to Riemann-Hilbert problems which have been studied in the framework of circle packings by E. Wegert and co-workers since 2009. The author demonstrates that the discrete Hilbert transform is well-defined in this framework by proving a conjecture on discrete problems formulated by Wegert. Moreover, he illustrates its properties by carefully chosen numerical examples.

Author : Laurent Najman,Pascal Romon
Publisher : Springer
Page : 353 pages
File Size : 41,8 Mb
Release : 2017-10-04
Category : Mathematics
ISBN : 9783319580029

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Modern Approaches to Discrete Curvature by Laurent Najman,Pascal Romon Pdf

This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 463 pages
File Size : 44,9 Mb
Release : 1999
Category : Combinatorial geometry
ISBN : 082185559X

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Advances in Discrete and Computational Geometry by Anonim Pdf