Advances In Discrete Differential Geometry

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Advances in Discrete Differential Geometry

Author : Alexander I. Bobenko
Publisher : Springer
ISBN 13 : 3662504472
Total Pages : 441 pages
Book Rating : 4.6/5 (625 download)

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Book Synopsis Advances in Discrete Differential Geometry by : Alexander I. Bobenko

Download or read book Advances in Discrete Differential Geometry written by Alexander I. Bobenko and published by Springer. This book was released on 2016-08-12 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Discrete Differential Geometry

Author : Alexander I. Bobenko
Publisher : American Mathematical Society
ISBN 13 : 1470474565
Total Pages : 432 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Discrete Differential Geometry by : Alexander I. Bobenko

Download or read book Discrete Differential Geometry written by Alexander I. Bobenko and published by American Mathematical Society. This book was released on 2023-09-14 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Discrete Differential Geometry

Author : Alexander I. Bobenko
Publisher : American Mathematical Soc.
ISBN 13 : 0821847007
Total Pages : 433 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Discrete Differential Geometry by : Alexander I. Bobenko

Download or read book Discrete Differential Geometry written by Alexander I. Bobenko and published by American Mathematical Soc.. This book was released on 2008 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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." "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."--BOOK JACKET.

An Excursion Through Discrete Differential Geometry

Author : American Mathematical Society. Short Course, Discrete Differential Geometry
Publisher : American Mathematical Soc.
ISBN 13 : 1470446626
Total Pages : 140 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis An Excursion Through Discrete Differential Geometry by : American Mathematical Society. Short Course, Discrete Differential Geometry

Download or read book An Excursion Through Discrete Differential Geometry written by American Mathematical Society. Short Course, Discrete Differential Geometry and published by American Mathematical Soc.. This book was released on 2020-09-02 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advances in the Discrete Differential Geometry of Surfaces

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (918 download)

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Book Synopsis Advances in the Discrete Differential Geometry of Surfaces by :

Download or read book Advances in the Discrete Differential Geometry of Surfaces written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Discrete Differential Geometry

Author : Alexander I. Bobenko
Publisher : Birkhäuser
ISBN 13 : 9783764392314
Total Pages : 341 pages
Book Rating : 4.3/5 (923 download)

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Book Synopsis Discrete Differential Geometry by : Alexander I. Bobenko

Download or read book Discrete Differential Geometry written by Alexander I. Bobenko and published by Birkhäuser. This book was released on 2009-09-03 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Variational Principles for Discrete Surfaces

Author : Junfei Dai
Publisher : International Press of Boston
ISBN 13 :
Total Pages : 160 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Variational Principles for Discrete Surfaces by : Junfei Dai

Download or read book Variational Principles for Discrete Surfaces written by Junfei Dai and published by International Press of Boston. This book was released on 2008 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This new volume introduces readers to some of the current topics of research in the geometry of polyhedral surfaces, with applications to computer graphics. The main feature of the volume is a systematic introduction to the geometry of polyhedral surfaces based on the variational principle. The authors focus on using analytic methods in the study of some of the fundamental results and problems of polyhedral geometry: for instance, the Cauchy rigidity theorem, Thurston's circle packing theorem, rigidity of circle packing theorems, and Colin de Verdiere's variational principle. The present book is the first complete treatment of the vast, and expansively developed, field of polyhedral geometry."--Back cover.

Differential Geometry and Topology

Author : Keith Burns
Publisher : CRC Press
ISBN 13 : 1420057537
Total Pages : 400 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Differential Geometry and Topology by : Keith Burns

Download or read book Differential Geometry and Topology written by Keith Burns and published by CRC Press. This book was released on 2005-05-27 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. The differential topology aspect of the book centers on classical, transversality theory, Sard's theorem, intersection theory, and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow. The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field.

Differential Geometry in Array Processing

Author :
Publisher :
ISBN 13 : 1783260858
Total Pages : pages
Book Rating : 4.7/5 (832 download)

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Book Synopsis Differential Geometry in Array Processing by :

Download or read book Differential Geometry in Array Processing written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometric Combinatorics

Author : Ezra Miller
Publisher : American Mathematical Soc.
ISBN 13 : 0821837362
Total Pages : 705 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric Combinatorics by : Ezra Miller

Download or read book Geometric Combinatorics written by Ezra Miller and published by American Mathematical Soc.. This book was released on 2007 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.

Digital and Discrete Geometry

Author : Li M. Chen
Publisher : Springer
ISBN 13 : 3319120999
Total Pages : 322 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Digital and Discrete Geometry by : Li M. Chen

Download or read book Digital and Discrete Geometry written by Li M. Chen and published by Springer. This book was released on 2014-12-12 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Discrete Geometry

Author : Jiri Matousek
Publisher : Springer Science & Business Media
ISBN 13 : 1461300398
Total Pages : 491 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Lectures on Discrete Geometry by : Jiri Matousek

Download or read book Lectures on Discrete Geometry written by Jiri Matousek and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.

Functional Differential Geometry

Author : Gerald Jay Sussman
Publisher : MIT Press
ISBN 13 : 0262019345
Total Pages : 249 pages
Book Rating : 4.2/5 (62 download)

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Book Synopsis Functional Differential Geometry by : Gerald Jay Sussman

Download or read book Functional Differential Geometry written by Gerald Jay Sussman and published by MIT Press. This book was released on 2013-07-05 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: An explanation of the mathematics needed as a foundation for a deep understanding of general relativity or quantum field theory. Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level. The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding.

Differential Geometry Applied to Dynamical Systems

Author :
Publisher :
ISBN 13 : 9814467634
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Differential Geometry Applied to Dynamical Systems by :

Download or read book Differential Geometry Applied to Dynamical Systems written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Discrete and Computational Geometry

Author : Csaba D. Toth
Publisher : CRC Press
ISBN 13 : 1351645919
Total Pages : 2879 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Handbook of Discrete and Computational Geometry by : Csaba D. Toth

Download or read book Handbook of Discrete and Computational Geometry written by Csaba D. Toth and published by CRC Press. This book was released on 2017-11-22 with total page 2879 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Shape Interrogation for Computer Aided Design and Manufacturing

Author : Nicholas M. Patrikalakis
Publisher : Springer Science & Business Media
ISBN 13 : 9783540424543
Total Pages : 428 pages
Book Rating : 4.4/5 (245 download)

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Book Synopsis Shape Interrogation for Computer Aided Design and Manufacturing by : Nicholas M. Patrikalakis

Download or read book Shape Interrogation for Computer Aided Design and Manufacturing written by Nicholas M. Patrikalakis and published by Springer Science & Business Media. This book was released on 2002-02-14 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shape interrogation is the process of extraction of information from a geometric model. It is a fundamental component of Computer Aided Design and Manufacturing (CAD/CAM) systems. The authors focus on shape interrogation of geometric models bounded by free-form surfaces. Free-form surfaces, also called sculptured surfaces, are widely used in the bodies of ships, automobiles and aircraft, which have both functionality and attractive shape requirements. Many electronic devices as well as consumer products are designed with aesthetic shapes, which involve free-form surfaces. This book provides the mathematical fundamentals as well as algorithms for various shape interrogation methods including nonlinear polynomial solvers, intersection problems, differential geometry of intersection curves, distance functions, curve and surface interrogation, umbilics and lines of curvature, geodesics, and offset curves and surfaces. This book will be of interest both to graduate students and professionals.

Lectures on Differential Geometry

Author : Iskander Asanovich Taĭmanov
Publisher : European Mathematical Society
ISBN 13 : 9783037190500
Total Pages : 224 pages
Book Rating : 4.1/5 (95 download)

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Book Synopsis Lectures on Differential Geometry by : Iskander Asanovich Taĭmanov

Download or read book Lectures on Differential Geometry written by Iskander Asanovich Taĭmanov and published by European Mathematical Society. This book was released on 2008 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry studies geometrical objects using analytical methods. Like modern analysis itself, differential geometry originates in classical mechanics. For instance, geodesics and minimal surfaces are defined via variational principles and the curvature of a curve is easily interpreted as the acceleration with respect to the path length parameter. Modern differential geometry in its turn strongly contributed to modern physics. This book gives an introduction to the basics of differential geometry, keeping in mind the natural origin of many geometrical quantities, as well as the applications of differential geometry and its methods to other sciences. The text is divided into three parts. The first part covers the basics of curves and surfaces, while the second part is designed as an introduction to smooth manifolds and Riemannian geometry. In particular, Chapter 5 contains short introductions to hyperbolic geometry and geometrical principles of special relativity theory. Here, only a basic knowledge of algebra, calculus and ordinary differential equations is required. The third part is more advanced and introduces into matrix Lie groups and Lie algebras the representation theory of groups, symplectic and Poisson geometry, and applications of complex analysis in surface theory. The book is based on lectures the author held regularly at Novosibirsk State University. It is addressed to students as well as anyone who wants to learn the basics of differential geometry.