Centre de documentation
scientifique

Advances in discrete differential geometry / Alexander I. Bobenko (2016)    

Public Titre : Advances in discrete differential geometry Type de document : Monographie Auteurs : Alexander I. Bobenko, Éditeur scientifique Editeur : Berlin, Heidelberg, Vienne, New York, ... : Springer Année de publication : 2016 Importance : 439 p. ISBN/ISSN/EAN : 978-3-662-50447-5 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Analyse mathématique [Termes IGN] géométrie différentielle Index. décimale : 23.30 Analyse mathématique Résumé : (Editeur) [Preface] In this book we take a closer look at discrete models in differential geometry and dynamical systems. The curves used are polygonal, surfaces are made from triangles and quadrilaterals, and time runs discretely. Nevertheless, one can hardly see the difference to the corresponding smooth curves, surfaces, and classical dynamical systems with continuous time. This is the paradigm of structure-preserving discretizations. The common idea is to find and investigate discrete models that exhibit properties and structures characteristic of the corresponding smooth geometric objects and dynamical processes. These important and characteristic qualitative features should already be captured at the discrete level. The current interest and advances in this field are to a large extent stimulated by its relevance for computer graphics, mathematical physics, architectural geometry, etc. The book focuses on differential geometry and dynamical systems, on smooth and discrete theories, and on pure mathematics and its practical applications. It demonstrates this interplay using a range of examples, which include discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, special texture mappings in computer graphics, and freeform architecture. It was written by specialists from the DFG Collaborative Research Center “Discretization in Geometry and Dynamics”. The work involved in this book and other selected research projects pursued by the Center was recently documented in the film “The Discrete Charm of Geometry” by Ekaterina Eremenko. Lastly, the book features a wealth of illustrations, revealing that this new branch of mathematics is both (literally) beautiful and useful. In particular the cover illustration shows the discretely conformally parametrized surfaces of the inflated letters A and B from the recent educational animated film “conform!” by Alexander Bobenko and Charles Gunn. At this place, we want to thank the Deutsche Forschungsgesellschaft for its ongoing support. Note de contenu : - Discrete Conformal Maps: Boundary Value Problems, Circle Domains, Fuchsian and Schottky Uniformization /Alexander I. Bobenko, Stefan Sechelmann and Boris Springborn - Discrete Complex Analysis on Planar Quad-Graphs / Alexander I. Bobenko and Felix Günther - Approximation of Conformal Mappings Using Conformally Equivalent Triangular Lattices / Ulrike Bücking - Numerical Methods for the Discrete Map Za / Folkmar Bornemann, Alexander Its, Sheehan Olver and Georg Wechslberger - A Variational Principle for Cyclic Polygons with Prescribed EdgeLengths / Hana Kouřimská, Lara Skuppin and Boris Springborn - Complex Line Bundles Over Simplicial Complexes and Their Applications / Felix Knöppel and Ulrich Pinkall - Holomorphic Vector Fields and Quadratic Differentials on Planar Triangular Meshes / Wai Yeung Lam and Ulrich Pinkall - Vertex Normals and Face Curvatures of Triangle Meshes / Xiang Sun, Caigui Jiang, Johannes Wallner and Helmut Pottmann - S-Conical CMC Surfaces. Towards a Unified Theory of Discrete Surfaces with Constant Mean Curvature / Alexander I. Bobenko and Tim Hoffmann - Constructing Solutions to the Björling Problem for Isothermic Surfaces by Structure Preserving Discretization / Ulrike Bücking and Daniel Matthes - On the Lagrangian Structure of Integrable Hierarchies /Yuri B. Suris and Mats Vermeeren - On the Variational Interpretation of the Discrete KP Equation / Raphael Boll, Matteo Petrera and Yuri B. Suris - Six Topics on Inscribable Polytopes / Arnau Padrol and Günter M. Ziegler - DGD Gallery: Storage, Sharing, and Publication of Digital Research Data / Michael Joswig, Milan Mehner, Stefan Sechelmann, Jan Techter and Alexander I. Bobenko Numéro de notice : 22744 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Recueil / ouvrage collectif En ligne : http://dx.doi.org/10.1007/978-3-662-50447-5 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=86051

Documents numériques

en open access 22744_Advances in discrete differential geometry Adobe Acrobat PDF