LEADER 06229 am 22007573u 450 001 9910161651103321 005 20230818161836.0 010 $a3-662-50447-2 024 7 $a10.1007/978-3-662-50447-5 035 $a(CKB)3710000000837590 035 $a(DE-He213)978-3-662-50447-5 035 $a(MiAaPQ)EBC5587059 035 $a(Au-PeEL)EBL5587059 035 $a(OCoLC)956981732 035 $a(MiAaPQ)EBC6422791 035 $a(Au-PeEL)EBL6422791 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/36876 035 $a(PPN)194801683 035 $a(EXLCZ)993710000000837590 100 $a20160812d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAdvances in Discrete Differential Geometry$b[electronic resource] /$fedited by Alexander I. Bobenko 205 $a1st ed. 2016. 210 $aCham$cSpringer Nature$d2016 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2016. 215 $a1 online resource (X, 439 p. 114 illus., 67 illus. in color.) 311 $a3-662-50446-4 327 $aDiscrete conformal maps: Boundary value problems, circle domains, Fuchsian and Schottky uniformization: Alexander I. Bobenko, Stefan Sechelmann, 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 edge lengths: Hana Kourimská, Lara Skuppin, 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, 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, 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. 330 $aThis 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. 606 $aDifferential geometry 606 $aFunctions of complex variables 606 $aDynamics 606 $aErgodic theory 606 $aComputer graphics 606 $aPhysics 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aComputer Graphics$3https://scigraph.springernature.com/ontologies/product-market-codes/I22013 606 $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021 610 $aDifferential Geometry 615 0$aDifferential geometry. 615 0$aFunctions of complex variables. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aComputer graphics. 615 0$aPhysics. 615 14$aDifferential Geometry. 615 24$aFunctions of a Complex Variable. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aComputer Graphics. 615 24$aNumerical and Computational Physics, Simulation. 676 $a516.36 700 $aBobenko$b Alexander I$4auth$065724 702 $aBobenko$b Alexander I$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910161651103321 996 $aAdvances in Discrete Differential Geometry$93359555 997 $aUNINA