國立虎尾科技大學 |

Advances in Discrete Differential Geometry

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Advances in Discrete Differential Geometry/ edited by Alexander I. Bobenko.
其他作者:	Bobenko, Alexander I.
面頁冊數:	X, 439 p. 114 illus., 67 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Differential geometry. -
電子資源:	https://doi.org/10.1007/978-3-662-50447-5
ISBN:	9783662504475

Advances in Discrete Differential Geometry
Advances in Discrete Differential Geometry[electronic resource] /edited by Alexander I. Bobenko. - 1st ed. 2016. - X, 439 p. 114 illus., 67 illus. in color.online resource.

Discrete 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.

Open Access

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.

ISBN: 9783662504475

Standard No.: 10.1007/978-3-662-50447-5doiSubjects--Topical Terms:

882213
Differential geometry.

LC Class. No.: QA641-670

Dewey Class. No.: 516.36

Advances in Discrete Differential Geometry
LDR:04795nam a22004215i 4500 001 970917
003 DE-He213
005 20200705023610.0
007 cr nn 008mamaa
008 201211s2016 gw | s |||| 0|eng d
020 $a 9783662504475 $9 978-3-662-50447-5
024 7 $a 10.1007/978-3-662-50447-5 $2 doi
035 $a 978-3-662-50447-5
050 4 $a QA641-670
072 7 $a PBMP $2 bicssc
072 7 $a MAT012030 $2 bisacsh
072 7 $a PBMP $2 thema
082 0 4 $a 516.36 $2 23
245 1 0 $a Advances in Discrete Differential Geometry $h [electronic resource] / $c edited by Alexander I. Bobenko.
250 $a 1st ed. 2016.
264 1 $a Berlin, Heidelberg : $b Springer Berlin Heidelberg : $b Imprint: Springer, $c 2016.
300 $a X, 439 p. 114 illus., 67 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
505 0 $a Discrete 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.
506 0 $a Open Access
520 $a 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.
650 0 $a Differential geometry. $3 882213
650 0 $a Functions of complex variables. $3 528649
650 0 $a Dynamics. $3 592238
650 0 $a Ergodic theory. $3 672355
650 0 $a Computer graphics. $3 561602
650 0 $a Physics. $3 564049
650 1 4 $a Differential Geometry. $3 671118
650 2 4 $a Functions of a Complex Variable. $3 672126
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 671353
650 2 4 $a Computer Graphics. $3 669895
650 2 4 $a Numerical and Computational Physics, Simulation. $3 1112293
700 1 $a Bobenko, Alexander I. $4 edt $4 http://id.loc.gov/vocabulary/relators/edt $3 679615
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783662504468
776 0 8 $i Printed edition: $z 9783662504482
776 0 8 $i Printed edition: $z 9783662570616
856 4 0 $u https://doi.org/10.1007/978-3-662-50447-5
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
912 $a ZDB-2-SOB
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)