Advances in Discrete Differential Geometry by Alexander Bobenko

Book Contents :-
1. Discrete Conformal Maps: Boundary Value Problems, Circle Domains, Fuchsian and Schottky Uniformization 2. Discrete Complex Analysis on Planar Quad-Graphs 3. Approximation of Conformal Mappings Using Conformally Equivalent Triangular Lattices 4. Numerical Methods for the Discrete Map Za 5. A Variational Principle for Cyclic Polygons with Prescribed Edge Lengths 6. Complex Line Bundles Over Simplicial Complexes and Their Applications 7. Holomorphic Vector Fields and Quadratic Differentials on Planar Triangular Meshes 8. Vertex Normals and Face Curvatures of Triangle Meshes 9. S-Conical CMC Surfaces: Towards a Unified Theory of Discrete Surfaces with Constant Mean Curvature 10. Constructing Solutions to the Björling Problem for Isothermic Surfaces by Structure Preserving Discretization 11. On the Lagrangian Structure of Integrable Hierarchies 12. On the Variational Interpretation of the Discrete KP Equation 13. Six Topics on Inscribable Polytopes 14. DGD Gallery: Storage, Sharing, and Publication of Digital Research Data

About this book :-
"Advances in Discrete Differential Geometry" by "Alexander Bobenko" is an in-depth exploration of "discrete differential geometry", a field that studies geometric structures in discrete rather than smooth settings. The book connects classical "differential geometry" with modern "computational geometry" and combinatorial methods, offering both theoretical foundations and practical insights. It is aimed at researchers, graduate students, and professionals interested in geometric modeling, applied mathematics, and computer graphics. The book covers core topics such as discrete curves, surfaces, nets, integrable systems, and variational principles. Bobenko emphasizes the role of "geometric algorithms" in computing and analyzing discrete structures, showing how classical geometric concepts like curvature, torsion, and transformations can be adapted to discrete settings. With numerous examples, illustrations, and step-by-step explanations, the text makes complex ideas accessible while maintaining mathematical rigor. Beyond theoretical content, the book highlights applications in computer graphics, numerical simulations, geometric modeling, and related fields. Its structured exposition, clear explanations, and focus on practical computation make it a valuable reference for anyone working in "discrete geometry", computational modeling, and applied mathematics. Bobenko’s work provides a thorough overview of the latest advances in discrete geometric structures and their algorithmic implementations, serving as an essential resource for researchers and students alike.

Book Detail :-
Title: Advances in Discrete Differential Geometry by Alexander Bobenko
Publisher: Springer
Year: 2016
Pages: 441
Type: PDF
Language: English
ISBN-10 #: 3662504464
ISBN-13 #: 978-3662504468
License: CC BY-NC 4.0
Amazon: Amazon

About Author :-
The author Alexander I. Bobenko is a leading "mathematician" and expert in "discrete differential geometry", "geometric algorithms", and "computational geometry". He is recognized for bridging classical "differential geometry" with discrete methods, making complex geometric structures accessible and applicable in modern computation. Bobenko’s research focuses on discrete curves, surfaces, nets, and integrable systems, emphasizing practical "geometric algorithms" for modeling and analyzing structures. As the author of "Advances in Discrete Differential Geometry", he provides a key resource for researchers, graduate students, and professionals in mathematics, computer graphics, and applied geometry, combining theory with computational applications effectively.

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