Classical and Discrete Differential Geometry: Theory, Applications and Algorithms

Name: Classical and Discrete Differential Geometry: Theory, Applications and Algorithms
Brand: Taylor & Francis
SKU: 9781032396200
Price: 4021.0 INR
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by David Xianfeng Gu

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ISBN13: 9781032396200
Binding: Paperback
Subject: N/A
Publisher: Taylor & Francis
Publisher Imprint: CRC Press
Publication Date: October 4, 2024
Pages: 568
Original Price: GBP 47.99
Language: English
Edition: N/A
Item Weight: 1060 grams
BISAC Subject(s): Geometry / Differential, Computer Science, and Computer Engineering

About The Book

This book introduces differential geometry and cutting-edge findings from the discipline by incorporating both classical approaches and modern discrete differential geometry across all facets and applications, including graphics and imaging, physics and networks.

With curvature as the centerpiece, the authors present the development of differential geometry, from curves to surfaces, thence to higher dimensional manifolds; and from smooth structures to metric spaces, weighted manifolds and complexes, and to images, meshes and networks. The first part of the book is a differential geometric study of curves and surfaces in the Euclidean space, enhanced while the second part deals with higher dimensional manifolds centering on curvature by exploring the various ways of extending it to higher dimensional objects and more general structures and how to return to lower dimensional constructs. The third part focuses on computational algorithms in algebraic topology and conformal geometry, applicable for surface parameterization, shape registration and structured mesh generation.

The volume will be a useful reference for students of mathematics and computer science, as well as researchers and engineering professionals who are interested in graphics and imaging, complex networks, differential geometry and curvature.

About The Author

David Xianfeng Gu is a SUNY Empire Innovation Professor of Computer Science and Applied Mathematics at State University of New York at Stony Brook, USA. His research interests focus on generalizing modern geometry theories to discrete settings and applying them in engineering and medical fields and recently on geometric views of optimal transportation theory. He is one of the major founders of an interdisciplinary field, Computational Conformal Geometry.

Emil Saucan is Associate Professor of Applied Mathematics at Braude College of Engineering, Israel. His main research interest is geometry in general (including Geometric Topology), especially Discrete and Metric Differential Geometry and their applications to Imaging and Geometric Design, as well as Geometric Modeling. His recent research focuses on various notions of discrete Ricci curvature and their practical applications.

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