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Discrete Differential Geometry - Integrable Structure
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Discrete Differential Geometry - Integrable Structure
Series: Graduate Studies in Mathematics
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An emerging field of discrete differential geometry aims at the
development of discrete equivalents of notions and methods of
classical differential geometry. The latter appears as a limit of a
refinement of the discretization. Current interest in discrete
differential geometry derives not only from its importance in pure
mathematics but also from its applications in computer graphics,
theoretical physics, architecture, and numerics. Rather
unexpectedly, the very basic structures of discrete differential
geometry turn out to be related to the theory of integrable
systems. One of the main goals of this book is to reveal this
integrable structure of discrete differential geometry. For a given
smooth geometry one can suggest many different discretizations.
Which one is the best? This book answers this question by providing
fundamental discretization principles and applying them to numerous
concrete problems. It turns out that intelligent theoretical
discretizations are distinguished also by their good performance in
applications. The intended audience of this book is threefold. It
is a textbook on discrete differential geometry and integrable
systems suitable for a one semester graduate course. On the other
hand, it is addressed to specialists in geometry and mathematical
physics. It reflects the recent progress in discrete differential
geometry and contains many original results. The third group of
readers at which this book is targeted is formed by specialists in
geometry processing, computer graphics, architectural design,
numerical simulations, and animation. They may find here answers to
the question ""How do we discretize differential geometry?""
arising in their specific field. Prerequisites for reading this
book include standard undergraduate background (calculus and linear
algebra). No knowledge of differential geometry is expected,
although some familiarity with curves and surfaces can be helpful.
General
Imprint: |
American Mathematical Society
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Country of origin: |
United States |
Series: |
Graduate Studies in Mathematics |
Release date: |
2008 |
Authors: |
Alexander I. Bobenko
• Yuri B. Suris
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Pages: |
404 |
ISBN-13: |
978-1-4704-7456-0 |
Categories: |
Books
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LSN: |
1-4704-7456-5 |
Barcode: |
9781470474560 |
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