This is one of the first books on a newly emergingÂ field of discreteÂ differential geometry and an excellent way to access this excitingÂ area. It surveys the fascinating connections between discrete modelsÂ in differential geometry and complex analysis, integrable systems andÂ applications in computer graphics.
The authors take a closer look at discrete models in differential
geometry and dynamical systems. Their curves are polygonal, surfacesare made from triangles and quadrilaterals, and time is discrete.
Nevertheless, the difference between the corresponding smooth curves,
surfaces and classicalÂ dynamical systems with continuousÂ time canÂ hardly be seen. This is the paradigm ofÂ structure-preservingÂ discretizations. Current advances in this field are stimulated to aÂ large extent by its relevance for computer graphics and mathematicalÂ physics. This book is written by specialists working together on aÂ common research project. It is about differential geometry andÂ dynamical systems, smooth and discrete theories, and on pureÂ mathematics and its practical applications. The interaction of theseÂ facets is demonstrated by concrete examples, including discreteÂ conformal mappings, discrete complex analysis, discrete curvatures andÂ special surfaces, discrete integrableÂ systems, conformal textureÂ mappings in computer graphics, and free-form architecture.
This richly illustrated book will convinceÂ readers that this newÂ branch of mathematics is both beautiful and useful. It will appeal toÂ graduate students and researchers in differential geometry, complexÂ analysis, mathematical physics, numerical methods, discrete geometry,Â as well as computer graphics and geometry processing.
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