Advances in Discrete Differential Geometry

This is one of the first books on a newly emergingfield of discretedifferential geometry and an excellent way to access this excitingarea. It surveys the fascinating connections between discrete modelsin differential geometry and complex analysis, integrable systems andapplications in computer graphics.The authors take a closer look at discrete models in differentialgeometry 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 classicaldynamical systems with continuoustime canhardly be seen. This is the paradigm ofstructure-preservingdiscretizations. Current advances in this field are stimulated to alarge extent by its relevance for computer graphics and mathematicalphysics. This book is written by specialists working together on acommon research project. It is about differential geometry anddynamical systems, smooth and discrete theories, and on puremathematics and its practical applications. The interaction of thesefacets is demonstrated by concrete examples, including discreteconformal mappings, discrete complex analysis, discrete curvatures andspecial surfaces, discrete integrablesystems, conformal texturemappings in computer graphics, and free-form architecture. This richly illustrated book will convincereaders that this newbranch of mathematics is both beautiful and useful. It will appeal tograduate students and researchers in differential geometry, complexanalysis, mathematical physics, numerical methods, discrete geometry,as well as computer graphics and geometry processing.