Publication year: 2016
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This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics.
Subject: Mathematics and Statistics, discrete conformal maps, discrete curvature, integrable systems, discrete complex analysis, triangle meshes, polyhedral surfaces, Differential Geometry, Functions of a Complex Variable, Dynamical Systems and Ergodic Theory, Computer Graphics, Numerical and Computational Physics, Simulation