By Alexander I. Bobenko (eds.)
This is likely one of the first books on a newly rising box of discrete differential geometry and a very good strategy to entry this fascinating region. It surveys the interesting connections among discrete versions in differential geometry and intricate research, integrable platforms and functions in laptop graphics.
The authors take a better examine discrete versions in differential
geometry and dynamical structures. Their curves are polygonal, surfaces
are made of triangles and quadrilaterals, and time is discrete.
Nevertheless, the variation among the corresponding tender curves,
surfaces and classical dynamical platforms with non-stop time can not often be noticeable. this is often the paradigm of structure-preserving discretizations. present advances during this box are encouraged to a wide quantity through its relevance for special effects and mathematical physics. This e-book is written via experts operating jointly on a standard learn undertaking. it truly is approximately differential geometry and dynamical structures, soft and discrete theories, and on natural arithmetic and its functional purposes. The interplay of those elements is tested by means of concrete examples, together with discrete conformal mappings, discrete advanced research, discrete curvatures and specific surfaces, discrete integrable platforms, conformal texture mappings in special effects, and free-form architecture.
This richly illustrated e-book will persuade readers that this new department of arithmetic is either appealing and helpful. it's going to entice graduate scholars and researchers in differential geometry, complicated research, mathematical physics, numerical equipment, discrete geometry, in addition to special effects and geometry processing.
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Extra resources for Advances in Discrete Differential Geometry
47 Fig. 28 Uniformizations of the hyperelliptic curves (67) with genus 2, 3, and 4. The triangulation of the surfaces is a regular 1-to-4 subdivision of the convex hull of the branch points. Due to the symmetries of these curves, the fundamental domains are regular hyperbolic 4g-gons. Since the triangulation is as symmetric as the curves, and because the solution of the discrete uniformization problem is unique, the fundamental domains of the polyhedral surfaces are also exactly regular hyperbolic 4g-gons.
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