Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. Current progress in this field is to a large extent stimulated by its relevance for computer graphics and mathematical physics. This collection of essays, which documents the main lectures of the 2004 Oberwolfach Seminar on the topic, as well as a number of additional contributions by key participants, gives a lively, multi-facetted introduction to this emerging field.

First book on a newly emerging field of discrete differential geometry, provides an excellent way to access this new exciting area Carefully edited collection of essays by key researchers in the field Surveys fascinating connections between discrete geometry and differential geometry: for instance circle patterns and triangulated surfaces on the discrete side connect to minimal surfaces and curvature line parametrizations on the differential side Includes supplementary material: sn.pub/extras

Autorentext
Peter Schröder hat als Diplomgeograph langjährige Unterrichtserfahrung am Geographischen Institut der Universität Tübingen und an der Pädagogischen Hochschule Ludwigsburg gesammelt. Inhaltliche Schwerpunkte seiner Arbeit sind das Klima und die Kartographie.
Zu diesen Themen hat er zahlreiche fach- und populärwissenschaftliche Artikel veröffentlicht.

Inhalt
Discretization of Surfaces: Special Classes and Parametrizations.- Surfaces from Circles.- Minimal Surfaces from Circle Patterns: Boundary Value Problems, Examples.- Designing Cylinders with Constant Negative Curvature.- On the Integrability of Infinitesimal and Finite Deformations of Polyhedral Surfaces.- Discrete Hashimoto Surfaces and a Doubly Discrete Smoke-Ring Flow.- The Discrete Green's Function.- Curvatures of Discrete Curves and Surfaces.- Curves of Finite Total Curvature.- Convergence and Isotopy Type for Graphs of Finite Total Curvature.- Curvatures of Smooth and Discrete Surfaces.- Geometric Realizations of Combinatorial Surfaces.- Polyhedral Surfaces of High Genus.- Necessary Conditions for Geometric Realizability of Simplicial Complexes.- Enumeration and Random Realization of Triangulated Surfaces.- On Heuristic Methods for Finding Realizations of Surfaces.- Geometry Processing and Modeling with Discrete Differential Geometry.- What Can We Measure?.- Convergence of the Cotangent Formula: An Overview.- Discrete Differential Forms for Computational Modeling.- A Discrete Model of Thin Shells.