Discrete Differential Geometry

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Discrete nonlinear hyperbolic equations. Classification of integrable cases (2007, neutral): “0016–2663/09/4301–0003 c©2009 Springer Science+Business Media, Inc. 3 Key words: integrability, quad-graph, multidimensional consistency, zero curvature representation, Bäcklund transformation, Bianchi permutability, Möbius transformation.”
Geometric Modeling with Conical Meshes and Developable Surfaces (2006, background): “PQ meshes have first been systematically addressed by R. Sauer, as summarized in his monograph [1970] on difference geometry, one of the precursors of discrete differential geometry [Bobenko and Suris 2005; Desbrun et al. 2005; Polthier 2002; Hildebrandt et al. 2005].”
Hierarchical mesh segmentation based on fitting primitives (2006, methodology): “Speciﬁcally, for each vertex v a restricted Voronoi area a (v) is computed, which corresponds to a third of the total area of the triangles incident at v [15] and belonging to the cluster under consideration.”
Universality in the 2D Ising model and conformal invariance of fermionic observables (2009, background): “At the same time, discrete holomorphic functions on isoradial graphs provide the simplest example of a discrete integrable system in the so-called “consistency approach” to the (discrete) integrable systems theory (see [5]).”