4 papers
Real Riemann Surfaces: Smooth and Discrete
Johanna Düntsch, Felix Günther
This paper develops a discrete theory of real Riemann surfaces based on quadrilateral cellular decompositions (quad-graphs) and a linear discretization of the Cauchy-Riemann equati…
The convergence of discrete period matrices
Felix Günther
We study compact polyhedral surfaces as Riemann surfaces and their discrete counterparts obtained through quadrilateral cellular decompositions and a linear discretization of the C…
The Gauss map of polyhedral vertex stars
Thomas F. Banchoff, Felix Günther
In discrete differential geometry, it is widely believed that the discrete Gaussian curvature of a polyhedral vertex star equals the algebraic area of its Gauss image. However, no…
Smooth polyhedral surfaces
Felix Günther, Caigui Jiang, Helmut Pottmann
Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for…