Minimal surfaces from circle patterns: Geometry from combinatorics

Abstract

The theory of polyhedral surfaces... In this paper, we investigate conformal discretizations of surfaces, i.e. discretizations in terms of circles and spheres, and introduce a new discrete model for minimal surfaces. See Figs. 1 and 2. In comparison with direct methods (see, in particular, [17]), leading usually to triangle meshes, the less intuitive discretizations of the present paper have essential advantages: they respect conformal properties of surfaces, possess a maximum principle, etc...