Author： Müller Christian
Publisher： Springer Publishing Company
ISSN： 0046-5755
Source： Geometriae Dedicata, Vol.154, Iss.1, 2011-10, pp. : 27-46
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Abstract
We explore discrete conformal and discrete minimal surfaces whose faces are planar hexagons throughout. Discrete conformal meshes are built of conformal hexagons for which we establish a dual construction. We apply this dual construction to conformal hexagonal meshes covering the sphere and get discrete hexagonal minimal surfaces via a discrete analogue to the Christoffel dual construction. We compare the smooth and the discrete settings by means of limit considerations and also by a discussion of Möbius invariants.
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