Conformal hexagonal meshes

C. Müller

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.

Bibtex:

@article{mueller-chm,
   author = {M{\"u}ller, Christian},
   title = {Conformal hexagonal meshes},
   journal = {Geometriae Dedicata},
   publisher = {Springer Netherlands},
   issn = {0046-5755},
   pages = {27-46},
   volume = {154},
   issue = {1},
   doi = {http://dx.doi.org/10.1007/s10711-010-9566-8},
   url = "http://www.geometrie.tuwien.ac.at/cmueller/dualhex.pdf",
   year = {2011}
}