We introduce hexagonal global parameterization, a new type of surface parameterization
in which parameter lines respect six-fold rotational symmetries (6-RoSy). Such
parameterizations enable the tiling of surfaces with nearly regular hexagonal or
triangular patterns, and can be used for triangular remeshing.
Our framework to construct a hexagonal parameterization, referred to as HEXCOVER,
extends the QUADCOVER algorithm and formulates necessary conditions for hexagonal
parameterization. We also provide an algorithm to automatically generate a 6-RoSy field
that respects directional and singularity features in the surface. We demonstrate the
usefulness of our geometry-aware global parameterization with applications such as
surface tiling with nearly regular textures and geometry patterns, as well as
triangular and hexagonal remeshing.