Open Access

Matthias Nieser, Jonathan Palacios, Konrad Polthier, Eugene Zhang

• We introduce hexagonal global parameterizations, a new type of surface parameterizations 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. To construct a hexagonal parameterization on a surface, we provide an automatic algorithm to generate a 6-RoSy field that respects directional and singularity features of the surface. This field is then used to direct a hexagonal global parameterization. The framework, called HexCover, extends the QuadCover algorithm and formulates necessary conditions for hexagonal parameterization. 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.