Abstract:
In this paper we introduce hexagonal global parameterizations, a new type of parameterization in which parameter lines respect six-fold rotational symmetries (6-RoSy). Such parameterizations enable the tiling of surfaces with regular hexagonal texture and geometry patterns and can be used to generate high-quality triangular remeshing. To construct a hexagonal parameterization given a surface, we provide an automatic technique to generate a 6-RoSy field that respects directional and singularity features in the surface. This is achieved by applying the trace-and-deviator decomposition to the curvature tensor, which allows us to identify regions of appropriate directional constraints. We also introduce a technique for automatically merging and cancelling singularities. This field will then be used to generate a hexagonal global parameterization by adapting the framework of QuadCover parameterization. In particular, we formulate the energy terms needed to solve for a hexagonal parameterization. We demonstrate the usefulness of our geometry-aware global parameterization with applications such as surface tiling with regular textures and geometry patterns and triangular remeshing.
