Hexagonal Global Parameterization of Arbitrary Surfaces

Authors:
Matthias Nieser;Jonathan Palacios;Konrad Polthier;Eugene Zhang
Affiliations:
Freie Universität Berlin, Berlin;Oregon State University, Corvallis;Freie Universität Berlin, Berlin;Oregon State University, Corvallis
Venue:
IEEE Transactions on Visualization and Computer Graphics
Year:
2012

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Abstract

We introduce hexagonal global parameterization, a new type of surface parameterization in which parameter lines respect sixfold 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.