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Hexagonal Global Parameterization of Arbitrary Surfaces

TitleHexagonal Global Parameterization of Arbitrary Surfaces
Publication TypeJournal Article
Year of Publication2012
AuthorsNieser, M., J. Palacios, K. Polthier, and E. Zhang
JournalIEEE Transactions on Visualization and Computer Graphics
Pagination865 - 878
Date Published06/2012
Keywordsgeometry synthesis, hexagonal global parameterization, pattern synthesis on surfaces, regular patterns, rotational symmetry, surface parameterization, texture synthesis, triangular remeshing

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.

Short TitleIEEE Trans. Visual. Comput. Graphics