4.7 Article

Hexagonal Global Parameterization of Arbitrary Surfaces

Journal

Publisher

IEEE COMPUTER SOC
DOI: 10.1109/TVCG.2011.118

Keywords

Surface parameterization; rotational symmetry; hexagonal global parameterization; triangular remeshing; pattern synthesis on surfaces; texture synthesis; geometry synthesis; regular patterns

Funding

  1. DFG research center MATHEON
  2. US National Science Foundation (NSF) [IIS-0546881, CCF-0830808, IIS-0917308]
  3. Direct For Computer & Info Scie & Enginr
  4. Div Of Information & Intelligent Systems [0917308] Funding Source: National Science Foundation
  5. Division of Computing and Communication Foundations
  6. Direct For Computer & Info Scie & Enginr [0830808] Funding Source: National Science Foundation

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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.

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