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Hexagonal Parameterization of Arbitrary Surfaces

Please always quote using this URN:urn:nbn:de:0296-matheon-8307
  • 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.

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Metadaten
Author:Matthias Nieser, Jonathan Palacios, Konrad Polthier, Eugene Zhang
URN:urn:nbn:de:0296-matheon-8307
Referee:Ralf Kornhuber
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/05/21
Release Date:2011/05/21
Tag:
Institute:Freie Universität Berlin
MSC-Classification:52-XX CONVEX AND DISCRETE GEOMETRY / 52Cxx Discrete geometry / 52C15 Packing and covering in 2 dimensions [See also 05B40, 11H31]
Preprint Number:792
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