Hexagonal global parameterization of arbitrary surfaces

TitleHexagonal global parameterization of arbitrary surfaces
Publication TypeConference Paper
Year of Publication2010
AuthorsNieser, M., J. Palacios, K. Polthier, and E. Zhang
Tertiary AuthorsCani, M. - P., and A. Sheffer
Conference NameACM SIGGRAPH ASIA 2010 Sketches
Pagination1 - 2
Date Published12/2010
PublisherACM Press
Conference LocationSeoul, Republic of Korea
ISBN Number9781450305235

This sketch introduces hexagonal global parameterization, a new type of periodic global parameterization that is ideal for tiling surfaces with patterns of six-fold rotational symmetries, i.e., 6-RoSy's [Palacios and Zhang 2007]. Being one of the two most fundamental rotational symmetries that are compatible with translational symmetries in the plane, 6-RoSy's appear in many places in nature, such as honeycombs, insect eyes, corals and crystals, as well as man-made objects such as Islamic patterns [Kaplan and Salesin 2004] and tri-axial weaving [Akleman et al. 2009]. Such symmetries can also provide optimal circle packing, which naturally have applications in architectural design [Schiftner et al. 2009]. A hexagonal global parameterization facilitates all of these applications. See Figure 1 for some examples. Furthermore, parameter lines in a hexagonal global parameterization intersect at an angle of π/3, which enables triangular remeshing of a mesh surface with close to ideal aspect ratios in the triangles. The dual mesh of such a triangulation provides a hexagon-dominant tiling of the surface.