Interactive geometry remeshing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Islamic star patterns in absolute geometry
ACM Transactions on Graphics (TOG)
Rotational symmetry field design on surfaces
ACM SIGGRAPH 2007 papers
ACM SIGGRAPH 2009 papers
Cyclic plain-weaving on polygonal mesh surfaces with graph rotation systems
ACM SIGGRAPH 2009 papers
Packing circles and spheres on surfaces
ACM SIGGRAPH Asia 2009 papers
SMI 2011: Full Paper: Cyclic twill-woven objects
Computers and Graphics
Connectivity editing for quadrilateral meshes
Proceedings of the 2011 SIGGRAPH Asia Conference
Beady: interactive beadwork design and construction
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
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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.