Rectangular Hexagonal Mesh Generation for Parametric Modeling

This paper addresses the problem of rectangular hexagonal mesh generation for surface modeling. Hexagonal grids are important for several applications such as the simulation of carbon nanostructures. A fast and accurate method to obtain a rectangular region over a hexagonal grid is proposed. Strips of hexagons defined by the Hamada indexes are constructed and stacked using a variation of the Bresenham's algorithm. The final hexagonal mesh is tessellated using half-edges in order to be suitable for several operations and simulation processes. This mesh can be used as a parameter space for obtaining different geometric models. Experimental results show that arbitrarily large meshes are generated fast. The enumeration of rectangular regions with high number of hexagons is accurate despite its dimensions. An evaluation of the method under several circumstances is presented indicating its high performance for the generation of a high number of hexagons.