Meshing of Hexagons into Convex Quadrilaterals

Efficient electromagnetic analysis of the composite metallic and dielectric structures in the frequency domain based on the Method of Moments applied to the Surface Integral Equations is provided, if building blocks have the form of bilinear surfaces (in particular, flat quads), and if analysis is supported by the higher order basis functions. Heterogenous surfaces of many 3D structures can be easily represented as a combination of connected non-overlapping polygons. Subdivision of the polygons into the minimal number of mutually connected flat quads of good shape is based on subdivision of the hexagons into the convex quads, with possible addition of new nodes only in the interior of the hexagons. We classified hexagons into 46 classes and for each class we found the subdivision scheme. We demonstrated that all subdivision schemes can be unified into four “cut and try” algorithms. The effectiveness of the approach is illustrated on a typical example. This method is implemented in the software tool for antenna design [6].