Optimized advance front method of packing dense ellipse for generating the convex polygon structure statistically equivalent with real material

A new constructive method, called optimized advance front method (OAFM), for ellipse packing is proposed. The OAFM allows particle rotation at several angles and movement along a local advance front. Combined with the ellipse approximated by four connected arcs and a series of sequential coordinate transformations, the OAFM generates dense ellipse packing with any imposed size, aspect ratio, and orientation distribution at a fastpacking speed, and the generated ellipse packing can satisfy an imposed spatial arrangement. Based on the approximation of ellipses by multicircles, Laguerre Voronoi Tessellation method constructs initial cells. The initial cells are then merged to create the convex polygon with the same size, aspect ratio, orientation, and location as that of the obtained ellipse. Three examples of ellipse packing and convex polygon demonstrate that the convex polygon generated can be statistically equivalent with the real material and satisfy an imposed spatial arrangement.