Characterizing Polygonality in Biological Structures
  Several systems involve spatial arrangements of elements such as molecules or cells, the characterization of which bears important implications to biological and physical investigations. Traditional approaches to quantify spatial order and regularity have relied on nearest neighbor distances or the number of sides of cells. The current work shows that superior features can be achieved by considering angular regularity. Voronoi tessellations are obtained for each basic element and the angular regularity is then estimated from the differences between the angles defined by adjacent cells and a reference angle. In case this angle is 60 degrees, the measurement quantifies the hexagonality of the system. Other reference angles can be considered in order to quantify other types of spatial symmetries. The performance of the angular regularity is compared with other measurements including the conformity ratio (based on nearest neighbor distances) and the number of sides of the cells, confirming its improved sensitivity and discrimination power. The superior performance of the haxagonality measurement is illustrated also with respect to a real application concerning the characterization of retinal mosaics. 
Luciano da Fontoura Costa, Fernando Rocha and Silene Araujo de Lima