Methods of axis-sorting and shape moments using radar charts.

(a) All possible permutations of the N = 5 mechanical properties of the collagenous tissues dataset, where the instance resulting in a maximal total area (12) is boxed with a dashed line. (b) The “permutated radar chart” yielding a maximal total area used for shape descriptor analyses. (c) The property profile of dentin (red), illustrating its area (A), centroidal distance (R), and the x,y-coordinates of point (a,b) located at the intersection of a vector passing through the profile’s centroid and the perimeter of a unit circle; the area of the property space (grey) of a regular pentagon is A5 ≈ 2.4. (d) The relative first moment of area Q′ about the outer limits of the property space (a,b) for the five materials across all 12 permutations; notice that the maximum values for Q′ are nearly equivalent to those of the maximal area permutation. Legend: dentin = red; bone = yellow; tendon = green; skin = blue; cartilage = purple; total permutation area () = black dashed line (right axis).