esda.shape.isoperimetric_quotient

esda.shape.isoperimetric_quotient(collection)

The Isoperimetric quotient, defined as the ratio of a polygon’s area to the area of the equi-perimeter circle.

Altman’s PA_1 measure [Alt98]

Construction:

let: p_d = perimeter of polygon a_d = area of polygon

a_c = area of the constructed circle r = radius of constructed circle

then the relationship between the constructed radius and the polygon perimeter is: p_d = 2 pi r p_d / (2 pi) = r

meaning the area of the circle can be expressed as: a_c = pi r^2 a_c = pi (p_d / (2pi))^2

implying finally that the IPQ is:

pp = (a_d) / (a_c) = (a_d) / ((p_d / (2*pi))^2 * pi) = (a_d) / (p_d**2 / (4PI))