Calculate Polsby-Popper as measure of compactness

polsby_popper.py

import math

from arcgis.geometry import Polygon


def get_simplified_polygon(geometry: Polygon, simplification_factor: float = 0.1) -> Polygon:
    
    # ensure working with a polygon
    assert isinstance(geometry, Polygon)

    # get a slice of the diameter if the area were a circle
    smpl_dst = math.sqrt(geometry.area / math.pi) * simplification_factor

    # generalize with no more deflection than a slice of the most compact geometry, a circle
    smpl_poly = geometry.generalize(smpl_dst)
    
    return smpl_poly


def get_polsby_popper_score(geometry: Polygon) -> float:
    
    # ensure it is a polygon
    assert isinstance(geometry, Polygon)
    
    # calculate the Polsby-Popper score
    pp_scr = 4 * math.pi * geometry.area / geometry.length ** 2
    
    return pp_scr


def get_simplified_polsby_popper_score(geometry: Polygon, simplification_factor: float = 0.1) - float:
    
    # make sure it is a polygon
    assert isinstance(geometry, Polygon)
    
    # simplify the geometry
    smpl_poly = get_simplified_polygon(geometry, simplification_factor)
    
    # get the Polsby-Popper score for the simplified polygon
    pp = get_polsby_popper_score(smpl_poly)
    
    return pp