Measuring compactness in Python [closed]

Question

I have set of polygons whom I would like to check their compactness.

I'm working in Jupyter Notebook and my geometry is GeoPandas.
I would like to try Polsby-Popper test and Schwartzberg test (and other test that are here: https://fisherzachary.github.io/public/r-output.html ) but I can't find any simple way to do it.

I don't find way to create the necessary circles, e.g "circle whose area is equal to the area of the polygon " or "circle whose circumference is equal to the perimeter of the polygon ".

I have found script to do find smallest enclosing circle but it seems like it works with points and I have polygon in GeoPandas (https://www.nayuki.io/res/smallest-enclosing-circle/smallestenclosingcircle.py).

If anyone knows any library/package/ any idea of how I can create circles from given perimeter or area. It's important to say that I have around 70k polygons to check so I also have the memory issue.

My end goal is to get ideas how can I calculate this in Python in Jupyter Notebook.

Edit: I have found this library but struggling with install it/use it (https://jblindsay.github.io/wbt_book/available_tools/gis_analysis_patch_shape_tools.html) (https://github.com/jblindsay/whitebox-tools/blob/master/src/tools/gis_analysis/related_circumscribing_circle.rs)

Answer 1

You don't need to create circles. The formula is derived from the ratio you mentioned.

Use the following script. You can apply the other formulas easily.

import geopandas as gpd
from math import pi, sqrt

def pp_compactness(geom): # Polsby-Popper
    p = geom.length
    a = geom.area    
    return (4*pi*a)/(p*p)
    
def s_compactness(geom): # Schwartzberg
    p = geom.length
    a = geom.area    
    return 1/(p/(2*pi*sqrt(a/pi)))

gdf = gpd.read_file("file/path")
        
gdf["Polsby_Popper"] = gdf.geometry.apply(pp_compactness)
gdf["Schwartzberg"] = gdf.geometry.apply(s_compactness)
    
print(gdf)

#      geometry            Polsby_Popper   Schwartzberg 
#  0   POLYGON ((552...    0.351956        0.593259  
#  1   POLYGON ((552...    0.550202        0.741756  
#  ..               ...         ...             ...  
#  130 POLYGON ((553...    0.434469        0.659142  
#  131 POLYGON ((553...    0.706016        0.840248