Calculating Azimuth from polygon in GeoPandas

Question

Is there a simple way / ready-to-go function to calculate the azimuth of 2D polygons in a GeoPandas DataFrame? My goal is to eventually compute azimuth angles of building footprints.

Most of the functions I have found explicitly calculate the azimuth for a line, which is not what I am looking for. I have been thinking along the following lines to calculate the azimuth of a polygon using its normal vector (2 dimensions). Is my approach going in the right direction?

I am a bit unsure how to adjust for the quadrants, also my results seem a bit odd.

azimuth = 90 - math.degrees(math.atan2(normal[1], normal[0]))
if azimuth >= 360.0:
    azimuth -= 360.0
elif azimuth < 0.0:
    azimuth += 360.0

Answer 1

Calculate the minimum rotated rectangle, find its longest side, calculate the angle of the side line:

import geopandas as gpd
import shapely
import math

df = gpd.read_file('/home/bera/GIS/Data/testdata/ak_riks.shp')

g = df.iloc[2].geometry #Select one polygon
a = g.minimum_rotated_rectangle #Calculate its minimum rotated rectangle
l = a.boundary #Extract the rectangle boundary as a line
coords = [c for c in l.coords] #List the line coordinates
segments = [shapely.geometry.LineString([a, b]) for a, b in zip(coords,coords[1:])] #Create the four side lines.
longest_segment = max(segments, key=lambda x: x.length) #Find the longest line (one of the long sides of the rotated rectangle)
    
p1, p2 = [c for c in longest_segment.coords] #List the start and end coordinates of it
angle = math.degrees(math.atan2(p2[1]-p1[1], p2[0]-p1[0])) #https://stackoverflow.com/questions/42258637/how-to-know-the-angle-between-two-points