Getting intersection of multiple polygons efficiently in Python

Question

I would like to get the intersection of multiple polygons. Using Python's shapely package, I can find the intersection of two polygons using the intersection function. Is there a similar efficient function for obtaining the intersection of multiple polygons?

Here is a code snippet to understand what I mean:

from shapely.geometry import Point

coord1 = ( 0,0 )
point1 = Point(coord1)
circle1 = point1.buffer(1)

coord2 = ( 1,1 )
point2 = Point(coord2)
circle2 = point2.buffer(1)

coord3 = ( 1,0 )
point3 = Point(coord3)
circle3 = point3.buffer(1) 

An intersection of two circles can be found by circle1.intersection(circle2). I can find the intersection of all three circles by circle1.intersection(circle2).intersection(circle3). However, this approach is not salable to a large number of polygons as it requires increasingly more code. I would like a function that takes an arbitrary number of polygons and returns their intersection.

Answer 1

One possible approach could be considering the combination of pairs of polygons, their intersections and finally the union of all the intersections via a cascaded union (like suggested here):

from shapely.geometry import Point
from shapely.ops import cascaded_union
from itertools import combinations

circles = [
    Point(0,0).buffer(1),
    Point(1,0).buffer(1),
    Point(1,1).buffer(1),
]

intersection = cascaded_union(
    [a.intersection(b) for a, b in combinations(circles, 2)]
)
print intersection

---

A more efficient approach should use a spatial index, like Rtree, in order to deal with a lot of geometries (not the case of the three circles):

from shapely.geometry import Point
from shapely.ops import cascaded_union
from rtree import index

circles = [
    Point(0,0).buffer(1),
    Point(1,0).buffer(1),
    Point(1,1).buffer(1),
]
intersections = []
idx = index.Index()

for pos, circle in enumerate(circles):
    idx.insert(pos, circle.bounds)

for circle in circles:
    merged_circles = cascaded_union([circles[pos] for pos in idx.intersection(circle.bounds) if circles[pos] != circle])
    intersections.append(circle.intersection(merged_circles))

intersection = cascaded_union(intersections)
print intersection

Answer 2

Why not use a iteration or recursivity? something like :

from shapely.geometry import Point

def intersection(circle1, circle2):
    return circle1.intersection(circle2)

coord1 = ( 0,0 )
point1 = Point(coord1)
circle1 = point1.buffer(1)

coord2 = ( 1,1 )
point2 = Point(coord2)    
circle2 = point2.buffer(1)


coord3 = ( 1,0 )
point3 = Point(coord3)
circle3 = point3.buffer(1)
circles = [circle1, circle2, circle3]
intersectionResult = None

for j, circle  in enumerate(circles[:-1]):

    #first loop is 0 & 1
    if j == 0:
        circleA = circle
        circleB = circles[j+1]
     #use the result if the intersection
    else:
        circleA = intersectionResult
        circleB = circles[j+1]
    intersectionResult = intersection(circleA, circleB)

result= intersectionResult

Answer 3

Give this code a shot. its pretty simple in concept and I believe gets you what you are looking for.

from shapely.geometry import Point
from itertools import combinations
dic ={}
dic['coord1']=Point(0,0).buffer(1)
dic['coord2']=Point(1,1).buffer(1)
dic['coord3']=Point(1,0).buffer(1)
inter = {k[0]+v[0]:k[1].intersection(v[1]) for k,v in combinations(dic.items(),2)}
print inter

and if you want the output to be stored as a shapefile use fiona:

from shapely.geometry import Point,mapping
import fiona
from itertools import combinations
schema = {'geometry': 'Polygon', 'properties': {'Place': 'str'}}
dic ={}
dic['coord1']=Point(0,0).buffer(1)
dic['coord2']=Point(1,1).buffer(1)
dic['coord3']=Point(1,0).buffer(1)
inter = {k[0]+v[0]:k[1].intersection(v[1]) for k,v in combinations(dic.items(),2)}
print inter
with fiona.open(r'C:\path\abid', "w", "ESRI Shapefile", schema) as output:
    for x,y in inter.items():
        output.write({'properties':{'Place':x},'geometry':mapping(y)})

this outputs -