I have Shapely polygon geometries, A circle(c) and list of polygons within the circle. I want to find the union of the circle with the intersections. (circle + intersections) circle



I was trying to make a MultiPolygon of difference and intersection:

poly_list = [poly_N, poly_E]

# finding the intersection of circle and polys
intersec_list = []
for poly in poly_list:

MP_intersec = MultiPolygon(intersec_list)

# finding the difference of circle and polygons
diff_list = []
for inter in intersec_list:
    diffi = c.difference(inter)

MP_diff = MultiPolygon(diff_list)

# find the union of circle and intersection
# output: a MultiPolygon or a geometric collection with 4 polygons and the difference of circle.  

MP_out = MultiPolygon([MP_diff, MP_intersec])

but MP_out gives invalid geometry probably because I have overlapping polygon as well.

  • 2
    Intersection isn't working because you want something else. Do you want a union or the union of the circle with the intersection? This is the sort of question that screams for a picture.
    – Vince
    May 31, 2020 at 4:22
  • I agree with @Vince, a picture often says a thousand words! I too would say it is a Union you want to do.
    – Hornbydd
    May 31, 2020 at 13:39
  • @Vince Yes I want to find the union of circle with the intersection
    – FJ_Abbasi
    May 31, 2020 at 18:13
  • 1
    By definition, the union of a shape and any shape that it had previously been intersected is the shape itself. A multipolygon cannot be composed of exterior rings that overlap at more than a point.
    – Vince
    May 31, 2020 at 19:46
  • Please add a picture which shows what exactly you need. I recommend you to read Shapely Manual. It's hard to tell what really you need just by reading your question text and comments. Jun 1, 2020 at 0:50

1 Answer 1


As far as I know, there is no a specific method performing what you want. The following script creates a geometry collection including the circle and intersected areas.

from shapely.geometry import Point, Polygon, GeometryCollection

# sample geometries. c: circle, r*: rectangles
c = Point(5, 5).buffer(3)
r1 = Polygon([(1, 6), (1, 9), (9, 9), (9, 6)])
r2 = Polygon([(9, 4), (9, 1), (1, 1), (1, 4)])
rectangles = [r1, r2]

geoms = [c] # create a list including circle
for r in rectangles:
    # add intersection to the list

# create shapely GeometryCollection
geom_collection = GeometryCollection(geoms)

enter code here

Then, you can get the geometries in the collection.

# OUT:
# True

# OUT:
# <shapely.geometry.base.HeterogeneousGeometrySequence at ...>

# OUT:
# [<shapely.geometry.polygon.Polygon at ...>, 
#  <shapely.geometry.polygon.Polygon at ...>,
#  <shapely.geometry.polygon.Polygon at ...>]

# OR use index
geom_collection.geoms[0] # gives the circle, because it is the first element
  • I have overlapping polygons so MultiPolygon is not working.
    – FJ_Abbasi
    May 31, 2020 at 22:42
  • Thank you it is very helpful. What if we want a geometry collection of intersected areas and difference of circle?
    – FJ_Abbasi
    Jun 2, 2020 at 12:44
  • For differences of circle, change c.intersection(r) into r.difference(c). If you want the collection not to include the circle, set geoms = [] (empty list) instead of geoms = [c]. Jun 2, 2020 at 13:09

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