Invalid multipolygon of valid individual polygons

Question

Could anyone please explain this to me? The polygons all have valid geometry but the resulting multipolygon somehow doesn't. The following script:

from shapely.geometry import Polygon, MultiPolygon

polygon1 = Polygon([(0,0), (1,0), (1,1), (0,1), (0,0)])
polygon2 = Polygon([(1,1), (2,1), (2,2), (1,2), (1,1)])
polygon3 = Polygon([(1,0), (2,0), (2,1), (1,1), (1,0)])
polygon_list = [polygon1,polygon2, polygon3]

mpolygon = MultiPolygon(polygon_list)

for item in polygon_list:
    print(item.is_valid)
for item in mpolygon:
    print(item.is_valid)

print(mpolygon.is_valid)

returns the following:

True
True
True
True
True
True
False

I believe this is causing me problems as I need to intersect a multilinestring with a multipolygon, and the intersection method requires for all the polygon geometries to be valid.

Why are the individual polygons valid while the full multipolygon is not?

Answer 1

It's because polygon1 and polygon3 that you created intersect along an infinite amount of points. Taken here from the Shapely documentation:

...On the left, a valid MultiPolygon with 2 members, and on the right, a MultiPolygon that is invalid because its members touch at an infinite number of points (along a line). Link

To fix this, you need to shift polygon3 so that it will have a maximum of one intersecting point with the other polygons (or none at all).

Your polygons plotted:

Answer 2

In addition to @15Step's answer, If you want to fix the invalidity, use buffer method. But if polygons are adjacent, you get polygon instead of multipolygon.

mpolygon = mpolygon.buffer(0)
print(mpolygon.is_valid)
print(type(mpolygon))
# OUT:
#   True
#   <class 'shapely.geometry.polygon.Polygon'>

If you need multipolygon, you have to convert polygon to multipolygon.

if isinstance(mpolygon, Polygon):
    mpolygon = MultiPolygon([mpolygon])