Inconsistencies with respect to the Polygon `within` and `intersection` methods.

Expected behavior and actual behavior.

I’ve been trying to use the intersection method to compute the intersection region of the 2 given shapely.geometry.Polygon instances. I was initially trying to verify the intersection results (let’s call it res) by checking if a point I know that lies in the result using the contains method.

I was then trying to dig into the source of this issue and I found that for a few cases the intersection result res when passed through poly.contains(res), the method returns False where ideally it is supposed to return a True value as the intersection of the polygon is supposed to be a part both the Polygons.

Steps to reproduce the problem.

• Adding it in the comments below as I was mainly dealing with huge GeoJSON data.

Operating system

Mac OS X Mojave, Ubuntu 18.04

Shapely version and provenance

Shapely - 1.7.0

[mwtoews]

Fundamentally, this is a floating point precision issue, and is not entirely a shapely issue. Yes, with a perfect precision model I would expect the result of an intersection of two geometries to be contained by each geometry. However, this cannot always be safely represented with a double precision model used by Shapely. JTS fails with this specific example too, except when the precision model is changed to a fixed with scale 1000.0.

You can apply a negative buffer with a very small amount, such as a number near machine epsilon of the fraction of square root of area of the intersected area, which should return the desired result:

from math import sqrt
eps = 1e-14
res2 = res.buffer(-sqrt(res.area) * eps)
assert shapely_poly1.contains(res2)
assert shapely_poly2.contains(res2)

note that these two geometries are nearly the same:

res2.area  # 2742.7512489986843
res.area   # 2742.7512489986875
assert abs(res2.area - res.area) / res.area < 1e-12

[RavicharanN]

Thanks for clarifying!