Which Shapely predicate should be used to distinquish between these LinearRings

In my project there are two use-cases. The red and blue shapes are not overlapping in the first case, but they do in the second.

case #1

case #2

In my test code I tried various predicates from Shapely but could not find anyway to tell them apart.

from shapely import LinearRing

# first use-case
blue_sq = LinearRing([(1, 1), (1, 2), (2, 2), (2, 1), (1, 1)])
red_one = LinearRing([(0, 0), (0, 3), (3, 3), (3, 2), (1, 2), (1, 0), (0, 0)])

print(blue_sq.overlaps(red_one))
print(blue_sq.intersects(red_one))
print(blue_sq.crosses(red_one))
print(blue_sq.contains(red_one))
print(blue_sq.touches(red_one))
print(blue_sq.within(red_one))

# second use-case
blue_ln = LinearRing([(2, 1), (2, 2), (7, 2), (7, 1), (2, 1)])
red_two = LinearRing([(1, 0), (1, 1), (2, 1), (2, 2), (3, 2), (3, 0), (1, 0)])

print(blue_ln.overlaps(red_two))
print(blue_ln.intersects(red_two))
print(blue_ln.crosses(red_two))
print(blue_ln.contains(red_two))
print(blue_ln.touches(red_two))
print(blue_ln.within(red_two))

The results are summarised in the table below.

Both cases appear to intersect and overlap, but neither case crosses, contains, touches or lies within the other. I feel sure that I am missing something obvious :-)

A LinearRing is still just a line... so considering that both cases are indeed very similar and there are no differences in the results of the predicates.

A difference appears when you consider the coordinates as the outer border of a surface. To use the lines like that you need to use them to create Polygons in shapely. If you do that, you get the expected different results.

Code sample:

from shapely import Polygon

# first use-case
blue_sq = Polygon([(1, 1), (1, 2), (2, 2), (2, 1), (1, 1)])
red_one = Polygon([(0, 0), (0, 3), (3, 3), (3, 2), (1, 2), (1, 0), (0, 0)])

print(f"{blue_sq.overlaps(red_one)=}")
print(f"{blue_sq.intersects(red_one)=}")
print(f"{blue_sq.crosses(red_one)=}")
print(f"{blue_sq.contains(red_one)=}")
print(f"{blue_sq.touches(red_one)=}")
print(f"{blue_sq.within(red_one)=}")

# second use-case
blue_ln = Polygon([(2, 1), (2, 2), (7, 2), (7, 1), (2, 1)])
red_two = Polygon([(1, 0), (1, 1), (2, 1), (2, 2), (3, 2), (3, 0), (1, 0)])

print(f"{blue_ln.overlaps(red_two)=}")
print(f"{blue_ln.intersects(red_two)=}")
print(f"{blue_ln.crosses(red_two)=}")
print(f"{blue_ln.contains(red_two)=}")
print(f"{blue_ln.touches(red_two)=}")
print(f"{blue_ln.within(red_two)=}")

Output:

blue_sq.overlaps(red_one)=False
blue_sq.intersects(red_one)=True
blue_sq.crosses(red_one)=False
blue_sq.contains(red_one)=False
blue_sq.touches(red_one)=True
blue_sq.within(red_one)=False
blue_ln.overlaps(red_two)=True
blue_ln.intersects(red_two)=True
blue_ln.crosses(red_two)=False
blue_ln.contains(red_two)=False
blue_ln.touches(red_two)=False
blue_ln.within(red_two)=False