Quirky behaviour with predicates

I have noticed some behaviour which does not seem to match with the Shapely documents. I don’t know if it is a bug, if the documentation is wrong, or I’m misunderstanding something about the package.

The manual says: The interior, boundary, and exterior sets of a feature are mutually exclusive and their union coincides with the entire plane.

It additionally says, of the .touches() method: Returns True if the objects have at least one point in common and their interiors do not intersect with any part of the other.

I’m going to set up three linestrings:

>>> Square = shapely.geometry.LineString([(0, 0), (0, 2), (2, 2), (2, 0), (0, 0)])
>>> Triangle = shapely.geometry.LineString([(1, 0), (0.5, 1), (1.5, 1), (1, 0)])
>>> TriangleMinusClosure = shapely.geometry.LineString([(1, 0), (0.5, 1), (1.5, 1)])

The triangle intersects the square in the middle of the bottommost segment. The TriangleMinusClosure is simply two legs of the triangle without the closing segment; it still intersects the square in the middle of the bottommost segment.

>>> Int1 = Square.intersection(Triangle)
>>> Int2 = Square.intersection(TriangleMinusClosure)
>>> type(Int1)
<class 'shapely.geometry.point.Point'>
>>> type(Int2)
<class 'shapely.geometry.point.Point'>
>>> Int1 == Int2
True

So far, so good. It falls apart when I try to apply .touches():

>>> Triangle.touches(Square)
False
>>> TriangleMinusClosure.touches(Square)
True

Both Triangle and TriangleMinusClosure have at least one point in common with Square. To fulfill the other half of the .touches() requirement, they must not have interior points intersecting with Square. Since the interior, boundary, and exterior of a given object are mutually exclusive, and the boundary of a linestring is its two endpoints, I would expect both to touch the square–their only interaction with the square is a boundary point.

I see that the closed linestring is reporting an empty boundary, which would imply (?) that the interior is is everything on the triangle, which would explain the False touch result.

>>> list(Triangle.boundary)
[]
>>> list(TriangleMinusClosure.boundary)
[<shapely.geometry.point.Point object at 0x00000223AC54A880>, <shapely.geometry.point.Point object at 0x00000223AC54A7F0>]

The DE-9IM code does seem to indicate a pointwise intersection of the triangle’s interior with the square’s interior:

>>> Triangle.relate(Square)
'0F1FFF1F2'
>>> TriangleMinusClosure.relate(Square)
'FF10F01F2'

Windows 10 Home 21H1

Shapely version 1.8.1.post1 via pip

[jorisvandenbossche]

Thanks! I see, and indeed a Point also doesn’t touch another identical Point (shapely.Point(1, 1).touches(shapely.Point(1, 1)) gives False), because in those case it are the interiors that intersect.

[dr-jts]

Something else I am wondering on this topic: our manual says that a Point is considered to have an interior of that single point, and an empty boundary. But if you follow that logic, a Point should never touch another geometry? (since the intersecting point will always lie in the interior) In practice, Points do touch other geometries (eg shapely.box(0, 0, 1, 1).touches(shapely.Point(0, 0)) gives True), so that is maybe special cases to give more sensible behaviour?

Here’s the definition of Touches from the SFS: It requires that the geometries intersect, but their interiors are disjoint. This is the case in the Polygon/Point case above - the Interior of the Point intersects the Boundary of the Polygon, but not its Interior.