Intersection of a line segment with the interior of a polygon

[normalhuman]

I understand that the Polygon class treats polygons mostly like curves rather than 2D shapes. Still, there are some methods (like encloses and area) which pertain to the region enclosed by the polygon.

In this direction someone asked about finding the Intersection between Segment and Interior of Polygon in SymPy on Stack Overflow. They wanted specifically the length, but I imagine one may also want to geometric object, union of line segments.

Should there be something like Polygon.fill().intersect(Segment) method, returning the intersection set? (I am not sure about the API here, do we want a FilledPolygon class object returned by Polygon.fill() method?) My answer on SO has a sketch of a possible approach to this.

[smichr]

I have shied away from such additions because there are much better options available for dealing with filled regions. After a quick look, I think it was shapely that I had looked at before.

One thing we haven't implemented yet is a footprint area which ignores self intersections of segments. (See this repo for a possible routine to use/modify and related discussion here.)

[smichr]

Oh yes, pyclipper was the other library.

[smichr]

To include interior points is a matter of adding to the intersection of two objects those vertices that are enclosed by the other object,

def filled_intersection(a, b):
    i = a.intersection(b)
    def pts(a):
        if hasattr(a, 'vertices'):
            return a.vertices
        if isinstance(a, Point):
            return [a]
        if isinstance(a, Segment):
            return a.args
        assert None, 'unrecognized object for points'
    for do in range(2):
        for j in pts(a):
            if b.encloses_point(j):
                i.append(j)
        a,b=b,a
    return convex_hull(*i)

But this will not work when a convex region of one polygon is contained in another.