Question

Greetings,

I would like to detect if a segment only ‘touches’ a polygon or cross it.

The Figure

explains my doubt. How to know the difference between cases A and B?
Note that in both situations the red line crosses the polygons in two vertices, one touching by outside and other crossing by inside. I have a segment-segment intersection algorithm, but I don’t know how to use it properly. Any help is appreciated.

Answer 1

I think there might not be any approach much easier than computing the details at a low level.
First, you will need robust code to compute the intersection between two segments.
This is discussed (with code) here. Once you have the intersection points, you need
to compute how the polygon boundary interacts with your segment in the neighborhoods of those
intersection points. This is essentially
repeated LeftOf( ) computations, using the notation in my book.
In your image, the segment passes through vertex b, while the adjacent vertices a and c
(in a consecutive sequence (a,b,c)) are both to the same side of b. Therefore, the segment
does not penetrate to the interior of the polygon in the neighborhood of b. But if a and c
were on opposite sides of the segment, then it must penetrate.