Check if polygon is inside a polygon

Question

Yesterday I was looking to check if a point was inside a polygon and found this great script: https://github.com/tparkin/Google-Maps-Point-in-Polygon

But today at work I was told that our client needs to check if one polygon is inside another polygon. I am wondering if is there a formula where I can take, let's say, two coordinates (instead of one to check a point), and from those two coordinates generate a rectangle and check if that rectangle is inside a polygon.

I don't know if I'm asking a stupid question (a teacher in highschool used to say "there are no stupid questions, there is only fools who don't ask"), but if you don't understand me totally but just a bit, I'd be grateful if you just tell me where to start.

Answer 1

Perform line intersection tests for each pair of lines, one from each polygon. If no pairs of lines intersect and one of the line end-points of polygon A is inside polygon B, then A is entirely inside B.

The above works for any type of polygon. If the polygons are convex, you can skip the line intersection tests and just test that all line end-points of A are inside B.

If really necessary, you can speed up the line intersection tests using the sweep line algorithm.

Answer 2

First check that one of the corner points in the polygon is inside the other polygon using the script. Then check if any of the lines in the polygon crosses any of the lines in the other polygon. If they don't, the polygon is inside the other polygon.