Nothing is ever as fast as we want it to be. polyxpoly (part of the mapping toolbox) does a lot of work. And it needs to check for intersections between all pairs of segments. Of course this will take time that should grow roughly quadratically with the number of segments in the given polylines.
You could try Doug Schwarz's intersections code, found on the file exchange.
N = [25 50 100 150 200 250 300]';
xy1 = rand(n,2);xy2 = rand(n,2);
T(i,1) = timeit(@() polyxpoly(xy1(:,1),xy1(:,2),xy2(:,1),xy2(:,2)));
T(i,2) = timeit(@() intersections(xy1(:,1),xy1(:,2),xy2(:,1),xy2(:,2)));
legend('polyxpoly','intersections')
Intersections seems to have better behavior as the number of segments grows. The nearly linear slope in the loglog plot does have a slope of approximately 2, which reflects my claim of quadratic time algorithm. I don't think you can do much better than that.
And, as you can see, intersections was roughly 5 times as fast for curves with 300 segments. That disparity probably grows for larger problems. For smaller problems, polyxpoly seemed to have come out on top, at least in this test. But for smaller problems both tools were pretty fast.
polyfit(log(N),log(T(2,:)),1)
Find intersections on the FEX for download, here:
