See if two line segments intersect or not. This uses the vector cross product approach described here: http://stackoverflow.com/a/565282/786339. This derives its algorithm from: "Intersection of two lines in three-space" by Ronald Goldman.
Include the line-segments-intersect.js script in your HTML. Then call
doLineSegmentsIntersect(p, p2, q, q2) to see if the line segment between
the points p and p2 intersect with the line segment between q and q2.
I have included the unit tests I put together in the index html as an example.