Checking if two cubic Bézier curves intersect

Question

For a personal project, I\'d need to find out if two cubic Bézier curves intersect. I don\'t need to know where: I just need to know if they do. However, I\'d need to do it

Answer 1

If you're doing this for production code, I'd suggest the Bezier clipping algorithm. It's explained well in section 7.7 of this free online CAGD text (pdf), works for any degree of Bezier curve, and is fast and robust.

While using standard rootfinders or matrices might be more straightforward from a mathematical point of view, Bezier clipping is relatively easy to implement and debug, and will actually have less floating point error. This is because whenever it's creating new numbers, it's doing weighted averages (convex combinations) so there's no chance of extrapolating based on noisy inputs.