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

I don't know how fast it will be, but if you have two curves C1(t) and C2(k) they intersect if C1(t) == C2(k). So you have two equations (per x and per y) for two variables (t, k). You can solve the system using numerical methods with enough for you accuracy. When you've found t,k parameters you should check if there is a parameter on [0, 1]. If it is they intersects on [0, 1].