The intersection point between a spline and a line

Question

I'm trying to find a way to calculate the intersection between a b-spline and a straight line. So far Google hasn't been much help.

Answer 1

A pure mathematical approach:

• Transform the spline and the line so that the line lies on the X axis.
• Calculate the points on the spline where Y = 0 (depends on the order of the spline).
• Transform these points back to your original cordinate system.

If this is the way you are going I can work out the necessary formulas.

Answer 2

The most efficient algorithm that I've heard of is called Bezier clipping.

Here's a book chapter on curve and spline intersection (pdf).

Answer 3

Your best approach might be to break down your spline into individual line segments and test each line segment for intersection with the line. The spline may intersect the line in more than one point, so you'll also have to decide which one you're interested in.