Computing intersections of planar spline curves using knot insertion

We present a new method for computing intersections of two parametric B-Spline curves. We use an intersection of the control polygons as an approximation for an intersection of the curves in combination with knot insertion. The resulting algorithm is asymptotically Newton-like, but without the need of a starting value. Like Newton’s method, it converges quadratically at transversal intersections, the analogue to simple roots. It is a generalization of an algorithm developed by two of the authors for computing zeros of spline functions.