I have a B-Spline curve. I have all the knots, and the x,y coordinates of the Control Points.
I need to convert the B-Spline curve into Bezier curves.
My end goal is to be able to draw the shape on an html5 canvas element. The B-Spline is coming from a dxf file which doesn't support Beziers, while a canvas only supports Beziers.
I've found several articles which attempt to explain the process, however they are quite a bit over my head and really seem to be very theory intensive. I really need an example or step by step help.
Here's what I've found:
(Explains B-Splines),
(Convert B-Splines),
I can share my Nodes or Control Points if that would be useful. If someone would point me to a step-by-step procedure or help me with some psuedo(or actual)code, I would be so grateful.
Best Answer
What you need is something called "Boehm's algorithm" (after its originator, Wolfgang Boehm). It has a simple geometric interpretation, and drawing a few pictures should make it clear. There is a pretty good explanation (with pictures) in this document.
The algorithm is based on a process called "knot insertion". You keep inserting knots into the b-spline curve until each knot has multiplicity 3. Then, the b-spline control points of this refined curve give you the Bezier control points of its segments.
So, if you're writing code to do this, one approach is to write a knot insertion function first, and then call it repeatedly.
There is knot insertion code here.