Invisible wrote:

> Then there is a set of recursively-defined "basis functions". The spline 
> itself is made by just multiplying each control point by a basis 
> function and adding all the products together. So the number of basis 
> functions controls the number of control points.

Alternatively, apparently there's a modification of de Casteljau's 
algorithm that draws B-splines instead of Bezier splines. It's called de 
Boor's algorithm.

Looking at it, it's hard to see what the difference is. (Wikipedia 
helpfully uses a completely different notation for the two articles.) It 
turns out that they both interpolate between the control points, but de 
Casteljau's algorithm does so uniformly, while de Boor's algorithm 
adjusts the parameterisation based on the knot vector.

Implementing this correctly is going to be amusing...

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