comp.graphics.algorithms

Subject: Re: b-spline problem

You're saying:

'The B-spline need only pass through the points (x0 = -2, 0),
(x2 = 0, 1), (x4 = 2, 0). (3 equations) .'
Probably you mean: at x0=-1, x2=0, x4=2.

In this case we should have indeed the choice of given slopes
AND curvatures at both ends (two degrees of freedom are set free
because it's not expected that the curve hits the points at x1=-1
and x3=+1 .

But your case is somewhat unusual: normally the curve should
hit the points at x0,x1,x2 and x3 and then we can choose EITHER
the slopes at the ends OR the curvatures at the ends (reference
at end).

If the end point slopes are given, then it's called 'Clamped spline'.
If the end point curvatures are zero, then it's called 'Natural
spline'.
If the end point curvatures are given, then it's called 'End-point

I don't find a bug in your concept. I'm posting only because nobody
else responds.

The explanations and the nomenclature are based on 'Numerical
Methods Using MatLab' by John H. Mathews and Kurtis D.Fink.

Best regards --Gernot Hoffmann