**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

curvature adjusted spline'.

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

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