Talk:B-spline

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The definiton of B-spline is not correct:

1. Knots may repeat, i.e. t_i <= t_{i+1}, not t_i < t_{i+1} as article states.
2. S(t) domain is [0,1], but B-spline is defined in range [t_n, t_{m-n-1}] and thus additions are done across indexes i=0..m-n-1, not i=0..m.
3. Since knots may repeat, denominators appear in de Boor-Cox formula, i.e. t_{i+n}-t_i and t_{i+n+1} - t_{i+1} may eqaul zero. In such cases certain part of sum just disappear.
4. Count of control points is limited: n = m-k-1, where k is a degree of curves, and n is a max index of P.

And two notes:

1. The full name of Cox-de Boor formula is "Mansfield-de Boor-Cox".
2. B-spline is a shotening from "basis spline function", thus "basis B-spline" means "basis basis spline function" and it is quite redundant.

I am not native speaker, so I haven't touched the article. Someone, please consider my remarks.

[edit] Blending Function

What is the exact definition of a blending function?--SiriusB 08:18, 5 September 2005 (UTC)