Talk:De Boor's algorithm

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Untitled

In the definition of the 0-th degree B-spline basis functions, the closed interval between u[i] and u[i+1] should be replaced by the half-open interval between u[i] and u[i+1].

Expressed otherwise, the article presently gives the requirement that we should have u[i] <= x <= u[i+1] but this requirement should really be u[i] <= x < u[i+1].

I would make this change myself, but I do not know how to do this in MathML.

Rdfuhr (talk) 06:15, 14 June 2010 (UTC)[reply]

Why are n and p reversed?

I believe it is a fairly standard convention to have p be the degree of the curve and n either be the highest index (modus Peigl and Tiller), or the number of control points (highest index + 1).

Why is this convention reversed so that p is the number of control points and n is the degree?

CodieCodemonkey (talk) 08:52, 22 May 2012 (UTC)[reply]

Mistake with indexes?

I guess there is a mistake in the formula $N_{i}^{n}(x)$ . The simple example is a linear function $f(x)=x$ . We have knots $u=0..100$ and control inputs $d=0..100$ . Consider a first order spline: $n=1$ in point $x=12.5$ . The nonzero terms: $N_{11}^{1}=0.5$ and $N_{12}^{1}=0.5$ . Then the function value $s(12.5)=d_{11}*N_{11}^{1}+d_{12}*N_{12}^{1}=11.5$ , but it must be 12.5. I guess, the indexes should begin from 1.

95.140.92.35 (talk) 12:52, 20 December 2014 (UTC)Maxim[reply]