# 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)

Done. --TN (talk) 08:53, 4 August 2017 (UTC)

## 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)

In the introduction, there is some unclarity whether the autor is talking about 'control points' or 'internal knots'. Control points do not (neccessarily) lie on the b-spline curve. The introduction states that the curve should try to satisfy ${\displaystyle \mathbf {s} (u_{0})=\mathbf {d} _{0},\dots ,\mathbf {s} (u_{p-1})=\mathbf {d} _{p-1}}$, which would be valid if ${\displaystyle \mathbf {d} _{i}}$ were the knot points / internal knots, but not for the control points! Might be that I misunderstood the meaning, but it's not written very clearly. Timitry (talk) 13:20, 11 July 2016 (UTC)
The formulas in the "Outline of the algorithm" are wrong. I've tried to correct them. That attempt lead me to the impression that the complete article needs a re-write. I don't have the time for that right now. (Not in the next few month either.) The size of the knot sequence is wrong. This causes wrong indexes in the recursive formula (i.e., some undefined knots ${\displaystyle u_{i}}$ are used in the recursive formula). If ${\displaystyle p-2}$ is the number of inner knots and ${\displaystyle n}$ is the spline degree then the spline has ${\displaystyle p+n-1}$ degrees of freedom. (The first interval has ${\displaystyle n+1}$ dofs and each of the inner ${\displaystyle p-2}$ knots implies one additional dof.) For De-Boor's algorithm in its original form ${\displaystyle p+2n}$ knots are required but ${\displaystyle u}$ has only ${\displaystyle p}$ elements.
Maybe, I misinterpreted the meaning of ${\displaystyle p}$. If ${\displaystyle p}$ is the number of spline dofs as the first formula actually suggests. Then the number of knots should be ${\displaystyle p+n+1}$. That means the formulas in Section "Outline of the algorithm" remain wrong nevertheless. --TN (talk) 11:04, 4 August 2017 (UTC)