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In [[mathematics]], '''De Boor algorithm''' is an algorithm for evaluating [[spline]] curves.
The general setting is as follows. We would like to construct a curve passing through a sequence of points <math>\vec{d}_0, \vec{d}_1, \dots, \vec{d}_p</math>. The curve will be specified as a function <math> \vec{s}(x)</math> of one parameter ''x''. To pass through the sequence of points, the curve must satisfy <math>\vec{s}(u_0)=\vec{d}_0, \dots,
\vec{s}(u_p)=\vec{d}_p</math>. We assume that ''u<sub>0</sub>, ..., u<sub>p</sub>'' are given to us along with <math>\vec{d}_0, \vec{d}_1, \dots, \vec{d}_p</math>.
One approach to solving this problem is by [[spline]]s. A spline is a curve that is piecewise ''n<sup>th</sup>'' degree polynomial. This means that, on any interval ''[u<sub>i</sub>,u<sub>i+1</sub>)'', the curve must be equal to a polynomial of degree at most ''n''. It may be equal to a different polynomials on different intervals. The polynomials must be ''synchronized'': when the polynomials from intervals ''[u<sub>i-1</sub>,u<sub>i</sub>)'' and ''[u<sub>i</sub>,u<sub>i+1</sub>)'' meet at the point ''u<sub>i</sub>'', they must have the same value at this point and their derivatives must be equal (to ensure that the curve is smooth).
== Goal of the algorithm==
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