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De Boor algorithm is an algorithm which, given ''u<sub>0</sub>, ..., u<sub>p-1</sub>'' and <math>\vec{d}_0, \vec{d}_1, \dots, \vec{d}_{p-1}</math>, finds the value of spline curve <math>\vec{s}(x)</math> at a point ''x''. It uses [[Big O notation|O]](n<sup>2</sup>) operations. Notice that the running time of the algorithm depends only on degree ''n'' and not on the number of points ''p''.
== Outline of the
Suppose we want to evaluate the spline curve for a parameter value <math> x \in [u_{\ell},u_{\ell+1}) </math>.
We can express the curve as
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