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:<math> \mathbf{S}(x) = \sum_{i=k-p}^{k} \mathbf{c}_i B_{i,p}(x). </math>
It follows from <math> i \geq 0 </math> that <math> k \geq p </math>. Similarly, we see in the recursion that the highest queried knot ___location is at index <math> k + 1 + p </math>. This means that any knot interval <math> [t_k,t_{k+1}) </math> which is actually used must have at least <math> p </math> additional knots before and after. In a computer program, this is typically achieved by repeating the first and last used knot ___location <math> p </math> times. For example, for <math> p = 3 </math> and real knot locations <math> (0, 1, 2) </math>, one would pad the knot vector to <math> (0,0,0,0,1,2,2,2,2) </math>.
== The algorithm ==
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