De Boor's algorithm: Difference between revisions

Revision as of 21:51, 13 August 2006

Revision as of 20:16, 13 December 2006

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Due to the spline locality property,

:<math> \vec{s}(x) = \sum_{i=\ell-n}^{\ell} \vec{d}_i N_i^n(x) </math>

So the value <math>\vec{s}(x)</math> is determined by the controlpointscontrol points <math> \vec{d}_{\ell-n},\vec{d}_{\ell-n+1},\dots,\vec{d}_{\ell} </math>; the other control points <math>\vec{d}_i</math> have no influence. de Boor's algorithm, described in the next section, is a procedure which efficiently evaluates the expression for <math> \vec{s}(x) </math>.

== The algorithm ==