De Boor's algorithm: Difference between revisions

Revision as of 15:11, 19 March 2004

Revision as of 15:13, 19 March 2004

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Due to the spline locality property, we can write

:<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 controlpoints <math> \vec{d}_{\ell-n},\vec{d}_{\ell-n+1},\vec{d}_{\ell} </math>; the other control points have no influence. The goal of thede boredBoor's algorithm is to evaluate <math> \vec{s}(x) </math> efficiently.

== The algorithm ==