De Boor's algorithm: Difference between revisions

Revision as of 10:19, 30 November 2008

Revision as of 04:35, 4 March 2009

Line 23:

Due to the spline locality property,

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

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

== The algorithm ==