De Boor's algorithm: Difference between revisions

Revision as of 03:10, 11 April 2004

Revision as of 22:23, 1 June 2004

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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

:<math> \vec{s}(x) = \sum_{i=-n}^{p-1} \vec{d}_i N_i^n(x), </math>

where ''N_iⁿ(x)'' are polynomials in x with coefficients depending on ''u₀, ..., u_p'' but not <math>\vec{d}_i</math>.

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:<math> \alpha_{k,i} = \frac{x-u_i}{u_{i+n+1-k}-u_i}. </math>

Then <math> \vec{s}(x) = \vec{d}_{\ell}^{[n]} </math>.

[[Category:Algorithms]]