De Boor's algorithm: Difference between revisions

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== Introduction ==

A general introduction to B-splines is given in the [[B-spline|main article]]. Here we discuss de Boor's algorithm, an efficient and numerically stable scheme to evaluate a spline curve <math> \mathbf{S}(x) </math> at position <math> x </math>. The curve is buildbuilt from a sum of B-spline functions <math> B_{i,p}(x) </math> multiplied with potentially vector-valued constants <math> \mathbf{c}_i </math>, called control points,

:<math> \mathbf{S}(x) = \sum_i \mathbf{c}_i B_{i,p}(x). </math>