De Boor's algorithm: Difference between revisions

Revision as of 12:51, 12 August 2017

Revision as of 07:29, 18 August 2017

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

B-splines of order <math> p + 1 </math> are connected piece-wise polynomial functions of degree <math> p </math> defined over a grid of knots <math> {t_0, \dots, t_i, \dots, t_m} </math> (we always use zero-based indices in the following). De Boor's algorithm uses [[Big O notation|O]](p²) + [[Big O notation|O]](p) operations to evaluate the spline curve. Note: the [[B-spline|main article about B-splines]] usesand the classic publications<mathref>C. nde Boor [1971], "Subroutine package for calculating with B-splines", Techn.Rep. LA-4728-MS, Los Alamos Sci.Lab, Los Alamos NM; p. 109, 121.</mathref> foruse thea different notation. The order of the B-spline is called <math> n </math> with <math>n = p + 1</math>.

== Local support ==