De Boor's algorithm: Difference between revisions

Revision as of 08:00, 18 August 2017

Revision as of 05:35, 19 September 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]] and the classic publications<ref name="de_boor_paper"></ref> use a different notation.: Thethe B-spline is indexed as <math> B_{i,n}(x) </math> with <math>n = p + 1</math>.

== Local support ==