De Boor's algorithm: Difference between revisions

Revision as of 04:12, 15 November 2021

Revision as of 18:10, 22 February 2022

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B-splines have local support, meaning that the polynomials are positive only in a finite ___domain and zero elsewhere. The Cox-de Boor recursion formula<ref>C. de Boor, p. 90</ref> shows this:

:<math>B_{i,0}(x) := \left\{

\begin{matrixcases}

1 & \mathrmtext{if } \quad t_i \leq x < t_{i+1} \\

0 & \mathrmtext{otherwise}

\end{matrixcases}

\right.

</math>