De Boor's algorithm: Difference between revisions

Revision as of 18:11, 21 October 2010

Revision as of 06:01, 22 December 2010

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:<math> \mathbf{s}(x) = \sum_{i=0}^{p-1} \mathbf{d}_i N_i^n(x) , </math>

where<ref>http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-basis.html</ref>

<math>N_i^n(x)=\frac{x-u_i}{u_{i+n}-u_i}N_i^{n-1}(x) -+ \frac{u_{i+n+1}-x}{u_{i+n+1}-u_{i+1}}N_{i+1}^{n-1}(x) ,</math>

and

<math>N_i^0(x)=\left\{\begin{matrix} 1, & \mbox{if }x \in [u_{i},u_{i+1}] \\ 0, & \mbox{otherwise } \end{matrix}\right.</math>