De Boor's algorithm: Difference between revisions

Content deleted Content added
Line 11:
 
== Outline of the algorithm==
Suppose we want to evaluate the spline curve for a parameter value <math> x \in [u_{\ell},u_{\ell+1}][ </math>.
We can express the curve as
 
Line 18:
<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>