De Boor's algorithm: Difference between revisions

Revision as of 05:37, 19 September 2017

Revision as of 21:45, 8 November 2017

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Let <math> \mathbf{d}_{i,r} </math> be new control points with <math> \mathbf{d}_{i,0} := \mathbf{c}_{i} </math> for <math> i = k-p, \dots, k</math>. For <math> r = 1, \dots, p </math> the following recursion is applied:

:<math> \mathbf{d}_{i,r} = (1-\alpha_{i,r}) \mathbf{d}_{i-1,r-1} + \alpha_{i,r} \mathbf{d}_{i,kr-1}; \quad i=k-p+r,\dots,k </math>

:<math> \alpha_{i,r} = \frac{x-t_i}{t_{i+1+p-r}-t_i}.</math>