De Boor's algorithm: Difference between revisions

Revision as of 18:24, 30 November 2019

Revision as of 13:33, 16 April 2020

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

Let the index <math> k </math> define the knot interval that contains the position, <math> x \in [t_{k},t_{k+1}]) </math>. We can see in the recursion formula that only B-splines with <math> i = k-p, \dots, k </math> are non-zero for this knot interval. Thus, the sum is reduced to:

:<math> \mathbf{S}(x) = \sum_{i=k-p}^{k} \mathbf{c}_i B_{i,p}(x). </math>