![]() """ d = for j in range ( 0, p + 1 )] for r in range ( 1, p + 1 ): for j in range ( p, r - 1, - 1 ): alpha = ( x - t ) / ( t - t ) d = ( 1.0 - alpha ) * d + alpha * d return d See also t: Array of knot positions, needs to be padded as described above. Arguments - k: Index of knot interval that contains x. The following code in the Python programming language is a naive implementation of the optimized algorithm.ĭef deBoor ( k : int, x : int, t, c, p : int ): """Evaluates S(x). Here we discuss de Boor's algorithm, an efficient and numerically stable scheme to evaluate a spline curve S ( x ). Introduction Ī general introduction to B-splines is given in the main article. Simplified, potentially faster variants of the de Boor algorithm have been created but they suffer from comparatively lower stability. It is a generalization of de Casteljau's algorithm for Bézier curves. In the mathematical subfield of numerical analysis de Boor's algorithm is a polynomial-time and numerically stable algorithm for evaluating spline curves in B-spline form.
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