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Calculating and Plotting B-Spline Basis Functions

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Let be a nondecreasing sequence of real numbers, that is, , . The are called knots and is the knot vector. The B-spline basis function of degree (or order ), denoted by , is defined as

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and for , as

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This Demonstration assumes the knots are in order to calculate and plot the .

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Contributed by: Shutao Tang (November 2014)
(Northwestern Polytechnical University, Xi'an City, China)
Open content licensed under CC BY-NC-SA

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Details

For drawing the schematic diagram of the algorithm, see [2].

References

[1] L. Piegl and W. Tiller, The NURBS Book, 2nd ed., Berlin: Springer-Verlag, 1997 pp. 50–51.

[2] ShutaoTang. "Drawing the Schematic Diagram of Algorithm." Mathematica Stack Exchange. (Oct 18, 2014) mathematica.stackexchange.com/questions/63471/drawing-the-schematic-diagram-of-algorithm.

[3] Michael E2. Answer to "How to Deal with the Condition in B-Spline Basis Function?" Mathematica Stack Exchange. (Oct 15, 2014) mathematica.stackexchange.com/questions/63192/how-to-deal-with-the-condition-u-i-u-i1-in-b-spline-basis-function.

[4] Mr.Wizard. Answer to "A Problem about Sorting Final Result." Mathematica Stack Exchange. (Oct 18, 2014) mathematica.stackexchange.com/questions/63468/a-problem-about-sorting-final-result.

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