Bezier basis

For shape design purposes it is usually far more convenient to use a basis where the basis functions sum to f. All the coefficients then transform as points, and we call them control points. For polynomials this can be achieved by using the Bezier basis, which is a special case of the B-spline basis which will be encountered shortly. 

Higher degree B-splines can be constructed explicitly (using, for example, the Bezier basis for each span of the function) by recursion on degree, applying the same simple recipe ... 

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