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Bernstein polynomial

(polynomial form capable of producing arbitrary shapes)

Bernstein polynomials constitute a family of polynomials capable of approximating arbitrary function curves, sometimes used as basis functions in modeling. In the manner of a Fourier series expansion or Taylor series expansion, they offer a way to build a polynomial approximation of an arbitrary curve over a given finite interval. One use is the production of arbitrary statistical distributions by/for nonparametric models using Bayesian statistics. I imagine they offer a means to produce efficient expressions for calculating close approximations of functions, which can be helpful in computer graphics, particularly real-time computer animation, and also in increasing the efficiency of computationally-intensive numerical models.

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