Bernstein polynomial

The Bernstein polynomials of $n$ are defined by

B_{i}^{n}(t)={n\\choose i}t^{i}(1-t)^{n-i}\\quad\\quad i=0,1,2,\\dots,n

where ${n\\choose i}$ is the binomial coefficient.

Bernstein polynomials are used extensively in interpolation theory and in computer graphics. They can be computed efficiently using the de Casteljau’s algorithm.

References

1 Gerald Farin, Curves and Surfaces for CAGD, A Practical Guide, 5th edition,Academic Press, 2002.

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