# 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.
Title Bernstein polynomial BernsteinPolynomial 2013-03-22 14:15:25 2013-03-22 14:15:25 stitch (17269) stitch (17269) 9 stitch (17269) Definition msc 65D17 Bernstein basis polynomials Bernstein basis functions