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
Canonical name	BernsteinPolynomial
Date of creation	2013-03-22 14:15:25
Last modified on	2013-03-22 14:15:25
Owner	stitch (17269)
Last modified by	stitch (17269)
Numerical id	9
Author	stitch (17269)
Entry type	Definition
Classification	msc 65D17
Synonym	Bernstein basis polynomials
Synonym	Bernstein basis functions