Bernstein polynomial
The Bernstein polynomials of $n$ are defined by
$${B}_{i}^{n}(t)=\left(\genfrac{}{}{0pt}{}{n}{i}\right){t}^{i}{(1-t)}^{n-i}\mathit{\hspace{1em}\hspace{1em}}i=0,1,2,\mathrm{\dots},n$$ |
where $\left(\genfrac{}{}{0pt}{}{n}{i}\right)$ 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 |