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Bernstein polynomial
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(Definition)
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The Bernstein polynomials of degree  are defined by
where
 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.
- 1
- Gerald Farin, Curves and Surfaces for CAGD, A Practical Guide, 5th edition, Academic Press, 2002.
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"Bernstein polynomial" is owned by stitch. [ full author list (3) | owner history (2) ]
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(view preamble)
| Other names: |
Bernstein basis polynomials, Bernstein basis functions |
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Cross-references: algorithm, theory, interpolation, binomial coefficient
There are 3 references to this entry.
This is version 6 of Bernstein polynomial, born on 2004-03-14, modified 2007-08-27.
Object id is 5705, canonical name is BernsteinPolynomial.
Accessed 5341 times total.
Classification:
| AMS MSC: | 65D17 (Numerical analysis :: Numerical approximation and computational geometry :: Computer aided design ) |
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Pending Errata and Addenda
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![\includegraphics[scale=.5]{bp}](http://images.planetmath.org:8080/cache/objects/5705/l2h/img4.png "\includegraphics[scale=.5]{bp}")