Bernstein basis polynomials: Difference between revisions
m
Clarify what sort of polynomial we care can be cast into Bernstein form.
m (Fixed a neglected close-bold.) |
m (Clarify what sort of polynomial we care can be cast into Bernstein form.) |
||
Line 2:
The <math>n + 1</math> [[wp:Bernstein_polynomial|''Bernstein basis polynomials'']] of degree <math>n</math> are defined as
:<math>b_{k,n}(t) = \binom{n}{k} t^{k} \left( 1 - t \right)^{n - k},\quad k = 0,\ldots,n</math>
Any real polynomial can written as a linear combination of such Bernstein basis polynomials. Let us call the coefficients in such linear combinations ''Bernstein coefficients''.
The goal of this task is to write subprograms for working with degree-2 and degree-3 Bernstein coefficients. A programmer is likely to have to deal with such representations. For example, [[wp:OpenType|OpenType fonts]] store glyph outline data as as either degree-2 or degree-3 Bernstein coefficients.
| |||