Bernstein basis polynomials: Difference between revisions
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The <math>n + 1</math> [[wp:Bernstein_polynomial|''Bernstein basis polynomials'']] of degree <math>n</math> are defined as |
The <math>n + 1</math> [[wp:Bernstein_polynomial|''Bernstein basis polynomials'']] of degree <math>n</math> are defined as |
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:<math>b_{k,n}(t) = \binom{n}{k} t^{k} \left( 1 - t \right)^{n - k},\quad k = 0,\ldots,n</math> |
:<math>b_{k,n}(t) = \binom{n}{k} t^{k} \left( 1 - t \right)^{n - k},\quad k = 0,\ldots,n</math> |
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Any polynomial can written as a linear combination of such Bernstein basis polynomials. Let us call the coefficients in such linear combinations ''Bernstein coefficients''. |
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''. |
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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. |
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. |
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