|
In the mathematical field of numerical analysis, a Bernstein polynomial, named after Sergei Natanovich Bernstein, is a polynomial in the Bernstein form, that is a linear combination of Bernstein basis polynomials. A numerically stable way to evaluate polynomials in Bernstein form is de Casteljau's algorithm. Polynomials in Bernstein form were first used by Bernstein in a constructive proof for the Stone–Weierstrass approximation theorem. With the advent of computer graphics, Bernstein polynomials, restricted to the interval (), became important in the form of Bézier curves. ==Definition== The ''n'' + 1 Bernstein basis polynomials of degree ''n'' are defined as : where is a binomial coefficient. The Bernstein basis polynomials of degree ''n'' form a basis for the vector space Π''n'' of polynomials of degree at most ''n''. A linear combination of Bernstein basis polynomials : is called a Bernstein polynomial or polynomial in Bernstein form of degree ''n''. The coefficients are called Bernstein coefficients or Bézier coefficients. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bernstein polynomial」の詳細全文を読む スポンサード リンク
|