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Blossom (functional)
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Blossom (functional) : ウィキペディア英語版
Blossom (functional)
In numerical analysis, a blossom is a functional that can be applied to any polynomial, but is mostly used for Bézier and spline curves and surfaces.
The blossom of a polynomial ''ƒ'', often denoted \mathcal(), is completely characterised by the three properties:
* It is a symmetric function of its arguments:
:: \mathcal()(u_1,\dots,u_d) = \mathcal()\big(\pi(u_1,\dots,u_d)\big),\,
: (where ''π'' is any permutation of its arguments).
* It is affine in each of its arguments:
:: \mathcal()(\alpha u + \beta v,\dots) = \alpha\mathcal()(u,\dots) + \beta\mathcal()(v,\dots),\text\alpha + \beta = 1.\,
* It satisfies the diagonal property:
:: \mathcal()(u,\dots,u) = f(u).\,
==References==

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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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