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In [[numerical analysis]], a '''blossom''' is a [[functional (mathematics)|functional]] that can be applied to any [[polynomial]], but is mostly used for [[Bézier curve|Bézier]] and [[Spline (mathematics)|spline]] curves and surfaces.

The blossom of a polynomial ''ƒ'', often denoted <math>\mathcal{B}[f],</math>  is completely characterised by the three properties:
* It is a symmetric function of its arguments:
:: <math>\mathcal{B}[f](u_1,\dots,u_d) = \mathcal{B}[f]\big(\pi(u_1,\dots,u_d)\big),\,</math>
: (where ''&pi;'' is any [[permutation]] of its arguments).
* It is affine in each of its arguments:
:: <math>\mathcal{B}[f](\alpha u + \beta v,\dots) = \alpha\mathcal{B}[f](u,\dots) + \beta\mathcal{B}[f](v,\dots),\text{ when }\alpha + \beta = 1.\,</math>
* It satisfies the diagonal property:
:: <math>\mathcal{B}[f](u,\dots,u) = f(u).\,</math>

==References==
*{{cite paper | author=Ramshaw, Lyle | title = Blossoming: A Connect-the-Dots Approach to Splines | publisher=Digital Systems Research Center | year=1987 | url=ftp://ftp.digital.com/pub/compaq/SRC/research-reports/abstracts/src-rr-019.html | accessdate=2006-06-28}}

*{{cite paper | author=Casteljau, Paul de Faget de | authorlink = Paul de Casteljau | title = POLynomials, POLar Forms, and InterPOLation | year = 1992 | editor= Schumaker et al. | book = Mathematical methods in computer aided geometric design II | publisher = Academic Press Professional, Inc.}}

*{{cite book | author=Farin, Gerald | title = Curves and Surfaces for CAGD: A Practical Guide | year = 2001 | publisher = Morgan Kaufmann | edition = fifth | isbn = 1-55860-737-4 }}

[[Category:Numerical analysis]]