Blossom (functional)

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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 is completely characterised by the three properties:

  • It is a symmetric function of its arguments:
(where π is any permutation of its arguments).
  • It is affine in each of its arguments:
  • It satisfies the diagonal property:


  • Ramshaw, Lyle (1987). "Blossoming: A Connect-the-Dots Approach to Splines". Digital Systems Research Center. Retrieved 2006-06-28.[dead link]
  • Casteljau, Paul de Faget de (1992). "POLynomials, POLar Forms, and InterPOLation". In Larry L. Schumaker; Tom Lyche. Mathematical methods in computer aided geometric design II. Academic Press Professional, Inc. ISBN 978-0-12-460510-7.
  • Farin, Gerald (2001). Curves and Surfaces for CAGD: A Practical Guide (fifth ed.). Morgan Kaufmann. ISBN 1-55860-737-4.