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 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:
References[]
- Ramshaw, Lyle (1987). "Blossoming: A Connect-the-Dots Approach to Splines". Digital Systems Research Center. Retrieved 2019-04-19. Cite journal requires
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(help) - Ramshaw, Lyle (1989). "Blossoms are polar forms". Digital Systems Research Center. Retrieved 2019-04-19. Cite journal requires
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(help) - Casteljau, Paul de Faget de (1992). "POLynomials, POLar Forms, and InterPOLation". In Larry L. Schumaker; Tom Lyche (eds.). 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.
Categories:
- Numerical analysis
- Mathematical analysis stubs