Cross-polarized wave generation

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 $\mathcal{ℬ}[f],$ is completely characterised by the three properties:

• It is a symmetric function of its arguments:

$\mathcal{ℬ}[f](u_1,\dots ,u_d)=\mathcal{ℬ}[f](\pi (u_1,\dots ,u_d)),$

(where π is any permutation of its arguments).

• It is affine in each of its arguments:

$\mathcal{ℬ}[f](\alpha u+\beta v,\dots )=\alpha \mathcal{ℬ}[f](u,\dots )+\beta \mathcal{ℬ}[f](v,\dots ),\text{ when }\alpha +\beta =1.$

• It satisfies the diagonal property:

$\mathcal{ℬ}[f](u,\dots ,u)=f(u).$

References

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