The apolar bilinear form in geometric modeling

Vegter, Gert

doi:10.1090/S0025-5718-99-01144-8

The apolar bilinear form in geometric modeling
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Math. Comp. 69 (2000), 691-720 Request permission

Abstract:

Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a fixed degree, already known in 19th century invariant theory. Using a generalized version of this inner product, we derive in a straightforward way some of the recent results in CAGD, like Marsden’s identity, the expression for the de Boor-Fix functionals, and recursion schemes for the computation of B-patches and their derivatives.

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