Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

The apolar bilinear form in geometric modeling

Author(s): Gert Vegter.
Journal: Math. Comp. 69 (2000), 691-720.
MSC (1991): Primary 41A15, 65D17; Secondary 65D07, 41A63
Posted: April 28, 1999
MathSciNet review: 1654006
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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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