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- W1599437273 abstract "The classical Curry-Schoenberg Theorem is generalized to the multivariate setting. It is shown that every C k -continuous piecewise polynomial F of degree n over an arbitrary triangulation T = of ℝ s can be written as a linear combination of the normalized multivariate B-splines over an appropriate knot sequence κ as constructed in [4], where every vertex of the given triangulation T appears as knot of multiplicity m = n – k. The coefficients c I,λ in the resulting representation are given as c I,λ = , where f I is the polar form of the restriction F I of F to the simplex Δ ( I ) = [ t i 0 ,…, t i s ]." @default.
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- W1599437273 date "1992-01-01" @default.
- W1599437273 modified "2023-09-26" @default.
- W1599437273 title "Representing Piecewise Polynomials as Linear Combinations of Multivariate B-Splines" @default.
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- W1599437273 doi "https://doi.org/10.1016/b978-0-12-460510-7.50047-1" @default.
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