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- W2022932236 abstract "For a d-dimensional polyhedral complex P, the dimension of the space of piecewise polynomial functions (splines) on P of smoothness r and degree k is given, for k sufficiently large, by a polynomial f(P,r,k) of degree d. When d=2 and P is simplicial, Alfeld and Schumaker determined a formula for all three coefficients of f. However, in the polyhedral case, no formula is known. Using localization techniques and specialized dual graphs associated to codimension--2 linear spaces, we obtain the first three coefficients of f(P,r,k), giving a complete answer when d=2." @default.
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- W2022932236 date "2009-01-01" @default.
- W2022932236 modified "2023-09-26" @default.
- W2022932236 title "Piecewise polynomials on polyhedral complexes" @default.
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- W2022932236 doi "https://doi.org/10.1016/j.aam.2008.06.001" @default.
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