Piecewise Polynomials on Polyhedral Complexes
نویسنده
چکیده
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, in [1] Alfeld and Schumaker give 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.
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