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- TERRY MCDONALD
- 2008

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… (More)

Splines are piecewise polynomial functions of a given order of smoothness r on a triangulated region ∆ (or polyhedrally subdivided region) of R d. The set of splines of degree at most k forms a vector space C r k (∆). Moreover, a nice way to study C r k (∆) is to embed ∆ in R d+1 , and form the cone ∆ of ∆ with the origin. It turns out that the set of… (More)

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