A family of smooth quasi-interpolants defined over Powell-Sabin triangulations
نویسنده
چکیده
We investigate the construction of local quasi-interpolation schemes for a family of bivariate spline functions with smoothness r ≥ 1 and polynomial degree 3r−1. These splines are defined on triangulations with Powell-Sabin refinement, and they can be represented in terms of locally supported basis functions which form a convex partition of unity. Using the blossoming technique, we first derive a Marsden’s identity representing polynomials of degree 3r − 1 in such a spline form. Then we present a simple approach to construct various families of smooth quasi-interpolation schemes involving values and/or derivatives of a given function.
منابع مشابه
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