A Shepard-like Hermite interpolation operator with fourth approximation order

From a first order Hermite interpolant on a triangle written in terms of barycentric coordinates, a Shepard-like interpolation is defined. It achieves fourth order of approximation. Its performance is checked by considering well-known test functions as well different Delaunay triangulations. The novel operator is compared to a Shepard-type operator and to a Hermite cubic interpolant over a Powell–Sabin partition.