C1-Quartic Butterfly-Spline Interpolation on Type-1 Triangulations

In this paper, we construct and analyse C1 quartic interpolating splines on type-1 triangulations, approximating regularly distributed data. This is achieved by defining the associated Bernstein-Bézier coefficients from point values of the function to be approximated in such a way that C1 regularity is obtained for enough regular functions as well as the optimal order of approximation. We construct such interpolating splines by combining a quasi-interpolating spline with one step of an interpolatory subdivision scheme. Numerical tests confirming the theoretical results are provided.