C¹-Cubic Quasi-Interpolation Splines over a CT Refinement of a Type-1 Triangulation

C-1 continuous quasi-interpolating splines are constructed over Clough-Tocher refinement of a type-1 triangulation. Their Bernstein-Bezier coefficients are directly defined from the known values of the function to be approximated, so that a set of appropriate basis functions is not required. The resulting quasi-interpolation operators reproduce cubic polynomials. Some numerical tests are given in order to show the performance of the approximation scheme.