Construction of 2D Explicit Cubic Quasi-Interpolating Splines in Bernstein-Bézier Form

The authors propose the construction of C1-cubic Hermite splines on a uniform three-direction triangulation, where the Bernstein-Bézier coefficients are determined by the values of the function and its gradient at the vertices of the triangulation. The resulting quasi-interpolation operator is exact on quadratic polynomials.