In this paper a C2 interpolation scheme on a triangle is presented. The interpolant assumes given values and derivatives of orders up to 2 at the vertices of the triangle. It is made up of partial interpolants blended with weight functions. Any partial interpolant with respect to a vertex is a piecewise quintic defined on a split of the triangle and interpolates the data at the vertex and on the two sides sharing the vertex, while the corresponding weight function is a rational polynomial in the barycentric coordinates. The resulted interpolant is a piecewise rational polynomials. By using the Bernstein-Bezier representation of polynomials, the interpolant is easy to describe and evaluate.
