Weighted Combination Interpolation by Piecewise Cubic Polynomial on Triangulations

A new method for constructing polynomial interpolation surface on triangulations is given. Triangulating the given data points into triangle network, and the surface patch on each triangle is constructed by the weighted combination of three cubic patches, each of which interpolates the three vertices of the triangle and is C¹ continue on one edge respectively. All triangle patches are put together to form the whole surface with C¹ continuity, and the constructed triangular patch reproduces cubic polynomial surfaces. What´s more, a new method is proposed to estimate one order partial derivatives during the surface construction. Comparison examples are included.