Positivity-preserving scattered data interpolation scheme using the side-vertex method

A local surface interpolation scheme has been developed which interpolates and preserves the shape of the positive scattered data arranged over the triangular domain. The proposed interpolating surface has been constructed by using the side vertex method. A C1 piecewise rational cubic function with four parameters has been used for interpolation along each edge of a triangle and along line segments joining a vertex to the opposite edge. Simple sufficient data dependent constraints have been derived on the free parameters in the description of rational cubic function to ensure the shape of positive scattered data.