Surface interpolation using partial differentiation equation with positivity preserving cubic said-ball curves boundary condition

In this paper, the sufficient condition for the positive preservation of boundary curves for each edges of bicubic rectangular Said-Ball patches will be discussed. With the use of polynomial solution of fourth order linear PDEs, these curves are defined on rectangular grid for the purpose of enhancing the positivity preservation of the interpolating surface. Through an independent adjustment of the lower boundary of edge Said-Ball ordinates, a sufficient condition on boundary curves for individual edge of bicubic rectangular Said-Ball patches is derived. By employing two well recognized test functions, finding reveals that the approach proposed is appropriate with regard to positive preservation of boundary curves and that there is improvement in the positive preservation of the whole interpolating surfaces.