C 1 Monotone Scattered Data Interpolation
A local C1 surface construction scheme is presented to preserve the shape of the monotone scattered data arranged over the triangular grid. Each boundary curve of the triangle is constructed by the rational cubic function and this rational function is also used for the side-vertex interpolation. The final surface patch is constructed by taking the convex combination of three side-vertex interpolants. For each triangular patch there are three boundary curves and three side vertex interpolant. Simple sufficient data dependent constraints are derived on the free parameters in the description of rational function to preserve the shape of monotone scattered data. The developed scheme is local, computationally economical and visually pleasing.