C1C1 positive scattered data interpolation

A local C1C1 surface construction scheme is presented to preserve the shape of positive scattered data arranged over a triangular grid. Each boundary curve of the triangle is constructed by a rational cubic function with two free parameters, 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 interpolants. Simple sufficient data dependent constraints are derived on these free parameters to preserve the shape of the positive scattered data. The developed scheme is not only local and computationally economical but visually pleasing as well.