Monotony Preserving Scattered Data Interpolation Scheme Using Side-vertex Method

Abstract

This paper addresses the problem of monotone scattered data interpolation. An interpolation scheme is developed to interpolate the scattered data assembled over the triangular grid. The developed interpolation scheme utilizes a family of rational cubic function. The edges of each triangle are interpolated by the rational cubic function. The rational cubic function is also used to join vertices to their opposite edges. This practice provide three vertex boundary interpolating functions. Resultant rational triangular function is the convex combination of these vertex boundary interpolants. The developed rational interpolating scheme assures continuity at each vertex of triangle and along the boundaries of each triangle. Since the rational function has parameters in its definition, so these are inherited in rational triangular function. The constraints are developed on half of these parameters to preserve the shape of data while remaining are free for shape modification.