Shape-Preserving Rational Interpolation Scheme for Regular Surface Data

Rational shape-preserving interpolation schemes are developed for positive and monotone regular surface data. The data points are arranged over the rectangular grid. A Bézier like bivariate rational cubic function is constructed. This Bézier like bivariate rational interpolant involves eight free parameters in each rectangular patch. Data dependent constraints are developed on four of these free parameters to preserve the positive and monotone shape of regular surface data. The rest of the parameters are used for shape refinement. The scheme is further extended to more general constraints when data is bounded below by another surface and it desired that Bézier like bivariate rational interpolant must obey the aforesaid restriction.