Shape-preserving surfaces with constraints on tension parameters

The C1 rational bi-cubic local interpolation schemes are presented for the shape preservation of convex, monotone and positive surface data. The shape of the surface is controlled locally with the help of eight tension parameters over each rectangular patch. Data dependent constraints are developed on half of the tension parameters to preserve the intrinsic shapes of the surface data. The remaining ones are unconstrained, thus free to be used to obtain the smoothest surface.