$$\hbox {GC}^{1}$$ GC 1 Shape-Preserving Trigonometric Surfaces

Abstract

A $$GC^{1}$$GC1 bi-quadratic trigonometric interpolation scheme with four free parameters in each rectangular patch is developed. The free parameters are constrained to avoid unnecessary oscillations, resulting in smooth positive and monotone surfaces for the positive and monotone 3D data. The formulated schemes are local and the degree of the interpolant is unique over the whole domain.