Gridded Data Interpolation with Restrictions on the First Order Derivatives

This paper is concerned with restricted interpolation of data sets given on rectangular grids using biquadratic C 1 and biquartic C 2 splines on refined grids. In extension of monotonicity preserving constraints, we consider piecewise constant lower and upper bounds for the first partial derivatives. Utilizing the corresponding univariate results as well as the tensor product structure, sufficient conditions for fulfilling the considered restrictions are constructed. Furthermore, the solvability of the arising inequalities can always be assured for strictly compatible data when placing the additional knots suitably.