Gridded Data Interpolation with Restrictions on the First Order Derivatives

Interpolation with tensor product splines subject to derivative constraints

“…Based on the nonnegativity lemma [l] the following Proposition can be established. See [3] and the references therein. P r o p o s i t i o n 2.…”

“…This can be done by applying the technique from the preceding paper [3]. In [3] the values p i j = r,,j, qi,j = g i , j , Ti,j = 0 are used in order to construct refinements assuring the existence of restricted biquadratic C' interpolants. In general, the present choice of the mixed second derivatives leads to visualized more pleasant splines.…”

Speed limit quasi splines and their application to interpolation with bounded first order derivative

“…Schmidt et al . have reported extensive work on interpolation subject to upper and lower bounds. In a series of papers, they consider different types of bounds and offer solutions to the problem using various types of spline families.…”

“…In , generalizations of these univariate methods are suggested, for performing bivariate interpolation over a rectangular grid subject to bounded partial derivatives. In , an algorithm to produce a cubic C 2 spline is suggested.…”

“…Throughout their work, Schmidt et al . assume a certain ‘compatibility condition’, which appears to be somehow restrictive, in the sense that there are cases where a smooth solution exists, but the ‘compatibility condition’ is not satisfied. The basic procedures suggested by Schmidt et al .…”