Scattered data interpolation subject to piecewise quadratic range restrictions (Q1815884)

The authors describe the construction of univariate and bivariate \(C^1\) interpolants to scattered data in the case where the range of the interpolant is restricted a priori by lower and upper obstacles given as piecewise quadratic functions. This is, indeed, a realistic assumption in many applications and the problem of nonnegative interpolation can be seen as a special case of this. In many important cases the resulting systems are shown to be solvable. The solutions are usually not unique; the selection of a visually pleasant one is then based on the minimization of a choice functional. For an implementation of the algorithm the reader is referred to the Diplomarbeit of the first author. However, the paper contains a graphical description of an interesting application.