ABSTRACT
In this paper, we are concerned with new direct methods for positivity preserv ing interpolation of gridded data. The idea is to consider particular rational splines defined on the grids introduced by the data. It is of importance that the smoothness conditions do not depend on the occurring rationality pa rameters. Therefore, these quantities can be used exclusively for meeting the positivity constraints. The resulting procedures are elementary. In the uni variate case they are even local. Of course, the interpolants obtained in this way may be improved by applying more expensive methods, e.g., by curvature minimizing methods.
