Scattered data interpolation applying rational quadratic C-1 splines on refined triangulations

This paper is concerned with bivariate scattered data interpolation. It is assumed that an admissible triangulation of the data sites has been constru cted which then is refined in the sense of Powell and Sabin. The aim is to show that a special class of rational quadratic C-1 splines exists which al lows the Hermite interpolation problem with given functions values and grad ients to be uniquely solvable. The proof is essentially based on Heindl's C -1 condition which is valid also for the present spline class. The occurrin g tension or rationality parameters may be used to meet further requirement s; if the tension parameters increase the rational quadratic interpolants t end, at least on the interior of the triangles, to piecewise linear spline interpolating the function values.