--ZusammenfassungPowelI-Sabin Splines in Range Restricted Interpolation of Scattered Data. The construction of range restricted bivariate C 1 interpolants to scattered data is considered. In particular, we deal with quadratic spline interpolation on a Powell-Sabin refinement of a triangulation of the data sites subject to piecewise constant lower and upper bounds on the values of the interpolant. The derived sufficient conditions for the fulfillment of the range restrictions result in a solvable system of linear inequalities for the gradients as parameters, which is separated with respect to the data sites. Since there exists an infinite number of spline interpolants meeting the constraints, the selection of a visually pleasant solution is based on the minimum norm modification of a suitable initial interpolant or on the minimization of the thin plate functional. While the first proposal reduces to the solution of independent local quadratic programs, the second proposal results in a global quadratic optimization problem. AMS Subject Classifications: 65D05, 65D07, 41A15Key words: Shape preserving interpolation of scattered data, range restrictions, Powell-Sabin splines, minimum norm modification, thin plate functional. Powell-Sabin-Splines bei der restringierten Interpolation unregelm[iflig verteilter

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