Given scattered data \(\{x_j,f_j\}\), the authors investigate some representations in terms of the radial function \(\varphi_j= [c^2+ |x-x_j|^2]^{1/2}\) and, for constant \(x_{j+1}-x_j=h\), the symmetric difference \(\psi_i=(\varphi_{i+1}- 2\varphi_i+\varphi_{i-1})/2h\). The coefficients of the approximating functions are divided differences. For two such formulas, the authors prove that they are shape preserving (i.e., positive, monotone, convex) and, for the second of the formulas, that the limit in approximation of a \(C^1\)-function \(f\) is itself \(C^1\).