The author considers the problem of constructing for a given set of data \((x_i,f_i,f'_i,f''_i),i=0,\dots,n\), a \(C^2\) function \(s\) which takes at \(x_i\) the values \(f_i\), has the first and second derivatives equal to \(f'_i\) and \(f''_i\) and is shape preserving in the sense that it is comonotone (or coconvex) with the data in each subinterval \([x_i,x_{i+1}]\). As in her previous work [J. Comput. Appl. Math. 69, No. 1, 143-157 (1996; Zbl 0858.65007)] she represents the graph of \(s(x)\) as the image of a bidimensional parametric curve with cubic splines as components. It turns out that the tension parameters can always be chosen in such a way that comonotonicity (or coconvexity) is guaranteed. The method proposed is local: a change in the data at \(x_i\) only reflects in \([x_{i-1},x_{i+1}]\). When the data are taken from a monotone and/or convex \(C^3\) function \(f\), the order of approximation of the shape preserving interpolating function \(s\) is at least three. For data from a convex \(C^4\) function \(f\), interpolation provides a fourth order accurate \(s\) approximation to \(f\). Three numerical examples are given.