Splines over triangulation are a fundamental tool in finite element analysis (FEM), due to their ability to perform local refinements and accurately represent complex geometries. An important example is the \(C^1\) quadratic splines on the Powell-Sabin (PS) 6-split triangulations. This spline space is characterized by specifying discrete values and first derivative values at the vertices of the triangulation on which it is defined. However, a common challenge arises in many applications where only functional evaluations are known at equally spaced nodes, making the direct application of the Powell-Sabin finite element method impractical. To address this limitation in this setting, we present a novel technique for approximating derivative values at the set of vertices, essential for effectively defining the Powell-Sabin finite element. The idea of this technique lies in leveraging the provided functional evaluations and approximating the partial derivatives at the data points using an interpolation-regression operator.