In this Chapter, we exploit two main approximation methods to define the a THB-spline model: reweighted least-square (rWLS) approximation and the Quasi-Interpolation (QI) schemes. In particular, we first focus on two very well established classical methods: interpolation and weighted least squares, and extend the latter as an adaptive rWLS fitting scheme. Subsequently, we present a hierarchical QI scheme with THB-spline.