  We introduce an adaptive scattered data fitting scheme as extension of local
least squares approximations to hierarchical spline spaces. To efficiently deal
with non-trivial data configurations, the local solutions are described in
terms of (variable degree) polynomial approximations according not only to the
number of data points locally available, but also to the smallest singular
value of the local collocation matrices. These local approximations are
subsequently combined without the need of additional computations with the
construction of hierarchical quasi-interpolants described in terms of truncated
hierarchical B-splines. A selection of numerical experiments shows the
effectivity of our approach for the approximation of real scattered data sets
describing different terrain configurations.
