  We present a new step in our systematic effort to develop self-consistent
dynamical models with a finite radial extent. The focus is on models with
simple analytical density profiles allowing for analytical calculations of many
dynamical properties. In this paper, we introduce a family of models, termed
Wendland models, based on compactly supported radial basis functions. The
family of models is characterised by a parameter $k$ that controls the
smoothness of the transition at the truncation radius. In the limit
$k\to\infty$, the Wendland model reduces to a non-truncated model with a
Gaussian density profile. For each Wendland model, the density, mass and
gravitational potential are simple truncated polynomial functions of radius.
Via the SpheCow tool we demonstrate that all Wendland models can be supported
by isotropic distribution functions. Surprisingly, the isotropic distribution
function exhibits varied behaviour across different Wendland models.
Additionally, each model can be supported by a continuum of Osipkov--Merritt
orbital structures, ranging from radially anisotropic to completely tangential
at the truncation radius. To the best of our knowledge, the Wendland models
presented here are the first family of models accommodating both radial and
tangential Osipkov--Merritt distribution functions. Using linear superposition,
these models can easily be combined to generate Wendland models with even more
diverse orbital structures. While the Wendland models are not fully
representative of real dynamical systems due to their Gaussian-like density
profile, this study lays important groundwork for constructing more realistic
models with truncated density profiles that can be supported by a range of
orbital structures.
