  Recent work introduced a unified framework for steerable and directional
wavelets in two and three dimensions that ensures many desirable properties,
such as a multi-scale structure, fast transforms, and a flexible angular
localization. We show that, for an appropriate choice for the radial window
function, these wavelets also have closed form expressions for, among other
things, the spatial representation, the filter taps for the fast transform, and
the frame representation of the Laplace operator. The numerical practicality
and benefits of our work are demonstrated using signal estimation from
non-uniform, point-wise samples, as required for example in ray tracing, and
for reconstructing a signal over a lower-dimensional sub-manifold, with
applications for instance in medical imaging.
