  Generative models that produce point clouds have emerged as a powerful tool
to represent 3D surfaces, and the best current ones rely on learning an
ensemble of parametric representations. Unfortunately, they offer no control
over the deformations of the surface patches that form the ensemble and thus
fail to prevent them from either overlapping or collapsing into single points
or lines. As a consequence, computing shape properties such as surface normals
and curvatures becomes difficult and unreliable.
  In this paper, we show that we can exploit the inherent differentiability of
deep networks to leverage differential surface properties during training so as
to prevent patch collapse and strongly reduce patch overlap. Furthermore, this
lets us reliably compute quantities such as surface normals and curvatures. We
will demonstrate on several tasks that this yields more accurate surface
reconstructions than the state-of-the-art methods in terms of normals
estimation and amount of collapsed and overlapped patches.
