  We introduce NeuralMLS, a space-based deformation technique, guided by a set
of displaced control points. We leverage the power of neural networks to inject
the underlying shape geometry into the deformation parameters. The goal of our
technique is to enable a realistic and intuitive shape deformation. Our method
is built upon moving least-squares (MLS), since it minimizes a weighted sum of
the given control point displacements. Traditionally, the influence of each
control point on every point in space (i.e., the weighting function) is defined
using inverse distance heuristics. In this work, we opt to learn the weighting
function, by training a neural network on the control points from a single
input shape, and exploit the innate smoothness of neural networks. Our
geometry-aware control point deformation is agnostic to the surface
representation and quality; it can be applied to point clouds or meshes,
including non-manifold and disconnected surface soups. We show that our
technique facilitates intuitive piecewise smooth deformations, which are well
suited for manufactured objects. We show the advantages of our approach
compared to existing surface and space-based deformation techniques, both
quantitatively and qualitatively.
