  Many natural shapes have most of their characterizing features concentrated
over a few regions in space. For example, humans and animals have distinctive
head shapes, while inorganic objects like chairs and airplanes are made of
well-localized functional parts with specific geometric features. Often, these
features are strongly correlated -- a modification of facial traits in a
quadruped should induce changes to the body structure. However, in shape
modelling applications, these types of edits are among the hardest ones; they
require high precision, but also a global awareness of the entire shape. Even
in the deep learning era, obtaining manipulable representations that satisfy
such requirements is an open problem posing significant constraints. In this
work, we address this problem by defining a data-driven model upon a family of
linear operators (variants of the mesh Laplacian), whose spectra capture global
and local geometric properties of the shape at hand. Modifications to these
spectra are translated to semantically valid deformations of the corresponding
surface. By explicitly decoupling the global from the local surface features,
our pipeline allows to perform local edits while simultaneously maintaining a
global stylistic coherence. We empirically demonstrate how our learning-based
model generalizes to shape representations not seen at training time, and we
systematically analyze different choices of local operators over diverse shape
categories.
