  In this work, we explore the idea that effective generative models for point
clouds under the autoencoding framework must acknowledge the relationship
between a continuous surface, a discretized mesh, and a set of points sampled
from the surface. This view motivates a generative model that works by
progressively deforming a uniform sphere until it approximates the goal point
cloud. We review the underlying concepts leading to this conclusion from
computer graphics and topology in differential geometry, and model the
generation process as deformation via deep neural network parameterization.
Finally, we show that this view of the problem produces a model that can
generate quality meshes efficiently.
