  Previous approaches to generate shapes in a 3D setting train a GAN on the
latent space of an autoencoder (AE). Even though this produces convincing
results, it has two major shortcomings. As the GAN is limited to reproduce the
dataset the AE was trained on, we cannot reuse a trained AE for novel data.
Furthermore, it is difficult to add spatial supervision into the generation
process, as the AE only gives us a global representation. To remedy these
issues, we propose to train the GAN on grids (i.e. each cell covers a part of a
shape). In this representation each cell is equipped with a latent vector
provided by an AE. This localized representation enables more expressiveness
(since the cell-based latent vectors can be combined in novel ways) as well as
spatial control of the generation process (e.g. via bounding boxes). Our method
outperforms the current state of the art on all established evaluation
measures, proposed for quantitatively evaluating the generative capabilities of
GANs. We show limitations of these measures and propose the adaptation of a
robust criterion from statistical analysis as an alternative.
