  3D shape models are naturally parameterized using vertices and faces, \ie,
composed of polygons forming a surface. However, current 3D learning paradigms
for predictive and generative tasks using convolutional neural networks focus
on a voxelized representation of the object. Lifting convolution operators from
the traditional 2D to 3D results in high computational overhead with little
additional benefit as most of the geometry information is contained on the
surface boundary. Here we study the problem of directly generating the 3D shape
surface of rigid and non-rigid shapes using deep convolutional neural networks.
We develop a procedure to create consistent `geometry images' representing the
shape surface of a category of 3D objects. We then use this consistent
representation for category-specific shape surface generation from a parametric
representation or an image by developing novel extensions of deep residual
networks for the task of geometry image generation. Our experiments indicate
that our network learns a meaningful representation of shape surfaces allowing
it to interpolate between shape orientations and poses, invent new shape
surfaces and reconstruct 3D shape surfaces from previously unseen images.
