  Polygon meshes are an efficient representation of 3D geometry, and are of
central importance in computer graphics, robotics and games development.
Existing learning-based approaches have avoided the challenges of working with
3D meshes, instead using alternative object representations that are more
compatible with neural architectures and training approaches. We present an
approach which models the mesh directly, predicting mesh vertices and faces
sequentially using a Transformer-based architecture. Our model can condition on
a range of inputs, including object classes, voxels, and images, and because
the model is probabilistic it can produce samples that capture uncertainty in
ambiguous scenarios. We show that the model is capable of producing
high-quality, usable meshes, and establish log-likelihood benchmarks for the
mesh-modelling task. We also evaluate the conditional models on surface
reconstruction metrics against alternative methods, and demonstrate competitive
performance despite not training directly on this task.
