We introduce a method for learning to generate the surface of 3D shapes. Ourapproach represents a 3D shape as a collection of parametric surface elementsand, in contrast to methods generating voxel grids or point clouds, naturallyinfers a surface representation of the shape. Beyond its novelty, our new shapegeneration framework, AtlasNet, comes with significant advantages, such asimproved precision and generalization capabilities, and the possibility togenerate a shape of arbitrary resolution without memory issues. We demonstratethese benefits and compare to strong baselines on the ShapeNet benchmark fortwo applications: (i) auto-encoding shapes, and (ii) single-view reconstructionfrom a still image. We also provide results showing its potential for otherapplications, such as morphing, parametrization, super-resolution, matching,and co-segmentation.