  This work considers a new task in geometric deep learning: generating a
triangulation among a set of points in 3D space. We present PointTriNet, a
differentiable and scalable approach enabling point set triangulation as a
layer in 3D learning pipelines. The method iteratively applies two neural
networks: a classification network predicts whether a candidate triangle should
appear in the triangulation, while a proposal network suggests additional
candidates. Both networks are structured as PointNets over nearby points and
triangles, using a novel triangle-relative input encoding. Since these learning
problems operate on local geometric data, our method is efficient and scalable,
and generalizes to unseen shape categories. Our networks are trained in an
unsupervised manner from a collection of shapes represented as point clouds. We
demonstrate the effectiveness of this approach for classical meshing tasks,
robustness to outliers, and as a component in end-to-end learning systems.
