  Recent advances in geometric deep-learning introduce complex computational
challenges for evaluating the distance between meshes. From a mesh model, point
clouds are necessary along with a robust distance metric to assess surface
quality or as part of the loss function for training models. Current methods
often rely on a uniform random mesh discretization, which yields irregular
sampling and noisy distance estimation. In this paper we introduce MongeNet, a
fast and optimal transport based sampler that allows for an accurate
discretization of a mesh with better approximation properties. We compare our
method to the ubiquitous random uniform sampling and show that the
approximation error is almost half with a very small computational overhead.
