  This article presents a novel method to sampling on manifolds based on the
Dirichlet distribution. The proposed strategy allows to completely respect the
underlying manifold around which data is observed, and to do massive samplings
with low computational effort. This can be very helpful, for instance, in
neural networks training process, as well as in uncertainty analysis and
stochastic optimization. Due to its simplicity and efficiency, we believe that
the new method has great potential. Three manifolds (two dimensional ring,
Mobius strip and spider geometry) are considered to test the proposed
methodology, and then it is employed to an engineering application, related to
gas seal coefficients.
