Using Fast Marching for the incremental computation of distance maps across the sampling domain, we obtain an efficient farthest point sampling technique (FastFPS). The method is based on that of Eldar et al. (1992, 1997) but extends more naturally to the case of non-uniform sampling and is more widely applicable. Furthermore, it can be applied to both planar domains and curved manifolds and allows for weighted domains in which different cost is associated with different points on the surface. We conclude with considering the extension of FastFPS to the sampling of point clouds without the need for prior surface reconstruction.