Among different approaches available for meshing surfaces, Delaunay meshing is often favored because of its directional independence and good quality in general. Computing a Delaunay mesh for domains such as smooth surfaces, polyhedral surfaces with provable guarantees is a hard problem. We present an approach that combines the classical farthest point placement strategy of Delaunay refinement with the epsilon-sampling theory developed for surface reconstruction to mesh an implicit surface and remesh a polygonal surface. The remeshing algorithm has been implemented and we show some results.