Boissonnat, J. D.Oudot, S.Gershon Elber and Nicholas Patrikalakis and Pere Brunet2016-02-172016-02-1720043-905673-55-X1811-7783https://doi.org/10.2312/sm.20041381The notion of e-sample, as introduced by Amenta and Bern, has proven to be a key concept in the theory of sampled surfaces. Of particular interest is the fact that, if E is an e-sample of a smooth surface S for a suf ciently small e, then the Delaunay triangulation of E restricted to S is a good approximation of S, both in a topological and in a geometric sense. Hence, if one can construct an e-sample, one also gets a good approximation of the surface. Moreover, correct reconstruction is ensured by various algorithms. In this paper, we introduce the notion of loose e-sample. We show that the set of loose e-samples contains and is asymptotically identical to the set of e-samples. The main advantage of loose e-samples over e-samples is that they are easier to check and to construct. We also present a simple algorithm that constructs provably good surface samples and meshes.I.3.5 [Computer Graphics]Curvesurfacesolidand object representations10.2312/sm.20041381101-112