J.-D. Boissonnat, S. Y. Oudot. An effective condition for sampling surfaces with guarantees. Proc. 9th ACM Sympos. on Solid Modeling and Applications, pp. 101-112, 2004.


The notion of r-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 r-sample of a smooth surface S for a sufficiently small r, 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 r-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 r-sample. We show that the set of loose r-samples contains and is asymptotically identical to the set of r-samples. The main advantage of loose r-samples over r-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.


 author = {J.-D. Boissonnat and S. Y. Oudot},
 title = {An effective condition for sampling surfaces with guarantees},
 booktitle = {Proc. 9th ACM Sympos. on Solid Modeling and Spplications},
 pages = {101--112},
 year = {2004}