Estimating the in/out function of a surface represented by points

We present a method to estimate the in/out function of a closed surface represented by an unorganized set of data points. From the in/out function, we compute an approximation of the signed distance function to a surface M whose sampling are given by this set of points. The procedure correctly detects the interior and the exterior of M, even if M is multiply connected. The representation of the signed distance function combines the advantages of two previously known schemes, "Implicit Simplicial Models" and "Adaptively Sampled Distance Fields", incorporating new features deriving from the concept of a Binary Multitriangulation.