Creating an interpolating mesh from an unorganized set of oriented points is a difficult problem which is often overlooked. Most methods focus indeed on building a watertight smoothed mesh by defining some function whose zero level set is the surface of the object. However in some cases it is crucial to build a mesh that interpolates the points and does not fill the acquisition holes: either because the data are sparse and trying to fill the holes would create spurious artifacts or because the goal is to explore visually the data exactly as they were acquired without any smoothing process. In this paper we detail a parallel implementation of the Scale-Space Meshing algorithm, which builds on the scale-space framework for reconstructing a high precision mesh from an input oriented point set. This algorithm first smoothes the point set, producing a singularity free shape. It then uses a standard mesh reconstruction technique, the Ball Pivoting Algorithm, to build a mesh from the smoothed point set. The final step consists in back-projecting the mesh built on the smoothed positions onto the original point set. The result of this process is an interpolating, hole-preserving surface mesh reconstruction. Source Code The ANSI C++ source code permitting to reproduce results from the on-line demo is available at the IPOL web page of this article 1. The scale-space meshing algorithm uses the Ball Pivoting Algorithm which is linked to patent US6968299B1. It is made available for the exclusive aim of serving as a scientific tool to verify the soundness and completeness of the algorithm description.