Creating an interpolating mesh from an unorganized set of oriented points is a difficult problemwhich is often overlooked. Most methods focus indeed on building a watertight smoothed meshby defining some function whose zero level set is the surface of the object. However in some casesit 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 artifactsor because the goal is to explore visually the data exactly as they were acquired without anysmoothing process. In this paper we detail a parallel implementation of the Scale-Space Meshingalgorithm, which builds on the scale-space framework for reconstructing a high precision meshfrom an input oriented point set. This algorithm first smoothes the point set, producing asingularity free shape. It then uses a standard mesh reconstruction technique, the Ball PivotingAlgorithm, 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 ofthis process is an interpolating, hole-preserving surface mesh reconstruction.