An investigation on methods for axis detection of high-density generic axially symmetric mechanical surfaces for automatic geometric inspection

The detection of the symmetry axis from discrete axially symmetric surfaces is an interesting topic, which is transversal to various fields: from geometric inspection to reverse engineering, archeology, etc. In the literature, several approaches have been proposed for estimating the axis from high-density triangular models of surfaces acquired by three-dimensional (3D) scanning. The axis evaluation from discrete models is, in fact, a very complex task to accomplish, due to several factors that inevitably influence the quality of the estimation and the accuracy of the measurements and evaluations depending on it. The underlying principle of each one of these approaches takes advantage of a specific property of axially symmetric surfaces. No investigations, however, have been carried out so far in order to support in the selection of the most suitable algorithms for applications aimed at automatic geometric inspection. In this regard, ISO standards currently do not provide indications on how to perform the axis detection in the case of generic axially symmetric surfaces, limiting themselves to addressing the issue only in the case of cylindrical or conical surfaces. This paper first provides an overview of the approaches that can be used for geometric inspection purposes; then, it applies them to various case studies involving one or more generic axially symmetric surfaces, functionally important and for which the axis must be detected since necessary for geometric inspection. The aim is to compare, therefore, the performances of the various methodologies by trying to highlight the circumstances in which these ones may fail. Since this investigation requires a reference (i.e. the knowledge of the true axis), the methodologies have been applied to discrete models suitably extracted from CAD surfaces.