A Voronoi diagram based framework for fast and accurate evaluation of 2D free-form profile errors

Abstract

Free-form objects which have vast engineering applications are inspected using coordinate measuring machines (CMM) and non-contact scanners. The output from the devices, that is the measured point-set, must be registered with the reference profile and later inspected for the profile error. Registration is accomplished in two phases, that is coarse registration and fine registration. The most crucial step in the fine-registration stage is the profile error estimation at each point of the measured point-set. Generally, this is accomplished using the point-inversion method, which has relatively high time complexity. This work proposes a two-stage framework based on the Voronoi diagram concept for profile error estimation of 2D free-form profiles. A discretized profile is prepared for the measurement process in the first stage. The profile errors are estimated from the measured point-set using the discretized profile in the second stage. Two profile error estimation technique has been proposed based on Voronoi vertices and the Voronoi edges. The effective time-complexity of the proposed framework is O(lm log n). Implementations were executed on simulated NURBS profiles and practically measured CT-scanner data of two machined airfoils modelled as NURBS profiles. The validation results illustrate that the proposed framework’s accuracy is on par with that of the point-inversion method and is at least 56% faster than the latter; thus making it a fast and accurate alternative for CMM (operated in continuous scanning mode), CNC machine-based (in-situ) and vision-based 2D profile inspection.