Modelling and simulation of the contour error evaluation based on spherically-approximated patches for freeform surface

Abstract

The mathematical modelling of contour error evaluation in Computer Aided Manufacture (CAM) system is critical for high-precision measurement and manufacture of free-form surface. The existing methods of evaluating the contour errorfor free-form surface have been developed based on various models. Nevertheless, there still exist some of the shortcomings when applied practically, including the inaccurate distance model between the measured point cloud (MPC) and ideal surface, numerical search required for the correspondence, possible local optimum of solution, the inapplicability to all the surfaces, the huge point cloud required, and heavy computational load in the registration iteration, and so forth. Toovercome those shortcomings, this work proposes the spherically-approximated patch (SAP) registrationmethod for the contour error evaluation of free-form surface. The significance of registration between MPC and the SAP set is theoretically analyzed. The SAP set for the ideal surface is efficiently generated based on the centroid-midpoint search of parametric triangle subdivision (CMSPTS). And the tactics of efficiently computing the shortest distance from the MPC to the SAP set based on a local spreading search function (LSSF) is provided. Finally, the scheme of evaluating contour error based on the Point-To-SAP (PTSAP) registration is developed. The comparative simulation and experiment demonstrate that the proposed method raises the registration level between MPC and the ideal surface and produces the evaluation result closer to the theoretical one with an acceptable efficiency, and reduces the size of ideal point cloud compared with the existing methods.