Determination of the optimal parameters for freeform surface measurement and data processing in reverse engineering

One objective of this work is to determine the optimal combination of the probe diameter and grid distance for freeform surface measurement, and another is to determine the optimal parameters for the local Shepard interpolation. The optimal combination of the probe diameter and grid distance for freeform surface measurement was determined through a Taguchi matrix experiment. The smaller the probe diameter and grid distance, the better the accuracy of the surface normal based on the configured matrix experimental result. The optimal parameters, namely the exponent g and the radius R, for the local Shepard interpolation were determined by using the minimisation method of the root-mean-square normalised error (RMSNE) between the measured data points and the theoretical data points on a standard steel ball surface. The optimal parameters determined were actually applied to the measurement of a freeform surface (mouse surface) on a coordinate measuring machine (CMM). The local Shepard interpolation method was used to interpolate 16 control points from 1054 measured data points. Bi-cubic Bezier- and B-spline surface CAD models were constructed through these interpolated control points.