metrology; coordinate measuring machine; reverse engineering; uncertainty; interpolation; approximation; least squares method
In this article, a method of cubic spline curve fitting to a set of points passing at a prescribed distance from input points obtained by measurement on a coordinate measuring machine is described. When reconstructing the shape of measured object from the points obtained by real measurements, it is always necessary to consider measurement uncertainty (tenths to tens of micrometres). This uncertainty is not zero, therefore interpolation methods, where the resulting curve passes through the given points, do not lead to acceptable results in practice. Also, conventional B-spline approximation methods cannot be used because, for real distances between measured points (tenths to units of millimetres), the distance of the input data from the resulting approximation curve is much greater than the measurement uncertainty considered. The proposed reconstruction method allows to control the maximum distance of the resulting curve from the input data and thus to respect the uncertainty with which the input data was obtained.