Profile measurement via circle-line spline fitting

For quality control purposes, it is necessary to measure an object's dimensions, and compare them with a CAD model; this is effectively a reverse engineering task. The specific example addressed in this paper is the measurement and modelling of cold rolled steel profiles. The profile of the steel tubing can be measured with an arrangement of light sectioning heads, whereby the measurement data must be modelled to extract the measured dimensions, e.g., radii, angles, etc. The manufactured tubing is designed such that its profile is composed of only straight lines and circular arcs which are mutually tangent at each vertex. In this paper we develop an algorithm for fitting such a “circle-line spline” by orthogonal distance least squares. We derive the tangency constraints for such a spline and show that the optimization can be performed with constrained Gauss-Newton optimization. Through numerical testing we show that the algorithm effectively models the profile dimensions, and is stable in the presence of measurement noise.