Dimensional inspection of engineering components comprising free-form surfaces demands accurate measurement of a large number of discrete points, such that the actual shape may be fully characterised. This paper presents a methodology for CAD-based measurement of such components using a coordinate measuring machine equipped with a touch-trigger probe. The main shortcomings of the conventional methodology have been identified to be in relation to registration and probe radius compensation. The proposed measurement process involves the following main steps: registration, definition of measurement points, probe path generation, path optimisation and verification, measurement and probe radius compensation. By employing the CAD model at every step, the implemented methodology maximises the measurement accuracy and this is verified through a detailed simulation study. In addition, the implemented tools for CMM programming achieve accurate control of the overall measurement process and provide a high level of confidence when dealing with complex component geometry.

Fast and accurate fitting of non-uniform rational B-spline (NURBS) curves and surfaces through large sets of measured data is an important problem in applications such as reverse engineering and geometric modelling. This paper presents a method for realising significant improvements in the computational efficiency of this task. The basic idea is that the sparsity structures of the relevant matrices that are specific to the problem of NURBS fitting can be precisely defined and that full exploitation of these structures leads to significant savings in both computational and storage requirements. These savings allow for a large number of control points to be used in order to define the surface and consequently to improve the accuracy of shape representation. The achieved computational complexity is linear in both the number of measured points and the number of control points while the storage requirements of the algorithm are linear with the number of control points only. The complexity analysis, as well as the analysis of actual running times is presented. The results demonstrate that, using this approach, highly complex shapes may be modelled accurately with a single NURBS surface.

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Probe radius compensation is necessary in metrology applications that employ contact probes, but it can be a signi® cant source of systematic measurement errors when dealing with freeform part geometry. The paper presents implementation and performance analysis of a proposed new compensation technique based on the nominal computer aided design (CAD) model, which is assumed to be de® ned using non-uniform rational B-splines (NURBS). Errors associated with the conventional compensation approach are assessed on the basis of experiments using a modern coordinate measuring machine (CMM), providing clear motivation for this work. The proposed method consists of a number of steps, including measurement, generation of oVset nominal surfaces, registration, surface ® tting, data smoothing and calculation of compensating oVsets. Critical steps include registration and NURBS surface ® tting and their implementation is presented. Simulation studies are used to analyse the registration accuracy and the accuracy of the overall method in comparison with the conventional one. The proposed method is shown to produce superior results in situations involving non-uniform measurement distribution, measurement noise, free-form geometry with no clear datums, deformation relative to the nominal shape and component misalignment.

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