CAD-based triangulation of unordered data using trimmed NURBS models

Applications in engineering manufacture, such as dimensional inspection, often require triangulation of large sets of measured 3D data. The CAD models of relevant complex parts are usually defined using trimmed NURBS (non-uniform rational B-spline). With such situations in mind, the paper proposes a new triangulation procedure which achieves high efficiency and robustness by utilising the CAD model as an available 2D manifold which approximates the shape of the actual part. The steps in this procedure are alignment between the data and the model, registration of the measured points to the model entities, triangulation in the R2 domain provided by the parametric surface entities, 3D mesh improvement, stitching of mesh patches and smoothing of the final mesh. The method does not assume any prior knowledge about the point ordering and performs well in the presence of the measurement noise, while also bypassing the problems of occlusion and overlap that are commonly associated with range imaging. The performance of the proposed method was analysed in relation to some other methods using models of real engineering parts. The results are highly encouraging, leading to a conclusion that the methods is well suited to practical engineering applications.