Smooth-surface approximation and reserve engineering (Q1182352)

The paper describes a sequence of steps for the so-called reverse engineering process, which is an industrial jargon for the problem of scanning the geometry of an already manufactured part and putting its data (coordinates, normal vectors) into a CAD database. The main steps involved in this process are the following ones: Since we are dealing with \(3D\)-objects, a method for dividing the given surface into several subregions is needed. The authors propose the use of a boundary detection method using the Gaussian Laplacian operator. After the parametrization of the measured data points, in each region the surface is approximated by a cubic \(B\)-spline-surface, where the approximation is optimized in the least squares sense. This is done using a nonlinear optimization technique. Finally, the boundary between two surfaces fitted in two adjacent regions must be recomputed in order to obtain a continuous surface of the whole objects. This is done by a surface-intersection algorithm which falls into the category of lattice evaluation methods. Several figures and results of numerical tests illustrate the method.