The paper identifies the steps involved in the reverseengineering process. The procedure begins with the division of the whole array of measurement data points into regions, according to shape-change detection. In each region, points are parameterized, and knots are selected. Smooth parametric surface approximation is obtained by the least-square fitting of B-splines. Nonlinear least-square minimization is applied for parameter optimization with simple bounds on the parameter values. The objective function minimized is the explicit error expression for the sum of the squares of error values at the data points.
reverse engineering, CAD~CAM, surface approximation
With the advent of high-resolution laser scanning machines and computer-controlled measurement machines, designers can now create and/or modify the design of an object based on a manufactured part that might have been modified from the existing design while in production. The industrial jargon for this process is reverse engineering. In the die and mould industry, the existing design is often modified on the shop floor, depending on the production requirements. The product geometry changes with such modifications. The idea behind reverse engineering is to retrieve this new geometry from the manufactured part by scanning, and to modify the existing CAD database. The coordinates and the normal vectors of the part surface, with respect to a given datum, are the entries in a CAD database that are often modified on the basis of the output of the reverse-engineering techniques. These techniques mainly involve parametric surface approximation.
A few papers have been published on the problem of approximating 3D data by parametric surfaces 1-3. However, these papers describe the approximation procedure for a single isolated surface, and the optimization of parameters involves repetitive fitting.