On the Classification of Fitting Problems for Single Patch Free-Form Surfaces in Reverse Engineering

The design and manufacture of free-form surfaces increased in industrial applications, especially for the re-manufacture of spare parts, or in the die and mold industry. Reverse engineering has become the status quo technique in reproducing parts whose original designs are no longer existing or for parts, which assume slightly different shapes after manufacturing as in the case of die and mold industry. Laser scanners have been used extensively in sampling points from parts surfaces. The sampled points are then fitted with a free-form surface using one of the geometric modeling techniques such as Bezier or B-Spline surfaces. Since Non-Uniform Rational B-Splines (NURBS) is the most general form of geometric modeling techniques, this paper presents the possible formulations of the fitting problem optimization and presents some guidelines of the choice of the independent NURBS parameters, once the control points are evaluated using least squares fitting. The work shows that the use of NURBS weights can provide better improvements for the significant reduction of the fitting error, rather than the widely used knot values. In addition the work shows that parts with semi planar surfaces do not need further refinement using non-linear optimization methods.