Abstract
Creating unavailable geometric models from existing parts plays an important role in the process of reverse engineering, for which the accuracy and fitting time of the created models are important factors. This paper proposes the use of Tabu Search (TS) technique in the optimal fitting of NURBS (Non Uniform Rational B-Spline) surfaces to laser-scanned point clouds of free-form surfaces for existing parts. The fitting process involves the initial estimation of the NURBS surface control points using least-squares approximation, followed by optimization of NURBS weights to minimize fitting error. Optimization is performed using a hybrid coding scheme, namely; Modified Continuous Reactive Tabu Search (M-C-RTS), in which a combinatorial optimization component, based on Reactive Tabu Search (RTS), co-operates with Sequential Quadratic Programming (SQP), as a local minimizer. The developed fitting algorithm was applied to a number of simulated free-form surfaces in addition to a laser-scanned PC mouse. Implementation was carried out using MATLAB software and the results were compared to those obtained using Genetic Algorithms (GAs) in an earlier publication. The results show the superiority of the proposed algorithm to the GA-based method with respect to the number of objective function evaluations (about 50% reduction). In addition to this time saving achievement, and surprisingly, M-C-RTS proved to be capable of finding better solutions than GAs.