Abstract: Fitting data points to curves (usually referred to as curve reconstruction) is a major issue in computeraided design/manufacturing (CAD/CAM). This problem appears recurrently in reverse engineering, where a set of (possibly massive and noisy) data points obtained by 3D laser scanning have to be fitted to a freeform parametric curve (typically a B-spline). Despite the large number of methods available to tackle this issue, the problem is still challenging and elusive. In fact, no satisfactory solution to the general problem has been achieved so far. In this paper we present a novel hybrid evolutionary approach (called IMCHGAPSO) for B-spline curve reconstruction comprised of two classical bio-inspired techniques: genetic algorithms (GA) and particle swarm optimization (PSO), accounting for data parameterization and knot placement, respectively. In our setting, GA and PSO are mutually coupled in the sense that the output of one system is used as the input of the other and vice versa. This coupling is then repeated iteratively until a termination criterion (such as a prescribed error threshold or a fixed number of iterations) is attained. To evaluate the performance of our approach, it has been applied to several illustrative examples of data points from real-world applications in manufacturing. Our experimental results show that our approach performs very well, being able to reconstruct with very high accuracy extremely complicated shapes, unfeasible for reconstruction with current methods.

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