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The approximation approach is particularly well suited when data are not exact but subjected to measurement errors. Such a distance is usually measure along the normal vector to the curve at that point. On the contrary, approximation does not require the fitting curve to pass through the data points, but just close to them, according to prescribed distance criteria. This approach is typically employed for sets of data points that are sufficiently accurate and smooth. In the former, a parametric curve is constrained to pass through all input data points. Depending on the nature of these data points, two different approaches can be employed: interpolation and approximation. The primary goal in these cases is to obtain a sequence of cross-sections of the object in order to construct the surface passing through them, a process called surface skinning.Īnother different approach consists of reconstructing the curve directly from a given set of data points, as it is typically done in reverse engineering for computer-aided design and manufacturing (CAD/CAM), by using 3D laser scanning, tactile scanning, or other digitizing devices. This is a typical problem in many research and application areas such as medical science and biomedical engineering, in which a dense cloud of data points of the surface of a volumetric object (an internal organ, for instance) is acquired by means of noninvasive techniques such as computer tomography, magnetic resonance imaging, and ultrasound imaging. A classical approach in this field is to construct the curve as a cross-section of the surface of an object. The problem of recovering the shape of a curve/surface, also known as curve/surface reconstruction, has received much attention in the last few years. Furthermore, our scheme outperforms some popular previous approaches in terms of different fitting error criteria. Our experimental results show that the presented method performs very well, being able to fit the data points with a high degree of accuracy. The method has been applied to three illustrative real-world engineering examples from different fields. In our approach, this optimization problem is solved by applying the firefly algorithm, a powerful metaheuristic nature-inspired algorithm well suited for optimization. This requires to solve a difficult continuous, multimodal, and multivariate nonlinear least-squares optimization problem.
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The proposed method computes all parameters of the B-spline fitting curve of a given order. This paper introduces a new method to compute the approximating explicit B-spline curve to a given set of noisy data points.