Recently, there are some needs in reverse engineering applications to employ pp functions for representing not only smooth curves, but also curves with non-trivial cases, i.e. The research interests commonly focused on finding the best smooth pp functions to represent complex functions or sampled data. The use of piecewise polynomial to approximate or to fit a complex function or a given data set became a popular research topic in 1970s to 1990s. The spline, especially in the form of B-spline, can easily capture various functions from continuous curves to discontinuous ones. The most well-known piecewise polynomial function is, perhaps, in a spline form. There are a few ways to represent a piecewise polynomial function from an explicit to an implicit form in Bezier or B-spline curve. Piecewise polynomial ( pp) functions are extensively used in many applications, such in the approximation of a complex function, data regression or data compression and in computing technology due to its simplicity and good properties. In addition, the method does not require excessive computational cost, which allows it to be used in automatic reverse engineering applications. It is also shown that, the proposed method can be applied for fitting any types of curves ranging from smooth ones to discontinuous ones. The proposed method is shown to be able to reconstruct B-spline functions from sampled data within acceptable tolerance. This paper also discusses the benchmarking of the proposed method to the existing methods in literature. The performance of the proposed method is validated by using various numerical experimental data, with and without simulated noise, which were generated by a B-spline function and deterministic parametric functions. The B-spline function is, therefore, obtained by solving the ordinary least squares problem. Secondly, the knots are optimized, for both locations and continuity levels, by employing a non-linear least squares technique. In the first step, the data is split using a bisecting method with predetermined allowable error to obtain coarse knots. A new two-step method for fast knot calculation is proposed. This paper presents a new strategy for fitting any forms of curve by B-spline functions via local algorithm. The most challenging task in these cases is in the identification of the number of knots and their respective locations in non-uniform space in the most efficient computational cost. in reverse engineering (RE) area, to employ B-spline curves for non-trivial cases that include curves with discontinuous points, cusps or turning points from the sampled data. B-spline functions are widely used in many industrial applications such as computer graphic representations, computer aided design, computer aided manufacturing, computer numerical control, etc.
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