In inspection or reverse engineering, free-form shapes are reconstructed from a large set of sampled points. Since point acquisition error is unavoidable, shape fitting should be based on a rigorous diagnostic phase. In this paper, a new parametrical form of regression spline is introduced. The method applies statistical regression analysis, with the error treated as a variable of the problem. Hence, during the reconstruction process we distinguish between the systematic behavior of the sampled points, which represents the part shape, and the hi-frequency behavior of noise. This distinction leads to realistic and efficient reconstruction of complex parts. Both the multi-valued and the closed curves and surfaces of smooth and non-homogeneous types are represented. This work presents the method and demonstrates its feasibility on freeform parts applied to a new parametrical form of regression spline.

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