When dealing with inspection or reverse modeling, the problem of free-form curves and surfaces reconstruction has to be faced starting from a set of measured points. Because in point sampling the acquisition error is unavoidable, curves and surfaces fitting should be based on a rigorous diagnostic phase. We consider statistical regression analysis in which, treating error as a variable of the problem, we distinguish between the systematic behavior of measured points and noise in the reconstruction of curves and surfaces. The model we introduce for a regression based free-form reconstruction is the so-called regression spline. It is a well known model in the literature, with a consolidated theory and applications in fields such as chemical, econometric, and biomedical. Our purpose is to discuss the application of this powerful and flexible approach in a reverse modeling environment.

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