An integrated fitting and fairing approach for object reconstruction using smooth NURBS curves and surfaces

This paper presents a new approach for object reconstruction by means of smooth NURBS curves and surfaces. Compared to the common object reconstruction algorithms that first, fit a curve or surface to a dataset and then, try to make it smooth in a post-processing fairing stage, this article proposes to apply the fitting and fairing procedures simultaneously to achieve desirable results. In the integrated fitting and fairing approach, the respective fitting and fairing objectives are met in a multi-objective optimization process. In the developed methodology, the structure of the reconstructed curves and surfaces (e.g. the arrangement of the knot vectors and location of control points) is optimized in such a way that the desired fairness will be locally achieved in every segment of the reconstructed object. The functionality of the developed method is investigated by some industrial case studies.