Curve fairing using integral spline operators

In the context of the reverse engineering process one of the main problems is the smoothing of curves and surfaces reconstructed starting from a set of scattered points. This process of smoothing is usually called fairing. In this paper we propose an efficient algorithm for planar curve fairing. This algorithm is automatic and is composed of two steps: first a global rough fairing is performed on the whole curve and then a local fine fairing is carried out to improve the quality of the final curve. The mathematical tool at the base of the algorithm is an integral spline operator characterized by a shape parameter. This operator is variation-diminishing. In order to choose the best value for the shape parameter, a suitable functional related to the curvature is minimized. Some test cases are presented in order to show the effectiveness of the proposed algorithm: both academic and a real world test case are considered.