Constrained fitting of B-Spline curves based on the Force Density Method

This paper presents a novel ap-proach for constrained B-Spline curve approximation based on the Force Density Method (FDM). This approach aims to define a flexible technique tool for curve fitting, which allows approximating a set of points taking into account shape constraints that may be related to the production process, to the material or to other technological requirements. After a brief introduction on the property of the FDM and the definition of the network used for the formulation of the fitting problem, the paper explains in detail the mathematical approach, the methods and the techniques adopted for the definition of the proposed constrained B-Spline curve approximation.The results suggest that the adoption of a mechanical model of bar networks allows developing a more flexible tool than the traditional least squared methods (LSM) usually adopted for fitting problems. Numerical examples show that the new approach is effective in fitting problems when the satisfaction of shape constraints, such as those related to production or to technological processes, are required.