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

Abstract

This paper presents a novelapproach 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 re- quirements. After a brief introduction on the property of the FDM and the definition of the network usedfor 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- Splinecurve approximation. The results suggest that the adoption of a mechanical model of bar networks allows develop- ing 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 prob- lems when the satisfaction of shape constraints, such as those related to production orto technological processes, are required.