Curve fitting and design by optimal control methods

The theory of optimal control is introduced as a new approach for handling curve fitting and design problems. Optimal control provides a uniform formal framework for stating and solving multiple problems in computer-aided geometric design (CAGD). As a result, new classes of curves are defined and known problems are analyzed from a new viewpoint. Often, families of curves which are defined by a minimization problem rely on parameters. Such problems are an appropriate base for handling curve fitting and design by optimal control methods. The methods suit a wide variety of problems. They are demonstrated on three applications of curve fitting and design: smoothing ν-splines, smoothing interpolating splines and approximating curves. All the applications are treated and solved using the uniform framework. The solution technique is based on the relaxation method