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Curve fitting and design by optimal control methods

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2 Author(s)
Alhanaty, M. ; Inst. of Comput. Sci., Hebrew Univ., Jerusalem, Israel ; Bercovier, M.

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

Published in:

Information Visualization, 1998. Proceedings. 1998 IEEE Conference on

Date of Conference:

29-31 Jul 1998