A Dynamical Systems Approach to the Polygonal Approximation of Plane Convex Compacts

Petar S. Kenderov and Nikolai K. Kirov

Key words: polygonal approximation of plane convex sets, dynamical systems, global optimization, variable knots spline approximation.


A connection is described between the polygonal approximation of a compact convex set in R^2 and some dynamical systems on the unit circumference in R^2. Basing on this a numerical procedure is proposed for finding a best approximating n-gon for an arbitrary compact convex set in R^2 (w.r.t. Hausdorff metric). The algorithm provides a solution to a specific global optimization problem where the function to be minimized has more than one local minimum. In one of its equivalent formulations the above approximation problem can be considered as a specific spline approximation problem. From this point of view our algorithm provides also a solution to a specific variable knots spline approximation problem.
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