Abstract:
The problem of analytic approximation of a smooth closed curve specified by a set of its points on the complex plane is proposed. An algorithmic method for constructing an approximating lemniscate is proposed and investigated. This method is based on a mapping of the curve to be approximated onto the phase circle; the convergence of the method is proved. The location of the lemniscate foci inside the curve provides the degrees of freedom for the focal approximation.
Key words:curves on the complex plane, approximation, basis, foci, ovals, lemniscates, shape, invariant, curve proximity criterion, algorithm, degrees of freedom, interactive control.
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