Abstract
A focal method for approximating an empirical geometric shape represented by a smooth closed curve is developed. The analytical basis of the method is multifocal lemniscates. The finite number of foci inside the lemniscate and its radius are control parameters of this method. In contrast to the harmonic representation, focal control parameters have of the same nature as the shape itself. In this paper we consider the more general class of multifocal curves from the point of view of using them as a basis for describing geometric shapes. Making the most general requirements for the metric distance function and the invariant description of geometric shapes sets gives a parameterized set of bases in the quasilemniscates class that meet these requirements. Properties of each basis, defined by different functions distances are also reflected in their approximate possibilities. The family multifocal lemniscates is distinguished as the limiting case of parameterized set of basic quasilemniscates. The focal representation of empirical geometric shapes by multifocal lemniscates makes it possible to apply them in different applications.
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Rakcheeva, T. (2021). Focal Curves in the Problem of Representing Smooth Geometric Shapes. In: Hu, Z., Petoukhov, S., He, M. (eds) Advances in Artificial Systems for Medicine and Education IV. AIMEE 2020. Advances in Intelligent Systems and Computing, vol 1315. Springer, Cham. https://doi.org/10.1007/978-3-030-67133-4_3
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DOI: https://doi.org/10.1007/978-3-030-67133-4_3
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