Interpolation by an closed algebraic curve (Q2718475)

The paper describes a trigonometric interpolation method of Lagrange type for connecting a given point sequence in \(\mathbb{R}^d\) by an algebraic (and therefore smooth) closed curve. The interpolation method is inherently global, but at the same time stable (or local) in the following sense: changing the position of a single point of the given sequence affects the interpolating curve only in the neighbourhood of this point.NEWLINENEWLINENEWLINEAn implicit description of the proposed curve appears in a paper by \textit{H. Stachel} [Darstellende Geometrie and Graphische Datenverarbeitung. In: J. L. Encarnação, J. Hoschek, J. Rix (eds.): Geometrische Verfahren der Graphischen Datenverarbeitung. Berlin: Springer-Verlag, 168-179 (1990; Zbl 0718.68003)].NEWLINENEWLINENEWLINEBesides its trigonometric parametrization the curve possesses a numerically efficient parametrization employing Chebyshev polynomials of the second kind. A practical application of the method is also presented. Finally, an extension for surface modelling is provided via the tensor product approach.