A closed algebraic interpolation curve Original Research Article

We introduce a new interpolation method employing a closed algebraic curve. This note describes a trigonometric interpolation method to connect a given point sequence in Rd by an algebraic and therefore smooth closed curve. The interpolation formula is of Lagrangian type and seems to be new. In contrast to spline interpolation our method does not work piecewise but global. Nevertheless the curve connects the given points in a quite natural manner preserving the given order and without overshooting tendency. The curves are, like spline curves, stable in the following sense: changing the position of a single point of the given sequence only changes the curve in the neighbourhood of this point essentially. Besides its trigonometric parametrization the curve possesses a numerically efficient parametrization on the basis of Chebyshev polynomials of the second kind. To what extend the new interpolation method can replace the spline method, the experts may decide.