Application of cubic splines for the analytic representation of a closed contour defined by a table of coordinates

We solve the problem of the analytic representation of a closed contour defined by a table of coordinates and by additional conditions that define the asymptotics of the contour near the endpoints. The equation of the contour is represented in the form of the product of two functions, one of which takes into account the given asymptotics of the contour and the other function is determined by the method of local approximation by cubic splines. The theoretical error of the approximation agrees with the results of test computations.