Cubic spline interpolation predictors over implicitly defined curves

The aim of this paper is to present a higher order predictor method for the numerical tracing of implicitly defined curves. This higher order predictor is described based upon the clamped cubic spline interpolation function using previously computed points on the curve to compute the coefficients via divided differences. Some applications are made to the numerical integration of closed implicitly defined curves. The line integral is approximated via a Gauss–Legendre quadrature of the interpolating function.