Parametric curve interpolation by combination of two conic sections

The problem of constructing a parametric cubic rational curve to interpolate a set of distinct data points is discussed. Unlike the existing methods which include the determination of knots, the new method constructs parametric curve without the process of determining knots. For each point, a quadratic rational Bézier curve is constructed by the five convex data points. For the data point, if there is no five convex data points, the quadratic rational Bézier curve is constructed with four or three points under a constraint. Between each pair of the two adjacent points, a parametric cubic rational curve is constructed by the combination of the two quadratic rational Bézier curves. The constructed cubic rational curve reproduces a conic section exactly if the given data points are taken from the conic section. The comparison of the new method with other ones is included.