Constrained rational cubic spline and its application (Q2725280)

This paper considers the constrained curve interpolation problem both on the shape and the second-order derivative of the interpolant. Sufficient conditions for the interpolating curves to be above a straight line and/or a quadratic curve in an individual knot interval and necessary and sufficient conditions for constraining the second order derivative of the interpolating function are derived. In fact, not only necessary and sufficient conditions are given, but also existence conditions for this constrained rational cubic interpolation are derived. More interesting is that, because the second-order derivative of the interpolant function can be controlled by this method, the convex interpolation conditions can be got easily as the consequent result.