A C2-continuous rational quintic interpolation scheme for curve data with shape control

A new rational quintic interpolation scheme for curve design is presented. The new scheme is suggested for scalar 2D data and has three free parameters that provide design flexibility. Constraints are developed on one of the free parameters to preserve the shape of positive and range restricted data. The other two parameters are free to guarantee design flexibility. The resulting rational quintic interpolation scheme is globally C2-continuous and its order of continuity is independent of the choice of free parameters and data values. Approximation order of the proposed interpolation scheme is three. Application of the C2-continuous rational quintic interpolation scheme and the role of free parameters are demonstrated by several examples.