For the CAD applications, a C1 monotonically shape preserving scheme has been developed. This scheme uses piecewise rational cubic functions. An algorithm has been developed, for the economical curve implementation and pleasant demonstration, which ultimately replaces the rational cubic locally in each of the interval into a constant, linear, rational quadratic or rational cubic functions according to the nature of the slopes and the parameters in that interval. Furthermore, O(h4) convergence result is also obtained with the appropriate derivative data approximations.
This paper reviews the two spline methods: one with interval tension; and the other with point tension. Another spline method has been described which provides point and interval tension control. This method recovers, as a special case, the above mentioned two spline methods and provides a well controlled shape designing. An efficient algorithm has been given to display the curve scheme for the case N equals 2.
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