Effeciently visualizing the scientific data preserving monotonicity

For the CAD applications, a C ¹ 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(h ⁴) convergence result is also obtained with the appropriate derivative data approximations.