Modeling rational spline for visualization of shaped data

Abstract

-The presented paper focuses on two objectives, the development of a new curve interpolation scheme and its application towards the visualization of shaped data. AC1 piecewise rational cubic function, with two parameter family, is developed and presented. The affect of parameters on the shape of the model curve is examined mathematically and illustrated graphically. Simple sufficient data dependent constraints are obtained on one family of the parameters to visualize positive, monotone and convex data. However, the other family of parameters can assume any positive values. The problem of visualization of constrained data is also addressed when the data is lying above a straight line and curve is required to lie on the same side of the line. Moreover, the approximation order of the proposed rational cubic function is also investigated and is found to be O(h3i ).