Shape Preserving Constrained data Visualization using Spline Functions

The main spotlight of this paper is the visual display of constrained data that looks smooth, pleasant and attractive. A C-1 piecewise rational cubic function has been constructed to preserve the shape of constrained data. The piecewise rational cubic function has three free parameters in its description. One free parameter is constrained to preserve the shape of data that is lying above a line while the other two are left for the user to refine the shape of curve. Further, the piecewise rational cubic function has been extended to rational bi-cubic function to preserve the shape of surface data arranged over a rectangular grid that is lying above a plane. The developed scheme is simple, local and economical as compared to existing schemes. The curve and surface schemes under discussion is C-1.