the rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. the rational bi-cubic function involves six parameters in each rectangular patch. data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...

The rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. The rational bi-cubic function involves six parameters in each rectangular patch. Data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...

This work has been contributed on the visualization of curves and surfaces for constrained data. A rational cubic function, with free shape parameters in its description, has been introduced and used. This function has been constrained to visualize the preservation of shape of the data by imposing constraints on free parameters. The rational cubic curve case has also been extended to a rational...

In this paper, an attempt has been made to construct a shape preserving rational bi-cubic interpolant (cubic/quadratic) with twelve free parameters to depict a more pleasant and smooth display of positive surface through positive data. Simple data dependent constraints are derived for four free parameters to preserve the positivity of data while the remaining eight are left free for designer’s ...

This paper deals with the shape preserving interpolation problem for visualization of 3D positive data. A required display of 3D data looks smooth and pleasant. A rational bi-cubic function involving six shape parameters is presented for this objective which is an extension of piecewise rational function in the form of cubic/quadratic involving three shape parameters. Simple data dependent cons...

The paper develops a rational bi-cubic G2 (curvature continuous) analogue of the non-uniform polynomial C2 cubic B-spline paradigm. These rational splines can exactly reproduce parts of multiple basic shapes, such as cyclides and quadrics, in one by default smoothly-connected structure. The versatility of this new tool for processing exact geometry is illustrated by conceptual design from basic...