Shape-Preserving Curve and Surface Data Embedding Algorithm

In this study, shape preserving data driven rational cubic schemes are developed. A rational cubic piecewise function (quadratic denominator and cubic numerator) with two parameters was transformed to C1 rational cubic piecewise function. Constraints were derived on free parameters by means of some mathematical derivations to train and demonstrate convex curve. The scheme, then, was advanced to partially blended rational bi-cubic function with eight free parameters which were controlled to ascertain convex surface. A numerical comparison with certain existing schemes manifested that the proposed method was economical. The proposed scheme was put into visualization of convex 2D and 3D data using MATLAB software packet. Additionally, the suggested approach produced a more visually appealing interpolating curve for scientific visualization for specific data sets.