Shape-Preserving Curve and Surface Data Embedding Algorithm

Farheen Ibraheem; Shamaila Samreen; Muhammad Bilal Riaz; Tayba Arooj

doi:10.32350/sir.72.01

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Shape-Preserving Curve and Surface Data Embedding Algorithm

Author(s)

Farheen Ibraheem Forman Christian College, A Chartered University-FCCU, Lahore, Pakistan

Shamaila Samreen University of Engineering and Technology, Lahore, Pakistan

Muhammad Bilal Riaz Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Poland

Tayba Arooj Lahore College for Women University, Lahore, Pakistan

Abstract

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.

Publication Details

Page(s) 1-37

DOI 10.32350/sir.72.01

Published Journal: Scientific Inquiry and Review, Volume: 7, Issue: 2, Year: 2023

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Keywords

Shape preservation, convex surface, convex data, rational functions