The (2n+1)2-point Scheme Based on Bivariate Quartic Polynomial. | [Mehran University Research Journal of Engineering and Technology • 2018]

Author(s):

1. Ghulam Mustafa: Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan

2. Mehwish Bari: Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan

3. Touseef UR Rehman: Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan

Abstract:

We are going to implement least squares approach to fit the bivariate quartic polynomial to (2n+1)2perceptions/data, where n>2. By taking different values of n, (2n+1)2-point approximating subdivision schemes are built. The proposed scheme can be applied for illustrate individual items as a part of 3D (Three Dimensional) space. The proposed scheme is based on fitting the local least squares bivariate quartic polynomial of degree four to the (2n+1)2-observations. The influence of the proposed scheme is shown by 2D example and its working is presented with the help of different quadrilateral meshes. Subdivision and topological rules are also explained with graphical and mathematical representation. Applications and visual exhibitions of the plan have additionally been displayed to show the implementation of the plan.

Page(s): 319-326

DOI: 10.22581/muet1982.1802.08

Published: Journal: Mehran University Research Journal of Engineering and Technology, Volume: 37, Issue: 2, Year: 2018

Keywords:

Least Squares , Quartic Polynomial , 3D Modeling

References:

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