The (2n+1)2-point Scheme Based on Bivariate Quartic Polynomial.

Ghulam Mustafa; Mehwish Bari; Touseef UR Rehman

doi:10.22581/muet1982.1802.08

Author(s)

Ghulam Mustafa Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan

Mehwish Bari Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan

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.

Publication Details

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

Request the full text from PASTIC

Keywords

Least Squares, Quartic Polynomial, 3D Modeling

References

Ko , K.P.,Lee , B.G.,Yoon , G.J.,PointApproximating, 2007.,[1] [2] [3] [4] [5] 190 -

Mustafa , G.,Xuefeng , L., 2005.“A Subdivision Scheme for Volumetric Models”,Applied Mathematics-A Journal of Chinese Universities 20 213 -224

Boye , S.,Guennebaud , G.,Schlick , C., 2010.,Computer Graphics Forum 29 2021 -2028

Conti , C.,Dyn, 2010.“Blending Based Corner Cutting Subdivision Scheme for Nets of Curves”,Computer Aided Geometric Design 27 340 -358

Deng , C.,Lin , H.,Computer-AidedDesign, 2014.“Progressive and Iterative Approximation for Least Squares B-Spline Curve and Surface Fitting”, 47 32 -44

Mustafa , G.,Li , H.,Deng, 2015.Regression Based Subdivision Schemes for Noisy Data”,ComputerAided Design 58 189 -199

Dyn , N.,Heard , A.,Hormann , K.,Sharona,Computer-AidedDesign, 2015.Univariate Subdivision Schemes for Noisy Data with Geometric Applications”, 37 85 -104

Mustafa , G.,Bari , M.,Nosheen , S., 2016.Modeling of 3D Objects by Subdivision Scheme”,Proceedings of 6th International Conference on Innovative Computing Technology -

Mustafa , G.,Bari , M., 2016.Wide-Ranging Families of Subdivision Schemes for Fitting Data”, 48 125 -134

Mustafa , G.,Bari , M.,Sadiq , A., 2017.The (2n)2-Point Scheme Based on Bivariate Cubic Polynomial”, 49 27 -35

Shi , B.Q.,Liang, 2016.An Integration Method for Scanned Multi-View Range Images (MRIs) Based on Local Weighted Least Squares (LWLS) Surface Fitting”, 77 64 -78

Vilca , F.,Romeiro , R.G.,Balakrishnan , N., “ A Bivariate,Birnbaum-Saunders Regression, 2016.,Computational Statistics and Data Analysis 97 169 -183

Bari , M.,Bashir , R.,Mustafa, 2017.“3n-Point Quaternary Shape Preserving Subdivision Scheme”, 36 489 -500

Bari,Mustafa, 2017.“A Family of 2n-Point Ternary Non-Stationary Interpolating Subdivision Scheme”, 36 921 -932

Bari , M., 2017.Stationary and Non-Stationary Subdivision Schemes and their Applications”,Ph.D. Thesis -