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Volume 12
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Article

A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes

by
Aamir Shahzad
1,
Faheem Khan
1,
Abdul Ghaffar
2,
Ghulam Mustafa
3,
Kottakkaran Sooppy Nisar
4,* and
Dumitru Baleanu
5,6,7
1
Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
2
Department of Mathematical Sciences, BUITEMS, Quetta 87300, Pakistan
3
Department of Mathematics, The Islamia University of bahawalpur, Punjab 63100, Pakistan
4
Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
5
Department of Mathematics, Cankaya University, Ankara 06530, Turkey
6
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40447, Taiwan
7
Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(1), 66; https://doi.org/10.3390/sym12010066
Submission received: 5 December 2019 / Revised: 20 December 2019 / Accepted: 22 December 2019 / Published: 1 January 2020
(This article belongs to the Special Issue Fixed Point Theory and Computational Analysis with Applications)
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Abstract

Subdivision schemes are extensively used in scientific and practical applications to produce continuous geometrical shapes in an iterative manner. We construct a numerical algorithm to estimate subdivision depth between the limit curves/surfaces and their control polygons after k-fold subdivisions. In this paper, the proposed numerical algorithm for subdivision depths of binary subdivision curves and surfaces are obtained after some modification of the results given by Mustafa et al in 2006. This algorithm is very useful for implementation of the parametrization.
Keywords: numerical analysis; algorithm; subdivision schemes; error bounds; subdivision depth numerical analysis; algorithm; subdivision schemes; error bounds; subdivision depth

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MDPI and ACS Style

Shahzad, A.; Khan, F.; Ghaffar, A.; Mustafa, G.; Nisar, K.S.; Baleanu, D. A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes. Symmetry 2020, 12, 66. https://doi.org/10.3390/sym12010066

AMA Style

Shahzad A, Khan F, Ghaffar A, Mustafa G, Nisar KS, Baleanu D. A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes. Symmetry. 2020; 12(1):66. https://doi.org/10.3390/sym12010066

Chicago/Turabian Style

Shahzad, Aamir, Faheem Khan, Abdul Ghaffar, Ghulam Mustafa, Kottakkaran Sooppy Nisar, and Dumitru Baleanu. 2020. "A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes" Symmetry 12, no. 1: 66. https://doi.org/10.3390/sym12010066

APA Style

Shahzad, A., Khan, F., Ghaffar, A., Mustafa, G., Nisar, K. S., & Baleanu, D. (2020). A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes. Symmetry, 12(1), 66. https://doi.org/10.3390/sym12010066

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