A Computational Method for Subdivision Depth of Ternary Schemes

Faheem Khan, Ghulam Mustafa, Aamir Shahzad, Dumitru Baleanu and Maysaa M. Al-Qurashi
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Faheem Khan: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Ghulam Mustafa: Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
Aamir Shahzad: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Dumitru Baleanu: Department of Mathematics, Cankaya University, Ankara 06530, Turkey
Maysaa M. Al-Qurashi: Department of Mathematics, King Saud University, Riyadh 11495, Saudi Arabia

Mathematics, 2020, vol. 8, issue 5, 1-22

Abstract: Subdivision schemes are extensively used in scientific and practical applications to produce continuous shapes in an iterative way. This paper introduces a framework to compute subdivision depths of ternary schemes. We first use subdivision algorithm in terms of convolution to compute the error bounds between two successive polygons produced by refinement procedure of subdivision schemes. Then, a formula for computing bound between the polygon at k -th stage and the limiting polygon is derived. After that, we predict numerically the number of subdivision steps (depths) required for smooth limiting shape based on the demand of user specified error (distance) tolerance. In addition, extensive numerical experiments were carried out to check the numerical outcomes of this new framework. The proposed methods are more efficient than the method proposed by Song et al.

Keywords: subdivision schemes; convolution; error bounds; subdivision depth; subdivision level (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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