A Computational Method for Subdivision Depth of Ternary Schemes

Clicks: 186
ID: 116209
2020
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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.
Reference Key
khan2020mathematicsa Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Faheem Khan;Ghulam Mustafa;Aamir Shahzad;Dumitru Baleanu;Maysaa M. Al-Qurashi;Khan, Faheem;Mustafa, Ghulam;Shahzad, Aamir;Baleanu, Dumitru;M. Al-Qurashi, Maysaa;
Journal Mathematics
Year 2020
DOI
10.3390/math8050817
URL
https://www.mdpi.com/2227-7390/8/5/817/htm
Keywords
subdivision schemes error bounds subdivision depth convolution subdivision level

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