A novel numerical algorithm to estimate the subdivision depth of binary subdivision schemes

Aamir Shahzad; Faheem Khan; Abdul Ghaffar; Ghulam Mustafa; Kottakkaran Sooppy Nisar; Dumitru Baleanu

doi:10.3390/SYM12010066

A novel numerical algorithm to estimate the subdivision depth of binary subdivision schemes

Aamir Shahzad
, Faheem Khan
, Abdul Ghaffar
, Ghulam Mustafa
, Kottakkaran Sooppy Nisar
, Dumitru Baleanu

Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

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.

Original language	English
Article number	5604
Journal	Symmetry
Volume	12
Issue number	1
DOIs	https://doi.org/10.3390/SYM12010066
State	Published - 2020

Keywords

Algorithm
Error bounds
Numerical analysis
Subdivision depth
Subdivision schemes

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10.3390/SYM12010066

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title = "A novel numerical algorithm to estimate the subdivision depth of binary subdivision schemes",

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 = "Algorithm, Error bounds, Numerical analysis, Subdivision depth, Subdivision schemes",

author = "Aamir Shahzad and Faheem Khan and Abdul Ghaffar and Ghulam Mustafa and Nisar, \{Kottakkaran Sooppy\} and Dumitru Baleanu",

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language = "English",

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AU - Shahzad, Aamir

AU - Khan, Faheem

AU - Ghaffar, Abdul

AU - Mustafa, Ghulam

AU - Nisar, Kottakkaran Sooppy

AU - Baleanu, Dumitru

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Algorithm

KW - Error bounds

KW - Numerical analysis

KW - Subdivision depth

KW - Subdivision schemes

UR - https://www.scopus.com/pages/publications/85082417022

U2 - 10.3390/SYM12010066

DO - 10.3390/SYM12010066

M3 - Article

AN - SCOPUS:85082417022

SN - 2073-8994

VL - 12

JO - Symmetry

JF - Symmetry

IS - 1

M1 - 5604

ER -

A novel numerical algorithm to estimate the subdivision depth of binary subdivision schemes

Abstract

Keywords

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