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Volume 27, Issue 1
A Unified Three Point Approximating Subdivision Scheme

Ghulam Mustafa, Faheem Khan, Muhammad Sadia Hashmi & Muhammad Zeshan Afzal

Anal. Theory Appl., 27 (2011), pp. 10-20.

Published online: 2011-01

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  • Abstract

In this paper, we propose a three point approximating subdivision scheme, with three shape parameters, that unifies three different existing three point approximating schemes. Some sufficient conditions for subdivision curve $C^0$ to $C^3$ continuity and convergence of the scheme for generating tensor product surfaces for certain ranges of parameters by using Laurent polynomial method are discussed. The systems of curve and surface design based on our scheme have been developed successfully in garment CAD especially for clothes modelling.

  • AMS Subject Headings

65D17, 65D07, 65D05

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COPYRIGHT: © Global Science Press

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@Article{ATA-27-10, author = {}, title = {A Unified Three Point Approximating Subdivision Scheme}, journal = {Analysis in Theory and Applications}, year = {2011}, volume = {27}, number = {1}, pages = {10--20}, abstract = {

In this paper, we propose a three point approximating subdivision scheme, with three shape parameters, that unifies three different existing three point approximating schemes. Some sufficient conditions for subdivision curve $C^0$ to $C^3$ continuity and convergence of the scheme for generating tensor product surfaces for certain ranges of parameters by using Laurent polynomial method are discussed. The systems of curve and surface design based on our scheme have been developed successfully in garment CAD especially for clothes modelling.

}, issn = {1573-8175}, doi = {https://doi.org/10.1007/s10496-011-0010-1}, url = {http://global-sci.org/intro/article_detail/ata/4574.html} }
TY - JOUR T1 - A Unified Three Point Approximating Subdivision Scheme JO - Analysis in Theory and Applications VL - 1 SP - 10 EP - 20 PY - 2011 DA - 2011/01 SN - 27 DO - http://doi.org/10.1007/s10496-011-0010-1 UR - https://global-sci.org/intro/article_detail/ata/4574.html KW - approximating subdivision scheme, shape parameters, Laurent polynomial. AB -

In this paper, we propose a three point approximating subdivision scheme, with three shape parameters, that unifies three different existing three point approximating schemes. Some sufficient conditions for subdivision curve $C^0$ to $C^3$ continuity and convergence of the scheme for generating tensor product surfaces for certain ranges of parameters by using Laurent polynomial method are discussed. The systems of curve and surface design based on our scheme have been developed successfully in garment CAD especially for clothes modelling.

Ghulam Mustafa, Faheem Khan, Muhammad Sadia Hashmi & Muhammad Zeshan Afzal. (1970). A Unified Three Point Approximating Subdivision Scheme. Analysis in Theory and Applications. 27 (1). 10-20. doi:10.1007/s10496-011-0010-1
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