Hyperbolic forms of ternary non-stationary subdivision schemes originated from hyperbolic B-splines

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• 作者：Shahid S. Siddiqi^a ; ^{shahidsiddiqiprof@yahoo.co.uk" class="auth_mail" title="E-mail the corresponding author} ; Wardat us Salam^b ; ^{wardahtussalam@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Kashif Rehan^c ; ^{kkashif_99@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Non-stationary subdivision schemes ; Ternary schemes ; Approximating ; Hyperbolic B-spline ; Curvature
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：1 August 2016
• 年：2016
• 卷：301
• 期：Complete
• 页码：16-27
• 全文大小：632 K

文摘

In this work ternary non-stationary subdivision schemes, based on hyperbolic B-spline basis functions, have been presented. The proposed hyperbolic, ternary three point and four point subdivision schemes, give pleasing as well as consistent curves with the control polygons as compared to the existing non-stationary subdivision schemes obtained from trigonometric B-splines. The main speciality of the hyperbolic schemes is that, they can reproduce hyperbolas and parabolas quite efficiently which has been demonstrated with the help of curvature plots.