Ternary approximating non-stationary subdivision schemes for curve design

Abstract: In this paper, an algorithm has been introduced to produce ternary 2m-point (for any integer m ≥ 1) approximating non-stationary subdivision schemes which can generate the linear spaces spanned by {1; cos (α.); sin (α.)}. The theory of asymptotic equivalence is being used to analyze the convergence and smoothness of the schemes. The proposed algorithm can be consider as the non-stationary counter part of the 2-point and 4-point existing ternary stationary approximating schemes, for different values of m. Moreover, the proposed algorithm has the ability to reproduce or regenerate the conic sections, trigonometric polynomials and trigonometric splines.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Ternary approximating non-stationary subdivision schemes for curve design ; volume:4 ; number:4 ; year:2014 ; pages:371-378 ; extent:8 ; Open engineering ; 4, Heft 4 (2014), 371-378 (gesamt 8)

Contributors, Places and Time

• Creator: Siddiqi, Shahid ; Younis, Muhammad

Further information

• DOI: 10.2478/s13531-013-0149-y
• URN: urn:nbn:de:101:1-2412141811257.738405457327
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:30 AM CEST