A Family of 6-Point n-Ary Interpolating Subdivision Schemes

  • Robina Bashir Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur.
  • Ghulam Mustafa Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur

Abstract

We derive three-step algorithm based on divided difference to generate a class of 6-point n-ary interpolating sub-division schemes. In this technique second order divided differences have been calculated at specific position and used to insert new vertices. Interpolating sub-division schemes are more attractive than approximating schemes in computer aided geometric designs because of their interpolation property. Polynomial generation and polynomial reproduction are attractive properties of sub-division schemes. Shape preserving properties are also significant tool in sub-division schemes. Further, some significant properties of ternary and quaternary sub-division schemes have been elaborated such as continuity, degree of polynomial generation, polynomial reproduction and approximation order. Furthermore, shape preserving property that is monotonicity is also derived. Moreover, the visual performance of proposed schemes has also been demonstrated through several examples.

Published
Oct 1, 2018
How to Cite
BASHIR, Robina; MUSTAFA, Ghulam. A Family of 6-Point n-Ary Interpolating Subdivision Schemes. Mehran University Research Journal of Engineering and Technology, [S.l.], v. 37, n. 4, p. 481-490, oct. 2018. ISSN 2413-7219. Available at: <http://publications.muet.edu.pk/index.php/muetrj/article/view/556>. Date accessed: 10 dec. 2018. doi: http://dx.doi.org/10.22581/muet1982.1804.03.
This is an open Access Article published by Mehran University of Engineering and Technolgy, Jamshoro under CCBY 4.0 International License