Open AccessA Family of 6-Point n-Ary Interpolating Subdivision Schemes
Author(s) -
Robina Bashir,
Ghulam Mustafa
Publication year - 2018
Publication title -
mehran university research journal of engineering and technology
Language(s) - English
Resource type - Journals
eISSN - 2413-7219
pISSN - 0254-7821
DOI - 10.22581/muet1982.1804.03
Subject(s) - division (mathematics) , subdivision , mathematics , interpolation (computer graphics) , monotonic function , polynomial , point (geometry) , degree (music) , property (philosophy) , ternary operation , discrete mathematics , combinatorics , algorithm , geometry , computer science , mathematical analysis , arithmetic , image (mathematics) , artificial intelligence , philosophy , physics , archaeology , epistemology , acoustics , history , programming language
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.