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.
Highlights
INTRODUCTIONSbranches of science such as CGGM (Computer Graphics, Geometric Modeling) and CAGD (Computer Aided Geometric Design)
We derive three-step algorithm based on divided difference to generate a class of 6-point n-ary interpolating sub-division schemes
Subdivision schemes became highly prominent compared to approximation schemes in geometric modeling
Summary
Sbranches of science such as CGGM (Computer Graphics, Geometric Modeling) and CAGD (Computer Aided Geometric Design). Mustafa and Khan [5] showed ternary 6-point interpolation subdivision scheme which used shape parameter for designing curves. Mustafa and Bashir [7] proposed a very potential but easy algorithm for producing 4-point n-ary interpolation scheme. Mustafa et al [8] gave a clear method to constract odd points n-ary, for every odd n 3 interpolation subdivision schemes. Cai [10] offered a 4point interpolation subdivision schemes, that is C1 continuous and discussed the monotonicity preservation of the limit curve. Shalom [14] presented a class of subdivision schemes with a finite support suitable for curve design and analyzed the monotonicity of the data. Numerical examples have been presented in the same part, and conclusion is presented in the last Section-4
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
