A Family of 6-Point n-Ary Interpolating Subdivision Schemes
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 mor...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Mehran University of Engineering and Technology
2018-10-01
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| Series: | Mehran University Research Journal of Engineering and Technology |
| Online Access: | http://publications.muet.edu.pk/index.php/muetrj/article/view/556 |
| Summary: | 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. |
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| ISSN: | 0254-7821 2413-7219 |