3n-Point Quaternary Shape Preserving Subdivision Schemes
In this paper, an algorithm is defined to construct 3n-point quaternary approximating subdivision schemes which are useful to design different geometric objects in the field of geometric modeling. We are going to establish a family of approximating schemes because approximating scheme provide maximu...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Mehran University of Engineering and Technology
2017-07-01
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| Series: | Mehran University Research Journal of Engineering and Technology |
| Subjects: | |
| Online Access: | http://publications.muet.edu.pk/research_papers/pdf/pdf1560.pdf |
| _version_ | 1818032373516730368 |
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| author | MEHWISH BARI ROBINA BASHIR GHULAM MUSTAFA |
| author_facet | MEHWISH BARI ROBINA BASHIR GHULAM MUSTAFA |
| author_sort | MEHWISH BARI |
| collection | DOAJ |
| description | In this paper, an algorithm is defined to construct 3n-point quaternary approximating subdivision schemes which are useful to design different geometric objects in the field of geometric modeling. We are going to establish a family of approximating schemes because approximating scheme provide maximum smoothness as compare to the interpolating schemes. It is to be observed that the proposed schemes satisfying the basic sum rules with bell-shaped mask go up to the convergent subdivision schemes which preserve monotonicity. We analyze the shape-preserving properties such that convexity and concavity of proposed schemes. We also show that quaternary schemes associated to the certain refinable functions with dilation 4 have higher order shape preserving properties. We also calculated the polynomial reproduction of proposed quaternary approximating subdivision schemes. The proposed schemes have tension parameter, so by choosing different values of the tension parameter we can get different limit curves of initial control polygon. We show in the table form that the proposed schemes are better than the existing schemes by comparing them on the behalf of their support and continuity. The visual quality of proposed schemes is demonstrated by different snapshots. |
| first_indexed | 2024-12-10T06:06:20Z |
| format | Article |
| id | doaj.art-724bf153e75e4c429ef74f06ca836d6a |
| institution | Directory Open Access Journal |
| issn | 0254-7821 2413-7219 |
| language | English |
| last_indexed | 2024-12-10T06:06:20Z |
| publishDate | 2017-07-01 |
| publisher | Mehran University of Engineering and Technology |
| record_format | Article |
| series | Mehran University Research Journal of Engineering and Technology |
| spelling | doaj.art-724bf153e75e4c429ef74f06ca836d6a2022-12-22T01:59:41ZengMehran University of Engineering and TechnologyMehran University Research Journal of Engineering and Technology0254-78212413-72192017-07-0136348950015603n-Point Quaternary Shape Preserving Subdivision SchemesMEHWISH BARIROBINA BASHIRGHULAM MUSTAFAIn this paper, an algorithm is defined to construct 3n-point quaternary approximating subdivision schemes which are useful to design different geometric objects in the field of geometric modeling. We are going to establish a family of approximating schemes because approximating scheme provide maximum smoothness as compare to the interpolating schemes. It is to be observed that the proposed schemes satisfying the basic sum rules with bell-shaped mask go up to the convergent subdivision schemes which preserve monotonicity. We analyze the shape-preserving properties such that convexity and concavity of proposed schemes. We also show that quaternary schemes associated to the certain refinable functions with dilation 4 have higher order shape preserving properties. We also calculated the polynomial reproduction of proposed quaternary approximating subdivision schemes. The proposed schemes have tension parameter, so by choosing different values of the tension parameter we can get different limit curves of initial control polygon. We show in the table form that the proposed schemes are better than the existing schemes by comparing them on the behalf of their support and continuity. The visual quality of proposed schemes is demonstrated by different snapshots.http://publications.muet.edu.pk/research_papers/pdf/pdf1560.pdfSubdivisionQuaternaryTension ControlBell-Shaped MaskConvexityConcavity |
| spellingShingle | MEHWISH BARI ROBINA BASHIR GHULAM MUSTAFA 3n-Point Quaternary Shape Preserving Subdivision Schemes Mehran University Research Journal of Engineering and Technology Subdivision Quaternary Tension Control Bell-Shaped Mask Convexity Concavity |
| title | 3n-Point Quaternary Shape Preserving Subdivision Schemes |
| title_full | 3n-Point Quaternary Shape Preserving Subdivision Schemes |
| title_fullStr | 3n-Point Quaternary Shape Preserving Subdivision Schemes |
| title_full_unstemmed | 3n-Point Quaternary Shape Preserving Subdivision Schemes |
| title_short | 3n-Point Quaternary Shape Preserving Subdivision Schemes |
| title_sort | 3n point quaternary shape preserving subdivision schemes |
| topic | Subdivision Quaternary Tension Control Bell-Shaped Mask Convexity Concavity |
| url | http://publications.muet.edu.pk/research_papers/pdf/pdf1560.pdf |
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