Approximation of conic sections by weighted Lupaş post-quantum Bézier curves
This paper deals with weighted Lupaş post-quantum Bernstein blending functions and Bézier curves constructed with the help of bases via (p,q)\left(p,q)-integers. These blending functions form normalized totally positive bases. Due to the rational nature of weighted Lupaş post-quantum Bézier curves a...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-08-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2022-0016 |
| _version_ | 1797998380339691520 |
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| author | Khan Asif Iliyas Mohammad Khan Khalid Mursaleen Mohammad |
| author_facet | Khan Asif Iliyas Mohammad Khan Khalid Mursaleen Mohammad |
| author_sort | Khan Asif |
| collection | DOAJ |
| description | This paper deals with weighted Lupaş post-quantum Bernstein blending functions and Bézier curves constructed with the help of bases via (p,q)\left(p,q)-integers. These blending functions form normalized totally positive bases. Due to the rational nature of weighted Lupaş post-quantum Bézier curves and positive weights, they help in investigating from geometric point of view. Their degree elevation properties and de Casteljau algorithm have been studied. It has been shown that quadratic weighted Lupaş post-quantum Bézier curves can represent conic sections in two-dimensional plane. Graphical analysis has been presented to discuss geometric interpretation of weight and conic section representation by weighted Lupaş post-quantum Bézier curves. This new generalized weighted Lupaş post-quantum Bézier curve provides better approximation and flexibility to a particular control point as well as control polygon due to extra parameter pp and qq in comparison to classical rational Bézier curves, Lupaş qq-Bézier curves and weighted Lupaş qq-Bézier curves. |
| first_indexed | 2024-04-11T10:47:50Z |
| format | Article |
| id | doaj.art-99f2091beb264934b0feeb10c2e3343b |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-04-11T10:47:50Z |
| publishDate | 2022-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-99f2091beb264934b0feeb10c2e3343b2022-12-22T04:29:00ZengDe GruyterDemonstratio Mathematica2391-46612022-08-0155132834210.1515/dema-2022-0016Approximation of conic sections by weighted Lupaş post-quantum Bézier curvesKhan Asif0Iliyas Mohammad1Khan Khalid2Mursaleen Mohammad3Department of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaSchool of Computer and System Sciences, SC & SS, J.N.U. New Delhi 110067, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaThis paper deals with weighted Lupaş post-quantum Bernstein blending functions and Bézier curves constructed with the help of bases via (p,q)\left(p,q)-integers. These blending functions form normalized totally positive bases. Due to the rational nature of weighted Lupaş post-quantum Bézier curves and positive weights, they help in investigating from geometric point of view. Their degree elevation properties and de Casteljau algorithm have been studied. It has been shown that quadratic weighted Lupaş post-quantum Bézier curves can represent conic sections in two-dimensional plane. Graphical analysis has been presented to discuss geometric interpretation of weight and conic section representation by weighted Lupaş post-quantum Bézier curves. This new generalized weighted Lupaş post-quantum Bézier curve provides better approximation and flexibility to a particular control point as well as control polygon due to extra parameter pp and qq in comparison to classical rational Bézier curves, Lupaş qq-Bézier curves and weighted Lupaş qq-Bézier curves.https://doi.org/10.1515/dema-2022-0016post-quantum integersweighted lupaş post-quantum bézier curverational bézier curvenormalized totally positive basisshape parameterconic sections65d1741a1041a2541a36 |
| spellingShingle | Khan Asif Iliyas Mohammad Khan Khalid Mursaleen Mohammad Approximation of conic sections by weighted Lupaş post-quantum Bézier curves Demonstratio Mathematica post-quantum integers weighted lupaş post-quantum bézier curve rational bézier curve normalized totally positive basis shape parameter conic sections 65d17 41a10 41a25 41a36 |
| title | Approximation of conic sections by weighted Lupaş post-quantum Bézier curves |
| title_full | Approximation of conic sections by weighted Lupaş post-quantum Bézier curves |
| title_fullStr | Approximation of conic sections by weighted Lupaş post-quantum Bézier curves |
| title_full_unstemmed | Approximation of conic sections by weighted Lupaş post-quantum Bézier curves |
| title_short | Approximation of conic sections by weighted Lupaş post-quantum Bézier curves |
| title_sort | approximation of conic sections by weighted lupas post quantum bezier curves |
| topic | post-quantum integers weighted lupaş post-quantum bézier curve rational bézier curve normalized totally positive basis shape parameter conic sections 65d17 41a10 41a25 41a36 |
| url | https://doi.org/10.1515/dema-2022-0016 |
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