Generalized B\'{e}zier curves based on Bernstein-Stancu-Chlodowsky type operators
In this paper, we use the blending functions of Bernstein-Stancu-Chlodowsky type operators with shifted knots for construction of modified Chlodowsky B\'{e}zier curves. We study the nature of degree elevation and degree reduction for B\'{e}zier Bernstein-Stancu-Chlodowsky functions with s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática
2022-02-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/52003 |
| _version_ | 1797633507898425344 |
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| author | Kejal Khatri Vishnu Narayan Mishra |
| author_facet | Kejal Khatri Vishnu Narayan Mishra |
| author_sort | Kejal Khatri |
| collection | DOAJ |
| description |
In this paper, we use the blending functions of Bernstein-Stancu-Chlodowsky type operators with shifted knots for construction of modified Chlodowsky B\'{e}zier curves. We study the nature of degree elevation and degree reduction for B\'{e}zier Bernstein-Stancu-Chlodowsky functions with shifted knots for $t \in [\frac{\gamma}{n+\delta},\frac{n+\gamma}{n+\delta}]$. We also present a de Casteljau algorithm to compute Bernstein B\'{e}zier curves with shifted knots. The new curves have some properties similar to B\'{e}zier curves. Furthermore, some fundamental properties for Bernstein B\'{e}zier curves are discussed. Our generalizations show more flexibility in taking the value of $\gamma$ and $\delta$ and advantage in shape control of curves. The shape parameters give more convenience for the curve modelling.
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| first_indexed | 2024-03-11T11:55:00Z |
| format | Article |
| id | doaj.art-a19d3c1c1ce9496bb6a6cf5b402f94d3 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-03-11T11:55:00Z |
| publishDate | 2022-02-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-a19d3c1c1ce9496bb6a6cf5b402f94d32023-11-08T19:49:19ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882022-02-014010.5269/bspm.52003Generalized B\'{e}zier curves based on Bernstein-Stancu-Chlodowsky type operatorsKejal Khatri0Vishnu Narayan Mishra1Govt. College SimalwaraIndira Gandhi National Tribal University In this paper, we use the blending functions of Bernstein-Stancu-Chlodowsky type operators with shifted knots for construction of modified Chlodowsky B\'{e}zier curves. We study the nature of degree elevation and degree reduction for B\'{e}zier Bernstein-Stancu-Chlodowsky functions with shifted knots for $t \in [\frac{\gamma}{n+\delta},\frac{n+\gamma}{n+\delta}]$. We also present a de Casteljau algorithm to compute Bernstein B\'{e}zier curves with shifted knots. The new curves have some properties similar to B\'{e}zier curves. Furthermore, some fundamental properties for Bernstein B\'{e}zier curves are discussed. Our generalizations show more flexibility in taking the value of $\gamma$ and $\delta$ and advantage in shape control of curves. The shape parameters give more convenience for the curve modelling. https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/52003 |
| spellingShingle | Kejal Khatri Vishnu Narayan Mishra Generalized B\'{e}zier curves based on Bernstein-Stancu-Chlodowsky type operators Boletim da Sociedade Paranaense de Matemática |
| title | Generalized B\'{e}zier curves based on Bernstein-Stancu-Chlodowsky type operators |
| title_full | Generalized B\'{e}zier curves based on Bernstein-Stancu-Chlodowsky type operators |
| title_fullStr | Generalized B\'{e}zier curves based on Bernstein-Stancu-Chlodowsky type operators |
| title_full_unstemmed | Generalized B\'{e}zier curves based on Bernstein-Stancu-Chlodowsky type operators |
| title_short | Generalized B\'{e}zier curves based on Bernstein-Stancu-Chlodowsky type operators |
| title_sort | generalized b e zier curves based on bernstein stancu chlodowsky type operators |
| url | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/52003 |
| work_keys_str_mv | AT kejalkhatri generalizedbeziercurvesbasedonbernsteinstancuchlodowskytypeoperators AT vishnunarayanmishra generalizedbeziercurvesbasedonbernsteinstancuchlodowskytypeoperators |