Recursive Process for Constructing the Refinement Rules of New Combined Subdivision Schemes and Its Extended Form
In this article, we present a new method to construct a family of 2N+2-point binary subdivision schemes with one tension parameter. The construction of the family of schemes is based on repeated local translation of points by certain displacement vectors. Therefore, refinement rules of the 2N+2-poin...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6639706 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832560116464877568 |
|---|---|
| author | Rabia Hameed Ghulam Mustafa Jiansong Deng Shafqat Ali |
| author_facet | Rabia Hameed Ghulam Mustafa Jiansong Deng Shafqat Ali |
| author_sort | Rabia Hameed |
| collection | DOAJ |
| description | In this article, we present a new method to construct a family of 2N+2-point binary subdivision schemes with one tension parameter. The construction of the family of schemes is based on repeated local translation of points by certain displacement vectors. Therefore, refinement rules of the 2N+2-point schemes are recursively obtained from refinement rules of the 2N-point schemes. Thus, we get a new subdivision scheme at each iteration. Moreover, the complexity, polynomial reproduction, and polynomial generation of the schemes are increased by two at each iteration. Furthermore, a family of interproximate subdivision schemes with tension parameters is also introduced which is the extended form of the proposed family of schemes. This family of schemes allows a different tension value for each edge and vertex of the initial control polygon. These schemes generate curves and surfaces such that some initial control points are interpolated and others are approximated. |
| format | Article |
| id | doaj-art-71c6d29d6f014de890f860481a1bfd66 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-71c6d29d6f014de890f860481a1bfd662025-02-03T01:28:27ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66397066639706Recursive Process for Constructing the Refinement Rules of New Combined Subdivision Schemes and Its Extended FormRabia Hameed0Ghulam Mustafa1Jiansong Deng2Shafqat Ali3Department of Mathematics, The Government Sadiq College Women University Bahawalpur, Bahawalpur, Punjab 63100, PakistanDepartment of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Punjab 63100, PakistanSchool of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, ChinaDepartment of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Punjab 63100, PakistanIn this article, we present a new method to construct a family of 2N+2-point binary subdivision schemes with one tension parameter. The construction of the family of schemes is based on repeated local translation of points by certain displacement vectors. Therefore, refinement rules of the 2N+2-point schemes are recursively obtained from refinement rules of the 2N-point schemes. Thus, we get a new subdivision scheme at each iteration. Moreover, the complexity, polynomial reproduction, and polynomial generation of the schemes are increased by two at each iteration. Furthermore, a family of interproximate subdivision schemes with tension parameters is also introduced which is the extended form of the proposed family of schemes. This family of schemes allows a different tension value for each edge and vertex of the initial control polygon. These schemes generate curves and surfaces such that some initial control points are interpolated and others are approximated.http://dx.doi.org/10.1155/2021/6639706 |
| spellingShingle | Rabia Hameed Ghulam Mustafa Jiansong Deng Shafqat Ali Recursive Process for Constructing the Refinement Rules of New Combined Subdivision Schemes and Its Extended Form Journal of Mathematics |
| title | Recursive Process for Constructing the Refinement Rules of New Combined Subdivision Schemes and Its Extended Form |
| title_full | Recursive Process for Constructing the Refinement Rules of New Combined Subdivision Schemes and Its Extended Form |
| title_fullStr | Recursive Process for Constructing the Refinement Rules of New Combined Subdivision Schemes and Its Extended Form |
| title_full_unstemmed | Recursive Process for Constructing the Refinement Rules of New Combined Subdivision Schemes and Its Extended Form |
| title_short | Recursive Process for Constructing the Refinement Rules of New Combined Subdivision Schemes and Its Extended Form |
| title_sort | recursive process for constructing the refinement rules of new combined subdivision schemes and its extended form |
| url | http://dx.doi.org/10.1155/2021/6639706 |
| work_keys_str_mv | AT rabiahameed recursiveprocessforconstructingtherefinementrulesofnewcombinedsubdivisionschemesanditsextendedform AT ghulammustafa recursiveprocessforconstructingtherefinementrulesofnewcombinedsubdivisionschemesanditsextendedform AT jiansongdeng recursiveprocessforconstructingtherefinementrulesofnewcombinedsubdivisionschemesanditsextendedform AT shafqatali recursiveprocessforconstructingtherefinementrulesofnewcombinedsubdivisionschemesanditsextendedform |