2019
DOI: 10.3390/math7070639
|View full text |Cite
|
Sign up to set email alerts
|

A New Class of 2q-Point Nonstationary Subdivision Schemes and Their Applications

Abstract: The main objective of this study is to introduce a new class of 2 q -point approximating nonstationary subdivision schemes (ANSSs) by applying Lagrange-like interpolant. The theory of asymptotic equivalence is applied to find the continuity of the ANSSs. These schemes can be nicely generalized to contain local shape parameters that allow the user to locally adjust the shape of the limit curve/surface. Moreover, many existing approximating stationary subdivision schemes (ASSSs) can be obtained as nonstat… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
5

Citation Types

0
7
0

Year Published

2020
2020
2022
2022

Publication Types

Select...
5
4

Relationship

3
6

Authors

Journals

citations
Cited by 15 publications
(7 citation statements)
references
References 32 publications
(90 reference statements)
0
7
0
Order By: Relevance
“…Much research has been done on continued fraction theory and its application by Tan [16]. Ghaffar et al discussed a new class of 2q-point nonstationary subdivision schemes and their application [17]. Ashraf et al analyzed the ternary four-point rational interpolating subdivision scheme's geometric properties [18,19].…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Much research has been done on continued fraction theory and its application by Tan [16]. Ghaffar et al discussed a new class of 2q-point nonstationary subdivision schemes and their application [17]. Ashraf et al analyzed the ternary four-point rational interpolating subdivision scheme's geometric properties [18,19].…”
Section: Introductionmentioning
confidence: 99%
“…Ashraf et al analyzed the ternary four-point rational interpolating subdivision scheme's geometric properties [18,19]. More subdivision schemes are studied in [17,[20][21][22].…”
Section: Introductionmentioning
confidence: 99%
“…Yonggang et al [3] proved that the trigonometric polynomial B-spline curves not only inherit the useful advantage of the polynomial curve but also have reconstructing property of the trigonometric curve. Due to its importance in generating images, several unifications to the nonstationary schemes such as interpolating and approximating are discussed in the literature [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Being two various subjects that had been improving individually and in parallel, the relation between curves and surfaces of SSs have sought after.…”
Section: Introductionmentioning
confidence: 99%
“…Zulkifli et al [18] discussed the application of new rational bi-cubic Ball function with six parameters in image interpolation, especially for the gray scale image. For more recent work on SS one may refer to References [19][20][21][22][23].…”
Section: Introductionmentioning
confidence: 99%