Ternary Even Symmetric 2n-Point Subdivision

Zheng, Haibin; Hu, Meigui; Peng, Guohua

doi:10.1109/cise.2009.5363033

Cited by 7 publications

(3 citation statements)

References 8 publications

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“… With the special values of parameter ( w 0  and 1 w 4  ), the subdivision schemes generated by B-splines of degree 4 and 6, respectively, are obtained from the schemes (8).  Moreover, the proposed scheme (8) is a generalized scheme, as the mask of the proposed scheme coincides with the mask of schemes [9,[11][12][13] in (9), the proposed 4-point scheme can also be considered as the general form of the stationary 4-point ternary approximating schemes of [8,13,16], respectively.  For substituting 21 w 8  …”

Section: Comparison and Applicationmentioning

confidence: 99%

The 4-Point α-Ary Approximating Subdivision Scheme

Ghaffar¹,

Mustafa

Qin

2013

OJAppS

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A general formula for 4-point -Ary approximating subdivision scheme for curve designing is introduced for any arity 2  . The new scheme is extension of B-spline of degree 6. Laurent polynomial method is used to investigate the continuity of the scheme. The variety of effects can be achieved in correspondence for different values of parameter. The applications of the proposed scheme are illustrated in comparison with the established subdivision schemes.

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Section: Comparison and Applicationmentioning

confidence: 99%

The 4-Point α-Ary Approximating Subdivision Scheme

Ghaffar¹,

Mustafa

Qin

2013

OJAppS

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“…Zheng et al [14] used B-spline to construct a 2n-ary SS. In 2013, Mustafa et al [15] worked on odd point ternary families of approximating SSs, in which they showed that their SSs have high smoothness.…”

Section: Introductionmentioning

confidence: 99%

Construction and Application of Nine-Tic B-Spline Tensor Product SS

et al. 2019

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In this paper, we propose and analyze a tensor product of nine-tic B-spline subdivision scheme (SS) to reduce the execution time needed to compute the subdivision process of quad meshes. We discuss some essential features of the proposed SS such as continuity, polynomial generation, joint spectral radius, holder regularity and limit stencil. Some results of the SS using surface modeling with the help of computer programming are shown. Author Contributions: Conceptualization, A.G., M.B. and M.I.; methodology, K.S.N. and D.B.; software, A.G., S.M.H. and R.M.; validation, A.G. and K.S.N.; formal analysis, S.M.H., D.B. and R.M.; writing-original draft preparation, A.G., M.I., M.B., S.M.H. and R.M.; writing-review and editing, K.S.N. and D.B. Funding: This research received no external funding. Conflicts of Interest:The authors declare no conflict of interest.

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“…Lian [10] offered 2m-point non-parametric interpolating even and odd ary schemes for curve design. Zheng et al [20] offered ternary even symmetric 271point subdivision scheme. Zheng et al [18] presented p-ary subdivision generalizing B-splines.…”

Section: Introductionmentioning

confidence: 99%

Generalized and Unified Families of Interpolating Subdivision Schemes

Mustafa¹

2014

NMTMA

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We present generalized and unified families of (2n)-point and (2n -1)point p-ary interpolating subdivision schemes originated from Lagrange polynomial for any integers n > 2 and p > 3. Almost all existing even-point and odd-point interpolating schemes of lower and higher arity belong to this family of schemes. We also present tensor product version of generalized and unified families of schemes. M oreover error bounds betw een limit curves and control polygons of schemes are also calculated. It has been observed th at error bounds decrease w hen complexity of the scheme decrease and vice versa. Furtherm ore, error bounds decrease w ith the increase of arity of the schemes. We also observe that in general the continuity of interpolating scheme do not increase by increasing complexity and arity of the scheme.

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Ternary Even Symmetric 2n-Point Subdivision

Cited by 7 publications

References 8 publications

The 4-Point α-Ary Approximating Subdivision Scheme

The 4-Point α-Ary Approximating Subdivision Scheme

Construction and Application of Nine-Tic B-Spline Tensor Product SS

Generalized and Unified Families of Interpolating Subdivision Schemes

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