The mask of (2b + 4)-point n-ary subdivision scheme

Mustafa, Ghulam; Rehman, Najma Abdul

doi:10.1007/s00607-010-0108-x

Cited by 20 publications

(11 citation statements)

References 12 publications

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“…Mustafa and Khan [5] showed ternary 6-point interpolation subdivision scheme which used shape parameter for designing curves. A general formulae was introduced by Muatafa and Rehman [6] to cover (2b+4)-point n-ary interpolation and approximation schemes for every integers b 0 and n2. Mustafa and Bashir [7] proposed a very potential but easy algorithm for producing 4-point n-ary interpolation scheme.…”

Section: Introductionmentioning

confidence: 99%

A Family of 6-Point n-Ary Interpolating Subdivision Schemes

Bashir

Mustafa

2018

Mehran Univ. res. j. eng. technol.

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We derive three-step algorithm based on divided difference to generate a class of 6-point n-ary interpolating sub-division schemes. In this technique second order divided differences have been calculated at specific position and used to insert new vertices. Interpolating sub-division schemes are more attractive than approximating schemes in computer aided geometric designs because of their interpolation property. Polynomial generation and polynomial reproduction are attractive properties of sub-division schemes.Shape preserving properties are also significant tool in sub-division schemes. Further, some significant properties of ternary and quaternary sub-division schemes have been elaborated such as continuity, degree of polynomial generation, polynomial reproduction and approximation order. Furthermore, shape preserving property that is monotonicity is also derived. Moreover, the visual performance of proposed schemes has also been demonstrated through several examples.

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Section: Introductionmentioning

confidence: 99%

A Family of 6-Point n-Ary Interpolating Subdivision Schemes

Bashir

Mustafa

2018

Mehran Univ. res. j. eng. technol.

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“…Mustafa and Khan [22] constructed a new 4-point quaternary approximating subdivision scheme having the higher smoothness and approximation order but smaller support than existing 4-point binary and ternary schemes. Mustafa and Rehman [24] have presented general formulae for the mask of (2b + 4)-point n-ary interpolating and approximating schemes for any integer b 0 and n 2. Ghaffar et al [12,13] have presented an explicit formulae for the mask of 3-point and 4-point a-ary approximating subdivision schemes, respectively.…”

Section: Introductionmentioning

confidence: 99%

A class of shape preserving 5-point n-ary approximating schemes

Bashir¹,

Mustafa²,

Agarwal³

2018

J. Math. Computer Sci.

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A new class of shape preserving relaxed 5-point n-ary approximating subdivision schemes is presented. Further, the conditions on the initial data assuring monotonicity, convexity and concavity preservation of the limit functions are derived. Furthermore, some significant properties of ternary and quaternary subdivision schemes have been elaborated such as continuity, Hölder exponent, polynomial generation, polynomial reproduction, approximation order, and support of basic limit function. Moreover the visual performance of schemes has also been demonstrated through several examples.

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“…Zheng et al [18] presented p-ary subdivision generalizing B-splines. Mustafa and Najma [14] unified all existing even-point interpolating and approximating schemes by offering general formula for the mask of (2b + 4 )-point even-ary subdivision scheme. Now we present brief review of higher arity schemes having odd-point complex ity.…”

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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The mask of (2b + 4)-point n-ary subdivision scheme

Cited by 20 publications

References 12 publications

A Family of 6-Point n-Ary Interpolating Subdivision Schemes

A Family of 6-Point n-Ary Interpolating Subdivision Schemes

A class of shape preserving 5-point n-ary approximating schemes

Generalized and Unified Families of Interpolating Subdivision Schemes

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