Error bounds for a class of subdivision schemes based on the two-scale refinement equation

Moncayo, M.; Amat, Sergio

doi:10.1016/j.cam.2011.06.031

Cited by 9 publications

(9 citation statements)

References 9 publications

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“…Here we present some preliminary notations and results. Readers are referred to [12] for more details.…”

Section: Preliminaries Resultsmentioning

confidence: 99%

“…In this paper, the modified version of the numerical algorithm of [4,11,12] have been presented to compute the subdivision depths of the SSs for curves and surfaces design. Our algorithm can be used when the computation techniques of [4,11] fail.…”

Section: Discussionmentioning

confidence: 99%

“…Note that in [4], if δ > 1 then the error bounds can not be computed. But by [12] and by using our technique, we increase the value of k 0 until D k 0 becomes less than one.…”

Section: Remarkmentioning

confidence: 99%

“…However, Mustafa and Hashmi [11] determined subdivision depth computation for n-ary subdivision curves/surfaces by using the first forward difference technique. Moncayo and Amat [12] estimated error bounds for the class of SSs based on the two-scale refinement equation. The authors in [4][5][6][7][8][9][10][11] imposed these conditions to find their results.…”

Section: Introductionmentioning

confidence: 99%

“…But, it has been observed that all SSs do not satisfy the imposed condition. Amat et al [12] relaxed the condition in [4] for estimating the error bounds of binary SSs for curve designing. In this paper, we relax the conditions in the work of [5][6][7][8][9][10][11] and generalize the work of [12] to estimating error bounds and subdivision depths of binary SSs for curve and regular surface design.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes

et al. 2020

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Subdivision schemes are extensively used in scientific and practical applications to produce continuous geometrical shapes in an iterative manner. We construct a numerical algorithm to estimate subdivision depth between the limit curves/surfaces and their control polygons after k-fold subdivisions. In this paper, the proposed numerical algorithm for subdivision depths of binary subdivision curves and surfaces are obtained after some modification of the results given by Mustafa et al in 2006. This algorithm is very useful for implementation of the parametrization.

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“…Here we present some preliminary notations and results. Readers are referred to [12] for more details.…”

Section: Preliminaries Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…Note that in [4], if δ > 1 then the error bounds can not be computed. But by [12] and by using our technique, we increase the value of k 0 until D k 0 becomes less than one.…”

Section: Remarkmentioning

confidence: 99%