1987
DOI: 10.1016/0167-8396(87)90001-x
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A 4-point interpolatory subdivision scheme for curve design

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Cited by 530 publications
(335 citation statements)
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“…Another category of interest is interpolating subdivision, which implies that the samples at level j also belong to level j + 1. A famous example is the four-point scheme proposed by N. Dyn, J. Gregory and D. Levin in [13] …”
Section: Review Of Subdivisionmentioning
confidence: 99%
“…Another category of interest is interpolating subdivision, which implies that the samples at level j also belong to level j + 1. A famous example is the four-point scheme proposed by N. Dyn, J. Gregory and D. Levin in [13] …”
Section: Review Of Subdivisionmentioning
confidence: 99%
“…Our approach is similar but we consider subdivision algorithms of a more specific form and base the theory on a generalization of the difference analysis used in [4].…”
Section: Introductionmentioning
confidence: 99%
“…Two well-known examples are the Chaikin and Catmull-Clark algorithms, which respectively generate quadratic and cubic B-spline curves. More recently, an interpolatory subdivision scheme with shape control was proposed, see Dyn, Gregory, Levin [4]. Our purpose is to provide a convergence theory for such subdivision schemes.…”
Section: Introductionmentioning
confidence: 99%
“…Dyn et al [2] introduced a 4-point interpolating subdivision scheme for curve design. Later on, Deslauriers and Dubuc [3] introduced a symmetric iterative interpolation process.…”
Section: Introductionmentioning
confidence: 99%