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http://bura.brunel.ac.uk/handle/2438/2080
Title: | Analysis of uniform binary subdivision schemes for curve design |
Authors: | Dyn, N Gregory, JA Levin, D |
Issue Date: | 1988 |
Publisher: | Brunel University |
Citation: | Maths Technical Papers (Brunel University). September 1988, pp 1-28 |
Abstract: | The paper analyses the convergence of sequences of control polygons produced by a binary subdivision scheme of the form .0,1,2,...kz,ikj,ifjbm0j1k12ifjam0j1k2if=∈+Σ==++Σ==+ The convergence of the control polygons to a Cu curve is analysed in terms of the convergence to zero of a derived scheme for the differences - . The analysis of the smoothness of the limit curve is reduced to kif the convergence analysis of "differentiated" schemes which correspond to divided differences of {/i ∈Z} with respect to the diadic parameteriz- kif ation = i/2kitk . The inverse process of "integration" provides schemes with limit curves having additional orders of smoothness. |
URI: | http://bura.brunel.ac.uk/handle/2438/2080 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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TR_06_88.pdf | 392.31 kB | Adobe PDF | View/Open |
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