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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,,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.
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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