ISSN:
1432-0940
Keywords:
41A15
;
65Q05
;
68U05
;
65D10
;
Curve design
;
Control polygon
;
Limit curve
;
Subdivision scheme
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The paper analyses the convergence of sequences of control polygons produced by a binary subdivision scheme of the form $$\begin{array}{*{20}c} {f_{2i}^{k + 1} = \sum\limits_{j = 0}^m {a_j f_{i + j}^k } ,} & {f_{2i + 1}^{k + 1} = \sum\limits_{j = 0}^m {b_j f_{i + j}^k ,} } & {i \in Z,k = 0,1,2,....} \\ \end{array}$$ The convergence of the control polygons to aC° curve is analysed in terms of the convergence to zero of a derived scheme for the differencesf i+1 k −f i k . The analysis of the smoothness of the limit curve is reduced to the convergence analysis of “differentiated” schemes which correspond to divided differences off i k ∶i∈ Z with respect to the diadic parametrizationt i k =i/2 k . The inverse process of “integration” provides schemes with limit curves having additional orders of smoothness.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01888150
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