In this paper, we present an algebraic perspective of the de Rham transform of a binary subdivision scheme and propose an elegant strategy for constructing dual m-ary approximating subdivision schemes of de Rham-type, starting from two primal schemes of aritym and 2, respectively. On the one hand, this new strategy allows us to show that several existing dual corner-cutting subdivision schemes fit into a unified framework. On the other hand, the proposed strategy provides a straightforward algorithm for constructing new dual subdivision schemes having higher smoothness and higher polynomial reproduction capabilities with respect to the two given primal schemes
Dual univariate m-ary subdivision schemes of de Rham-type / Costanza Conti;Lucia Romani. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 407:(2013), pp. 443-456. [10.1016/j.jmaa.2013.05.009]
Dual univariate m-ary subdivision schemes of de Rham-type
CONTI, COSTANZA;
2013
Abstract
In this paper, we present an algebraic perspective of the de Rham transform of a binary subdivision scheme and propose an elegant strategy for constructing dual m-ary approximating subdivision schemes of de Rham-type, starting from two primal schemes of aritym and 2, respectively. On the one hand, this new strategy allows us to show that several existing dual corner-cutting subdivision schemes fit into a unified framework. On the other hand, the proposed strategy provides a straightforward algorithm for constructing new dual subdivision schemes having higher smoothness and higher polynomial reproduction capabilities with respect to the two given primal schemesFile | Dimensione | Formato | |
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