Dual univariate \(m\)-ary subdivision schemes of de Rham-type. (English) Zbl 1306.65163
Summary: 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 arity \(m\) 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.
MSC:
| 65D17 | Computer-aided design (modeling of curves and surfaces) |
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
Keywords:
linear subdivision; arity \(m\); primal and dual parametrization; smoothness; polynomial reproductionReferences:
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