Subdivision schemes are iterative methods for creating smooth curves or surfaces by itera-tively refining a starting control mesh and applying specific topological rules.The m-ary 2N-point Dubuc-Deslauriers subdivision scheme is widely employed as an interpolatory scheme.When the aritym or N is large,the Dubuc-Deslauriers subdivision scheme encounters challenges related to computa-tional efficiency and stability due to the involvement of a relatively large number of control vertices.By dividing a single refinement operation into multiple smaller-scale operations,the recursive formula of the Dubuc-Deslauriers scheme effectively improves computational stability.This paper presents the expression for the generating function of the recursive formula for the m-ary 2N-point Dubuc-Deslauriers subdivision schemes and explores the special forms for the cases of binary and ternary subdivision schemes.
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