摘要
细分格式是一种在初始控制网格基础上,通过迭代局部加细并应用特定拓扑规则,逐步形成光滑曲线或曲面的迭代方法.m重2N点Dubuc-Deslauriers细分格式是一种广泛应用的插值型格式.当重数m或N较大时,由于涉及多个控制顶点,Dubuc-Deslauriers细分格式面临计算效率和稳定性的挑战.通过将一次加细操作分解为多次小范围操作,Dubuc-Deslauriers细分格式的递推公式形式有效提高了计算稳定性.给出了m重2N点Dubuc-Deslauriers细分格式递推公式的生成函数的表达式,并探讨了2重和3重情况的特殊形式.
Subdivision schemes are iterative methods for creating smooth curves or surfaces by iteratively refining a starting control mesh and applying specific topological rules.The m-ary 2 N-point Dubuc-Deslauriers subdivision scheme is widely employed as an interpolatory scheme.When the arity m or N is large,the Dubuc-Deslauriers subdivision scheme encounters challenges related to computational 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 2 N-point Dubuc-Deslauriers subdivision[JP2]schemes and explores the special forms for the cases of binary and ternary subdivision schemes.
作者
亓万锋
刘美彤
曹宏
孙雯雯
QI Wanfeng;LIU Meitong;CAO Hong;SUN Wenwen(School of Mathematics,Liaoning Normal University,Dalian 116081,China)
出处
《辽宁师范大学学报（自然科学版）》
CAS
2024年第1期16-20,共5页
Journal of Liaoning Normal University:Natural Science Edition
基金
辽宁省教育厅青年项目(LQ2020020)。
