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Interpolatory and Mixed Loop Schemes
Author(s) -
Shi Zhuo,
Lin Shujin,
Luo Xiaonan,
Wang Renhong
Publication year - 2008
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2008.01329.x
Subject(s) - subdivision , polygon mesh , scheme (mathematics) , interpolation (computer graphics) , loop (graph theory) , subdivision surface , limit (mathematics) , mathematics , simple (philosophy) , computer science , algorithm , mathematical optimization , topology (electrical circuits) , mathematical analysis , geometry , frame (networking) , combinatorics , telecommunications , philosophy , archaeology , epistemology , history
This paper presents a new interpolatory Loop scheme and an unified and mixed interpolatory and approximation subdivision scheme for triangular meshes. The former which is C 1 continuous as same as the modified Butterfly scheme has better effect in some complex models. The latter can be used to solve the “popping effect” problem when switching between meshes at different levels of resolution. The scheme generates surfaces coincident with the Loop subdivision scheme in the limit condition having the coefficient k equal 0. When k equal 1, it will be changed into a new interpolatory subdivision scheme. Eigen‐structure analysis demonstrates that subdivision surfaces generated using the new scheme are C 1 continuous. All these are achieved only by changing the value of a parameter k. The method is a completely simple one without constructing and solving equations. It can achieve local interpolation and solve the “popping effect” problem which are the method's advantages over the modified Butterfly scheme.