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Least Squares Subdivision Surfaces
Author(s) -
Boyé S.,
Guennebaud G.,
Schlick C.
Publication year - 2010
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.1467-8659.2010.01788.x
Subject(s) - subdivision , subdivision surface , heuristics , vertex (graph theory) , computer science , surface (topology) , key (lock) , triangle mesh , algorithm , polygon mesh , mathematical optimization , mathematics , theoretical computer science , geometry , computer graphics (images) , graph , archaeology , computer security , history
The usual approach to design subdivision schemes for curves and surfaces basically consists in combining proper rules for regular configurations, with some specific heuristics to handle extraordinary vertices. In this paper, we introduce an alternative approach, called Least Squares Subdivision Surfaces (LS), where the key idea is to iteratively project each vertex onto a local approximation of the current polygonal mesh. While the resulting procedure haves the same complexity as simpler subdivision schemes, our method offers much higher visual quality, especially in the vicinity of extraordinary vertices. Moreover, we show it can be easily generalized to support boundaries and creases. The fitting procedure allows for a local control of the surface from the normals, making LS 3 very well suited for interactive freeform modeling applications. We demonstrate our approach on diadic triangular and quadrangular refinement schemes, though it can be applied to any splitting strategies.