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A New Class of Guided C 2 Subdivision Surfaces Combining Good Shape with Nested Refinement
Author(s) -
Karčiauskas Kęstutis,
Peters Jörg
Publication year - 2018
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/cgf.13313
Subject(s) - subdivision , subdivision surface , polygon mesh , spline (mechanical) , quadrilateral , computer science , curvature , rendering (computer graphics) , surface (topology) , bounded function , mathematics , algorithm , geometry , computer graphics (images) , finite element method , mathematical analysis , physics , archaeology , structural engineering , engineering , history , thermodynamics
Converting quadrilateral meshes to smooth manifolds, guided subdivision offers a way to combine the good highlight line distribution of recent G‐spline constructions with the refinability of subdivision surfaces. This avoids the complex refinement of G‐spline constructions and the poor shape of standard subdivision. Guided subdivision can then be used both to generate the surface and hierarchically compute functions on the surface. Specifically, we present a C 2 subdivision algorithm of polynomial degree bi‐6 and a curvature bounded algorithm of degree bi‐5. We prove that the common eigenstructure of this class of subdivision algorithms is determined by their guide and demonstrate that their eigenspectrum (speed of contraction) can be adjusted without harming the shape. For practical implementation, a finite number of subdivision steps can be completed by a high‐quality cap. Near irregular points this allows leveraging standard polynomial tools both for rendering of the surface and for approximately integrating functions on the surface.