A New Class of Guided C2 Subdivision Surfaces Combining Good Shape with Nested Refinement

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dc.contributor.authorKarčiauskas, Kęstutisen_US
dc.contributor.authorPeters, Jörgen_US
dc.contributor.editorChen, Min and Benes, Bedrichen_US
dc.date.accessioned2018-08-29T06:55:59Z
dc.date.available2018-08-29T06:55:59Z
dc.date.issued2018
dc.description.abstractConverting 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 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.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 subdivision algorithm of polynomial degree bi‐6 and a curvature bounded algorithm of degree bi‐5.en_US
dc.description.number6
dc.description.sectionheadersArticles
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume37
dc.identifier.doi10.1111/cgf.13313
dc.identifier.issn1467-8659
dc.identifier.pages84-95
dc.identifier.urihttps://doi.org/10.1111/cgf.13313
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13313
dc.publisher© 2018 The Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectcurves and surfaces
dc.subjectgeometric modelling
dc.subjectsubdivision surfaces
dc.subjectcurvature continuity
dc.subjectnested refinement
dc.subjectfair shape
dc.subjectguided subdivision
dc.subjectCategories and Subject Descriptors (according to ACM CCS)
dc.titleA New Class of Guided C2 Subdivision Surfaces Combining Good Shape with Nested Refinementen_US
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