Tuning Subdivision by Minimising Gaussian Curvature Variation Near Extraordinary Vertices

dc.contributor.authorAugsdoerfer, U.H.en_US
dc.contributor.authorDodgson, N.A.en_US
dc.contributor.authorSabin, M.A.en_US
dc.date.accessioned2015-02-21T14:30:22Z
dc.date.available2015-02-21T14:30:22Z
dc.date.issued2006en_US
dc.description.abstractWe present a method for tuning primal stationary subdivision schemes to give the best possible behaviour near extraordinary vertices with respect to curvature variation.Current schemes lead to a limit surface around extraordinary vertices for which the Gaussian curvature diverges, as demonstrated by Karciauskas et al. [KPR04]. Even when coefficients are chosen such that the subsubdominant eigenvalues, , equal the square of the subdominant eigenvalue,, of the subdivision matrix [DS78] there is still variation in the curvature of the subdivision surface around the extraordinary vertex as shown in recent work by Peters and Reif [PR04] illustrated by Karciauskas et al. [KPR04].In our tuning method we optimise within the space of subdivision schemes with bounded curvature to minimise this variation in curvature around the extraordinary vertex. To demonstrate our method we present results for the Catmull-Clark [CC78], 4-8 [Vel01, VZ01] and 4-3 [PS03] subdivision schemes. We compare our results to previous work on the tuning of these schemes and show that the coefficients derived with this method give a significantly smaller curvature variation around extraordinary vertices.Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling, I.3.6 [Computer Graphics]: Methodology and Techniquesen_US
dc.description.number3en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume25en_US
dc.identifier.doi10.1111/j.1467-8659.2006.00945.xen_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages263-272en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2006.00945.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing, Incen_US
dc.titleTuning Subdivision by Minimising Gaussian Curvature Variation Near Extraordinary Verticesen_US
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