Tuning Subdivision by Minimising Gaussian Curvature Variation Near Extraordinary Vertices

Ursula Augsdörfer, Neil A. Dodgson, Malcolm A. Sabin

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Abstract

We 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 Karčiauskas 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 Karčiauskas et al. [ KPR04 ].
Original languageEnglish
Pages (from-to)263-272
JournalComputer Graphics Forum
Volume25
Issue number3
Publication statusPublished - Sep 2006

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Tuning Subdivision by Minimising Gaussian Curvature Variation Near Extraordinary Vertices. / Augsdörfer, Ursula; Dodgson, Neil A. ; Sabin, Malcolm A. .

In: Computer Graphics Forum, Vol. 25, No. 3, 09.2006, p. 263-272.

Research output: Contribution to journalArticleResearchpeer-review

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AB - We 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 Karčiauskas 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 Karčiauskas et al. [ KPR04 ].

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