Tuning Subdivision by Minimising Gaussian Curvature Variation Near Extraordinary Vertices

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

Research output: Contribution to journalArticle

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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