### Abstract

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 language | English |
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Pages (from-to) | 263-272 |

Journal | Computer Graphics Forum |

Volume | 25 |

Issue number | 3 |

Publication status | Published - Sep 2006 |

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### Cite this

*Computer Graphics Forum*,

*25*(3), 263-272.

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

Research output: Contribution to journal › Article › Research › peer-review

*Computer Graphics Forum*, vol. 25, no. 3, pp. 263-272.

}

TY - JOUR

T1 - Tuning Subdivision by Minimising Gaussian Curvature Variation Near Extraordinary Vertices

AU - Augsdörfer, Ursula

AU - Dodgson, Neil A.

AU - Sabin, Malcolm A.

PY - 2006/9

Y1 - 2006/9

N2 - 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 ].

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 ].

M3 - Article

VL - 25

SP - 263

EP - 272

JO - Computer Graphics Forum

JF - Computer Graphics Forum

SN - 0167-7055

IS - 3

ER -