# On triangle meshes with valence dominant vertices

Handle URI:
http://hdl.handle.net/10754/627199
Title:
On triangle meshes with valence dominant vertices
Authors:
Morvan, Jean-Marie
Abstract:
We study triangulations $\cal T$ defined on a closed disc $X$ satisfying the following condition: In the interior of $X$, the valence of all vertices of $\cal T$ except one of them (the irregular vertex) is $6$. By using a flat singular Riemannian metric adapted to $\cal T$, we prove a uniqueness theorem when the valence of the irregular vertex is not a multiple of $6$. Moreover, for a given integer $k >1$, we exhibit non isomorphic triangulations on $X$ with the same boundary, and with a unique irregular vertex whose valence is $6k$.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; King Abdullah University of Science and Technology, C.E.M.S.E, Thuwal 23955-6900, Saudi Arabia
Publisher:
arXiv
Issue Date:
16-Feb-2018
ARXIV:
arXiv:1802.05851
Type:
Preprint
http://arxiv.org/abs/1802.05851v1; http://arxiv.org/pdf/1802.05851v1
Appears in Collections:
Other/General Submission; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

DC FieldValue Language
dc.contributor.authorMorvan, Jean-Marieen
dc.date.accessioned2018-02-27T09:00:12Z-
dc.date.available2018-02-27T09:00:12Z-
dc.date.issued2018-02-16en
dc.identifier.urihttp://hdl.handle.net/10754/627199-
dc.description.abstractWe study triangulations $\cal T$ defined on a closed disc $X$ satisfying the following condition: In the interior of $X$, the valence of all vertices of $\cal T$ except one of them (the irregular vertex) is $6$. By using a flat singular Riemannian metric adapted to $\cal T$, we prove a uniqueness theorem when the valence of the irregular vertex is not a multiple of $6$. Moreover, for a given integer $k >1$, we exhibit non isomorphic triangulations on $X$ with the same boundary, and with a unique irregular vertex whose valence is $6k$.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1802.05851v1en
dc.relation.urlhttp://arxiv.org/pdf/1802.05851v1en
dc.rightsArchived with thanks to arXiven
dc.titleOn triangle meshes with valence dominant verticesen
dc.typePreprinten
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentKing Abdullah University of Science and Technology, C.E.M.S.E, Thuwal 23955-6900, Saudi Arabiaen
dc.eprint.versionPre-printen
dc.contributor.institutionUniversite de Lyon, CNRS UMR 5208, Universite Claude Bernard Lyon 1, Institut Camille Jordan, 43 blvd du 11 Novembre 1918, F-69622 Villeurbanne-Cedex, Franceen
dc.identifier.arxividarXiv:1802.05851en
kaust.authorMorvan, Jean-Marieen