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1、HexahedralMeshGenerationusingtheEmbeddedVoronoiGraphAllaSheffer,MichalEtzion,AriRappoport,MichelBercovierInstituteofComputerScience,TheHebrewUniversity,Jerusalem91904,Israel. sheffa michalsarirberco@cs.huji.ac.il.http://www.cs.huji.ac.il/sheffamichalsarirberco
2、.AbstractThisworkpresentsanewapproachforautomatichexahedralmeshing,basedontheembeddedVoronoigraph.TheembeddedVoronoigraphcontainsthefullsymbolicinformationoftheVoronoidiagramandthemedialaxisoftheobject,andageometricapproximationtotherealgeometry.TheembeddedVoronoigraphis
3、usedfordecomposingtheobject,withtheguidingprinciplethatresultingsub-volumesaresweepable.Sub-volumesaremeshedindependently,andtheresultingmeshesareeasilycombinedandsmoothedtoyieldthenalmesh.Theapproachpresentedhereisgeneralandautomatic.Ithandlesanyvolume,evenifitsmedialax
4、isisdegenerate.TheembeddedVoronoigraphprovidescompleteinformationregardingproximityandadjacencyrelationshipsbetweentheentitiesofthevolume.Hence,decompositionfacesaredeterminedunambiguously,withoutanyfurthergeometriccomputations.Thesub-volumescomputedbythealgorithmareguara
5、nteedtobewell-denedanddisjoint.Thesizeofthedecompositionisrelativelysmallsinceeverysub-volumecontainsadifferentVoronoiface.Meshqualityseemshighsincethedecompositionavoidsgenerationofsharpangles,andsweepandotherbasicmethodsareusedtomeshthesub-volumes.1IntroductionAutomati
6、cgenerationof3-Dniteelementmeshesisessentialfortheautomationoftheanalysisprocess.Re-searchanddevelopmenteffortonnewmeshingalgorithmshasresultedinseveralautomaticalgorithmsfor3-Dmeshing(see[7]forarecentreview).Mostoftheresearchhasfocusedonthegenerationofunstructuredtetra-
7、hedralelements.Thishasresultedinseveralsuccessfulautomaticmeshgenerationalgorithms,whichcanbecategorizedaccordingtothemainapproachesused:Delaunaytriangulation[10,28],octree-basedmethods[23,2]andadvancingfrontalgorithms[8].Inmanysituations,hexahedralmeshingismoreattractive
8、thantetrahedralmeshing.Theadditionalrequire-mentsofhexahedralmeshingmaketheproblemmoredemanding.
