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1、DelaunayMeshGenerationofThreeDimensionalDomainsTamalK.DeyyAbstractDelaunaymeshesareusedinvariousapplicationssuchas niteelementanalysis,com-putergraphicsrendering,geometricmodeling,andshapeanalysis.Astheapplicationsvary,sodothedomainstobemeshed.AlthoughmeshingofgeometricdomainswithDelaunays
2、impliceshavebeenaroundforawhile,provabletechniquestomeshvarioustypesofthreedimensionaldomainshavebeendevelopedonlyrecently.Wedevotethisarticletopresentingthesetechniques.Wesurveyvariousrelatedresultsanddetailafewcorealgorithmsthathaveprovableguaranteesandareamenabletopracticalimplementation
3、.Delaunayre ne-ment,aparadigmoriginallydevelopedforguaranteeingshapequalityofmeshelements,isacommonthreadinthesealgorithms.We nishthearticlebylistingasetofopenquestions.ResearchsupportedbyNSF,USA(CCF-0430735andCCF-0635008).yDepartmentofComputerScienceandEngineering,OhioStateUniversity,Ohio
4、,USA.Email:tamaldey@cse.ohio-state.edu11IntroductionTheneedformeshinggeometricdomainsinthreedimensionsisubiquitousinscienti cstudiesandengineeringapplications.Althoughavastliteratureexistsonmeshgeneration,therearenotmanyresultsthatprovidetheoreticalguaranteesaboutoutput.Inunstructuredmeshin
5、gwithtrianglesandtetrahedra,mainlytwoapproachesareknownthatcomewiththeseguar-antees;oneisoctreebased[5,45]andtheotherisDelaunaybased[9,32].InthissurveywefocusonDelaunaybasedmethods.TheliteratureonDelaunaybasedmeshingishugeanditisnotourintentiontosurveyallexistingalgorithmsonthesubject.Werec
6、ommendotherliterature[6,12,46,49]asacomplementtoours.Wefocusonvariousprovabletechniquesthatenablemeshingofdi erenttypesofgeometricdomainsinthreedimensions.AsacommonthemeweillustratehowanelegantalgorithmicparadigmcalledDelaunayre nementcanbeadaptedtothevarietyofdomains.Issues:Therearetwomajo
7、rissuesinDelaunaymeshgenerationofgeometricdomains:(i)conformationand(ii)elementquality.Iftheinputconsistsoflinearelementssuchassegments,planarfacets,andpolyhedra,conformationmeansthateachoftheseinputelementsappearsintheoutputasaunionofDelaunaysimplices.W
