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1、INTERNATIONALJOURNALFORNUMERICALMETHODSINENGINEERING,VOL.39,1475-1489(1996)GENERALIZED3-DPAVING:ANAUTOMATEDQUADRILATERALSURFACEMESHGENERATIONALGORITHMROGERJ.CASSANDSTEVENE.BENZLEYCivilEngineeringDepartment,BrighamYoungUnioersity,368CBProvo,UT84602,U.S.A.RAYJ.MEYERSANDTEDD.BLACKERComputationalMechan
2、icsandVisualizationDeportment.SandiaNationalLpboratories,Albuquerque,NM87185,U.S.A.SUMMARYThispaperdiscussestheextensionofthepavingalgorithmforallquadrilateralmeshgenerationtoarbitrarythree-dimensionaltrimmedsurfaces.Methodsofcalculatingangles,projectingelements,anddetectingcollisionsbetweenpavingb
3、oundaries,forgeneralsurfacesarepresented.Extensionsofthesmoothingalgorithmsforthreedimensionsaresetforth.Advancesintheuseofscalarsizingfunctionsarepresented.Thesefunctionscanbeusedtobetterapproximateinternalmeshdensityfromboundarydensitiesandsurfacecharacteristics.KEYWORDS:meshing;three-dimensional
4、;surfaces;quadrilateral;finiteelement1.INTRODUCTIONThefiniteelementmethodisapopularandpowerfulnumericalanalysistechniqueusedbyengineersinthedesignandanalysisofcomplicatedobjects.Oneofthebiggestobstaclestotheproperuseofthetechniqueisthediscretizationoftheproblemgeometryintoavalidfiniteelementmesh.Th
5、ismeshgenerationistediousanderrorprone.Inaddition,thecostandaccuracyofthenumericalanalysisisdirectlytiedtothequalityofthemesh.Thispaperpresentstheextensionofanautomaticmeshgenerationmethodknowaspavingfromflattwo-dimensionalsurfacestoarbitrarythree-dimensionaltrimmedsurfaces.Thereareseveralautomated
6、meshgenerationtechniquesbeingdeveloped.Thetechniquesincludetriangulation,'.2quadtreeandoctreemethod^,^-substructuring,6geometricdecompo-sitionwiththeuseofconjointprimitive^,^-domaincomposition,''andprogressivefronttechniques.IThetypeandcharacterofthemeshproducedwiththesevarioustechniquesvarieswidel
7、y.Mostconcentrateontriangularmeshgenerationalthoughsomehavebeenextendedtoquadrilateralmeshingwithvaryingdegreesofsuccess.Atechniqueknownaspavingwasrecentlyintroducedformeshingarbitrarytwo-dimensionalsurface
