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RecognitionofpasfeaturesforautomaticpartingsurfacegenerationininjectionmouldsKChung1,KLee2*andTKim31R&DTeam,INUSTechnology,Korea2SchoolofMechanicalandAerospaceEngineering,SeoulNationalUniversity,Korea3DepartmentofDigitalContents,SejongUniversity,KoreaAbstract:Thispaperproposesatopology-basedalgorithmforrecognizingpassagefeaturesusingtheconceptofamultifaceholeloop.Themultifaceholeloopisaconceptualholeloopthatisformedoverseveralconnectedfacesandservesasanentranceoranexitofapassage.Apassagefeatureisthusrecognizedbyidentifyingtwomultifaceholeloopscorrespondingtoitsentranceandexit.Togeneratethecoreandthecavityofaninjectionmouldforapartwithpassagefeatures,eithertheentranceortheexitofeachpassagemustbecoveredbyasurface,andthissurfaceconstitutesthepartingsurfaces.Thealgorithmproposedinthispapercheckstheconnectivityofthetwomultifaceholeloopstorecognizepassagefeatures.ThetotalnumberofpassagefeaturesinapartiscalculatedfromtheEulerequation,andtheidenticationprocedurecontinuesuntilthenumberofidentiedpassagefeaturesequalsthisnumber.Tondallofthemultifaceholeloopsinapart,theproposedapproachconsidersallofthecombinationsofconnectedfaces.Theedgeconvexityisusedtojudgethevalidityofmultifaceholeloops.Byusingthealgorithmproposedinthispaper,thepassagefeaturescouldberecognizedeVectively.Theapproachproposedisillustratedwithseveralexamplecases.Keywords:passagefeature,featurerecognition,multifaceholeloop,injectionmould1INTRODUCTIONInjectionmouldingisthemostprevalentprocessfortheproductionofthermoplasticpolymerparts.Inthisprocess,athermoplasticpolymerisinjectedintothecavityformedbythecoreandthecavity.Thismouldcavitydeterminestheshapeoftheplasticpart.ThegeneralcongurationofaninjectionmouldisshowninFig.1.Figure1representsasimpliedcongurationofaninjectionmouldandillustratestheplates,thecoreandthecavity.Theactualinjectionmouldhasmanystandardparts,ejectors,aslidesystemandacoolingsystem,inadditiontothoseshown.Historically,moulddesignershavegeneratedthetwo-dimensionaldrawingsofamouldusingatwo-dimensionalcomputeraideddesign(CAD)system.Recently,however,attemptstodesigninjectionmouldsusingthree-dimensionalCADsystemshavebeenmadeasthree-dimensionalCADsystemsrunningonpersonalcomputershavebecomewidelyavailable.Byusingathree-dimensionalCADsystemformoulddesign,manydesigntaskscanbeautomatedorfacili-tated.Inparticular,thepartingsurfacescanbegeneratedautomaticallyoratleastmuchmoreconveniently14.Partingsurfacesareusedtocuttheexternalblockenclos-ingtheparttobemouldedintotwopieces,i.e.thecoreandthecavity.Whentheparthaspassages,eithertheirentrancesorexitshavetobecoveredbythepartingsurfaces.Eventhoughthepartingsurfacesaregeneratedfairlyeasilybyextendingthepartinglinestowardstheoutsideofthepart,identifyingalthepassagefeaturesandcoveringthemwithpropersurfacesareerror-pronetaskswhentheshapeofthepartiscomplicated.Inthispaper,analgorithmforndingsuchpassagefeaturespassingthroughmultiplefaces,asshowninFig.2,isproposed.2BACKGROUNDANDMOTIVATIONIninjectionmoulddesignsystemsthatarebasedonthree-dimensionalCADsystems,thedesignprocess783B05601 IMechE2002 ProcInstnMechEngrsVol216PartB:JEngineeringManufactureTheMSwasreceivedon21May2001andwasacceptedafterrevisionforpublicationon21December2001.*Correspondingauthor:DepartmentofMechanicalandAerospaceEngineering,SeoulNationalUniversity,San56-1,Shillim-Dong,Kwanak-Gu,Seoul151-742,Korea.startsfromthethree-dimensionalCADmodelofapart.Then,thecoreandthecavityarecreatedfromthepartmodel.TheprocedureisshowninFig.3.ThecoreandthecavityofthepartmodelshowninFig.4aregeneratedasfollows.Firstly,adesignercreatesacubicblockenclosingthepartmodel,asillustratedinFig.5.Therectangularblockiscalledthecoreblock,whichwileventuallybecomethecoreandthecavity.Next,thepartingsur-faces,whichsplitthecoreblockintothecoreandthecavity,aregeneratedalongtheouterboundariesofthepartmodelasshowninFig.6a.Thepartingsurfaces,ifrequired,arealsogeneratedononeendofthepassagefeatureasshowninFig.6b.Thecoreblockissplitintothecoreandthecavitybythepartingsurfacesandthefacesofthepartmodel.Thecoreisthelowerportionofthecoreblock,andthecavityisitsupperportion.ThecreatedcoreandcavityareillustratedinFig.7.AsillustratedinFig.6b,thepartingsurfacesshouldbegeneratedononeendofeachpassagefeaturetosplitthecoreblockcompletelyintotwopieces,i.e.thecoreandthecavity.Inthecaseofasimplepassagefeature,asshownintheexample,thepartingsurfaceofthepassagefeatureiseasilygenerated.However,inthecaseofcomplicatedpassagefeaturesformedoverseveralfacesasillustratedinFig.8,therecognitionoftheloopsboundingtheendsofthepassagefeatureandtheFig.1GeneralcongurationofaninjectionmouldFig.2Passagefeaturepassingthroughmultiplefaces Fig.3Procedureforgeneratingthecoreandthecavity784 KCHUNG,KLEEANDTKIMProcInstnMechEngrsVol216PartB:JEngineeringManufacture B05601IMechE2002generationofthepartingsurfacesonthemareverydibullet3 cultandtimeconsumingtasks.Figure9showsapartmodelwiththepartingsurfaceswiththecorrespondingpassagefeatures,andFig.10showsthesurfacesthatwilformthepartingsurfacebycoveringthepassagefeatures.AsshowninFig.10,thesesurfacesforseparatingthepassageregionconsistofmanycomplicatedfaces.Mostplasticpartsfabricatedbyinjectionmouldinghavepassagefeaturespassingthroughmultiplefaces.Thismakesitdibullet3 culttorecognizepassagefeaturesandtogeneratethepartingsurfacesautomatically.Inthispaper,analgorithmtodetectpassagefeaturesisproposedasthebasisforautomaticpartingsurfacegeneration.Fig.4TopandbottomviewsofanexamplepartwithonepassagefeatureFig.5CoreblockFig.6GenerationofpartingsurfacesRECOGNITIONOFPASSFEATURESFORAUTOMATICPARTINGSURFACEGENERATION 785B05601 IMechE2002 ProcInstnMechEngrsVol216PartB:JEngineeringManufactureFig.7GenerationofthecoreandthecavityFig.8Simpliedfrontcoverofanaudiosystem786 KCHUNG,KLEEANDTKIMProcInstnMechEngrsVol216PartB:JEngineeringManufacture B05601IMechE20022.1RelatedworkSinceKyprianoupointedoutthenecessityforshapeclassicationinCADsystemsinhisPhDthesis5,featurerecognitioninsolidmodelshasbeenapopularresearchtopic.Untilnow,theextractionofmachiningfeaturesfromCADdatahasbenthemainsubjectofresearch,andfeaturerecognitiontechniqueshavebeenderivedtoextractmachiningfeatures,suchasholes,slotsandpocketfeatures6.Therearefourdistinctapproachestofeaturerecognition:(a)thegraphpatternmatchingapproach7,(b)theconvexhulldecompositionapproach8,9,(c)thecell-baseddecompositionapproach10,(d)thehint-basedreasoningapproach11.ThegraphpatternmatchingapproachwasintroducedbyJoshiandChang,andhasproventobethemostpopularmethodinthefeaturerecognitioneld12.Inthisapproach,theB-Repdatastructureofapartismappedontoagraphwhosenodesrepresentfacesandwhosebranchesrepresentedges.Thisgraphiscalledthefaceadjacencygraph(FAG).Then,asubgraphiso-morphismisusedtosearchsubgraphsthatmatchthefeaturetemplates.However,inthecaseofintersectingfeatures,thesubgraphsinthepartaredeformed,whichmakesfeaturerecognitionimpossible.Theconvexhulldecompositionapproachwaspro-posedbyWoo9.ThisapproachrecognizesthefeaturesFig.9SurfacesgeneratedfrompassagefeaturesthatconstitutepartingsurfacesFig.10SurfacescoveringpassagefeaturesRECOGNITIONOFPASSFEATURESFORAUTOMATICPARTINGSURFACEGENERATION 787B05601 IMechE2002 ProcInstnMechEngrsVol216PartB:JEngineeringManufacturebyBooleanoperationsbetweenapartmodelandaconvexhullsurroundingthepartmodel.TheBooleanoperationbetweenthepartmodelandconvexhullisappliedrecursively.WhentheoutputoftheBooleanoperationisempty,theoperationisterminated.Unfor-tunately,thedecompositionprocessmaynotnecessarilyconverge.Toovercomethisproblem,Kimproposedthealternatingsumofvolumeswithpartitioning(ASVP)decomposition9,whichrecognizesfeaturesbycompar-ingthepartmodelfaceswithitsconvexhullfaces.Thecell-baseddecompositionapproachwasproposedbySakuraiandChin10.Thismethodrecognizesfeaturesbydecomposingthedeltavolumeintominimalcellsandthencombiningthesecells.ThedeltavolumeisthediVerencebetweenastockandapartmodel.Usingthisapproach,thenumberofcellsderivedfromthedecomposeddeltavolumeislarge.Consequently,alargenumberofcombinationsareneededtorecognizethefeaturesbycombiningthecells.Thehint-basedreasoningapproachwasproposedbyVandenbrande1.Thisapproachwasproposedinordertorecognizeintersectingfeatures,whicharethemainproblemofthegraphpatternmatchingapproach.Thetechniquerecognizesfeaturesfromthetraditionaltracesoffeatures.Forexample,aslothintisgeneratedwhenapairofparallelopposingplanarfacesisencoun-tered,whichcorrespondtoslotwalls.Withsuchhints,thealgorithmrecognizestheslotfeaturebysearchingtheslotoorbetwentheslotwalls.Asissuggestedbytheabove,researchonmachiningfeaturerecognitionisbeingactivelypursued.Someresearchhasalsobenperformedonfeaturerecognitionspecicallyrelatedtomoulds,forexampleuponunder-cutfeatures13.However,asfarasthepresentauthorsareaware,noresearchhasbeenundertakentodateontherecognitionofpassagefeaturesforpartingsurfacegeneration.3OVERVIEWApassagefeatureiscomposedofapairofholeloopsandthefacesconnectingtheholeloops,andthuspassagefeaturerecognitionisaprocesofndingpairedholeloops.Becauseapassagefeaturecanpassthroughseveralconnectedfaces,theholeloopslyingoverseveralconnectedfacesshouldbeidentiedatrst.Whenaholeloopisfound,itspairholeloopissearched.Ifthepairofholeloopssatisesacertaincon-ditiontobecomeapassage,itisregisteredasapassagefeature.3.1DenitionSincethepassagefeaturespassingthroughmanycon-nectedfacesarethetargetfeaturestoberecognized,aspecialholeloop,calledamultifaceholeloop,formedoverseveralfaces,isdenedinthispaperasfollows:Foranypairofconnectedfaces,altheedgessharedbytwofacesinthepairareeliminatedandanexpandedfaceisgenerated.Ifinternalloopsofedgesinsidetheexpandedfaceexist,theseinternalloopsaredenedasmultifaceholeloops.AnexampleofamultifaceholeloopisillustratedinFig.11.3.2BasicconceptsApassagefeatureiscomposedoftwoholeloopsinclud-ingmultifaceholeloopsandthefacescouplingtheseholeloops.Thesefacesarecalledsidefaces.Thus,thepro-cedureforndingpassagefeaturescanbeconceptuallysimpliedtondtwoconnectedholeloops.ThedetailedprocedurewillbeexplainedinSection4.4ALGORITHMInthissectiontheproposedalgorithmwilbeexplainedindetail.Thedetailedalgorithmforrecognizingthesimplepassagefeaturewillbeexplainedrst,andthentheapproachusedtorecognizetheholeloopsonmultiplyconnectedfaceswilbedescribed.Apassagefeatureisdenedassimpleifitsentranceandexitlieoverasingleface.Finally,theconditionsnecessaryformultifaceholeloopstocomposeapassage,andthemethodforndingalthecombinationsofconnectedfaces,wilbeexplained.4.1AlgorithmforpassagefeaturerecognitionAsexplainedearlier,apassagefeatureiscomposedoftwoholeloopsconnectedtoeachotherbysidefaces.Thedetailedprocedureforpassagefeaturerecognitionisdescribedusingthefollowingexample.ThesamplepartillustratedinFig.12hasonepassagefeatureandeachsymbolisdenedasfollows:Fig.11Exampleofamultifaceholeloop788 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B05601IMechE2002atopfaceofthesamplepartbfaceconnectingthetopandbottomsurfacescbottomfaceofthesampleparte1edgesharedbyfaceaandfacebe2edgesharedbyfacecandfacebL1holeloopinfaceaL2holeloopinfacecIntheexamplepart,theloopscomposingthepassagefeatureareL1andL2,andthefaces,suchasfaceb,con-necttheseloops.Generally,theface(faceb)composingapassagefeaturehasedgessharedbytheneighbouringfaces(faceaandfacec),andtheseedgesformholeloopsintheneighbouringfaces(faceaandfacec).Thatis,facebisafacecomposingthepassagefeatureandisnamedthesideface.Facesaandcarenamedtheentrancefaceandtheexitfacerespectively.Thepro-cedureforndingthepassagefeaturesisasfollows:1.Searchforholeloopsinaface(entrancefaceofapassage).2.Searchforedgescomposingtheholeloopsearchedforinstep1.3.Searchforfaces(sidefaces)sharingtheedgessearchedforinstep2.4.Iftheedgesoftheface(sideface)searchedforinstep3formaholeloopinsideanotherface(exitface),thisholeloopandtheholelopsearchedforinstep1formapassagefeature.Thealgorithmexplainedaboveisforrecognizingpassagefeaturescomposedofholelopsresidingonasingleface.Torecognizethepassagefeaturescomposedofholeloopslyingovermultiplefaces,theconceptofthemulti-faceholeloopmustbeapplied.4.2RecognitionofholeloopsonmultiplyconnectedfacesAsdescribedearlier,amultifaceholeloopisdenedastheinternalloopformedoveranexpandedfaceformedbyremovingedgessharedbyconnectedfaces.Threestepsareneededinordertorecognizetheholeloopsonmultiplyconnectedfaces:(a)removetheedgessharedbytheconnectedfaces,(b)constructloopswiththeremainingedges,(c)identifytheinternalloop.Theprocedureforrecognizingamultifaceholeloopcanbedescribedasfollows.AsamplepartforexplainingthemultifaceholeloopisshowninFig.13,wherethegreyfacesaretheconnectedfacesbeinginvestigated.Thegreyfacesshareedgese1ande2.IfthesharededgesinFig.12ExampleusingasimplepassagefeatureFig.13ExampleforrecognizingamultifaceholeloopRECOGNITIONOFPASSFEATURESFORAUTOMATICPARTINGSURFACEGENERATION 789B05601 IMechE2002 ProcInstnMechEngrsVol216PartB:JEngineeringManufacturethetwofacesareremovedandthetwofacesareconsid-eredasoneface,asshowninFig.13b,twoloopsareformed,i.e.L1andL2.LoopL1correspondstotheinternalloopandloopL2correspondstotheperipheralloop.Consequently,themultifaceholeloopisloopL1inthiscase.Likewise,theinternalloopsformedovernarbitraryconnectedfacesaredenedasmultifaceholeloopsifinternalloopsexistwhenthesharededgesofconnectedfacesareremoved.Oncethemultifaceholeloopsareidentied,theprocedureforndingasimplepassagedescribedearliercanbeappliedinordertorecognizethepassagefeaturesinthemultiplefaces.4.3ConditionsnecessaryforamultifaceholeloptoformapassageForthemultifaceholeloopstocomposepassagefea-tures,twoconditionsarerequired.Firstofal,altheedgescomposingthemultifaceholeloopmustbeconvex.Forexample,forthepartillustratedinFig.14,loopL1isaholeloopinfaceF1,buttheedgescompos-ingtheholeloopL1donotcomposeapassagefeaturebecausetheyareconcave.Thismaybeanaturalconclu-sionconsideringthattheedgesofthemultifaceholeloopsbecomeeithertheentranceorexitofthepassageandonlyconvexedgesmayformtheboundaryoftheentranceortheexit.Therefore,aprocedureforjudgingtheconvexityofedgesisrequired.TheclassicationofedgesbyKyprianouisillustratedinFig.1514.Edgesareclassiedbytheanglebetweenthetwofacesthatsharethecorrespondingedge;i.e.iftheanglemeasuredinsideapartissmallerthan180,theedgeisconvex.Likewise,ifitislargerthan180,theedgeisconcave.IfthetwofacesareconnectedsmoothlyasshowninFigs15cord,theedgesareclassiedbythelocalcurvature14.Byjudgingtheconvexityoftheedges,themultifaceholeloopscomposedofconcaveorsmoothconcaveedgesareexcludedduringtheprocedureforrecognizingpassagefeatures.Evenifaltheedgessatisfytherstcondition,therearecaseswherepassagefeaturescannotbecomposedbecauseoftherelationshipbetweenthemultifaceholeloopsandthefacescomposingthemodel.Here,thesecondconditioncomesintoplay.ThemultifaceholeloopscanbeconsideredasacollectionofedgesthatwilboundthepartingsurfaceslaterforthecorrespondingpassageFig.14HoleloopthatdoesnotconstituteapassagefeatureFig.15Kyprianousedgeclassication14790 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B05601IMechE2002features.Sincethegeneratedpartingsurfacesmustnotoverlapthefacesofapart,multifaceholeloopswhoseinsideregionoverlapsthepartsurfacesmustbeexcludedfromconsideration.AmultifaceholeloopthatsatisessuchaconditionisshowninFig.16,andFig.17showsamultifaceholeloopthatviolatesthecondition.Inotherwords,thepartingsurfacetobegeneratedusingmultifaceholeloopL2showninFig.16b,whichisidentiedfromthemergedfaceshatchedinFig.16a,doesnotoverlapthefacescom-posingthepart.Mergedfacesareasetofconnectedfaceswithinwhichamultifaceholeloopissearchedfor.How-ever,thepartingsurfacetobegeneratedusingmultifaceholeloopL2inFig.17b,whichissearchedforamongthemergedfaceshatchedinFig.17a,overlapsthepartfaces.Therefore,thecaseinFig.17mustbeexcludedfromcon-siderationinndingthepassagefeatures.Thedetailedconditionforinvalidmultifaceholeloopsisasfollows.Thereadersmaywonderwhyanodsituationlikethisisconsidered.Allpossiblecasesofmultifaceholeloopshavetobeconsideredbecausetheyaregeneratedauto-maticallybymergingconnectedfaces.Thefacesthatsharetheedgescomposingamultifaceholeloopanddonotparticipateinthemergingprocessaresidefaces.Ifboththestartingpointandtheend-pointofanedgesharedbytwosidefacesareonthemultifaceholeloop,thisedgecancomposealoopwithseveralotheredgesthatbelongtothemultifaceholeloop.Apartingsurfacegeneratedusingthisloopshouldbethesamefaceasoneofthesidefaces,whichmakesthepartingsurfaceoverlapthepartface.Figure18brepresentsatwo-dimensionallayoutofthepartinFig.18a.FacesF1,F2,F3andF4correspondtothemergedfaces,andfacesS1,S2,S3,S4andS5correspondtothesidefaces.Theboundaryedgesofthemultifaceholeloopareindicatedbythicklines.EdgeashowninFig.18bisanedgesharedbythesidefaces,andboththestartingpointandtheend-pointofedgeaareonthemultifaceholeloop.Thus,edgeaformsalooptogetherwithotheredgesofS5thatalsobelongtothemultifaceholeloop.ThepartingsurfacegeneratedfromthisloopbecomestheexistingfaceS5,andthusthepartingsurfaceoverlapsS5.Inthisway,Fig.16ExampleofavalidmultifaceholeloopFig.17ExampleofaninvalidmultifaceholeloopRECOGNITIONOFPASSFEATURESFORAUTOMATICPARTINGSURFACEGENERATION 791B05601 IMechE2002 ProcInstnMechEngrsVol216PartB:JEngineeringManufacturetherecognitionofmultifaceholeloopsyieldinginvalidpartingsurfacescanbeavoidedbyinvestigatingtherelationshipbetweenthemultifaceholeloopsandtheendpointsofedgessharedbythesidefaces.4.4ProcedureforndingalsetsofconnectedfacesTondthemultifaceholeloopsinapart,aprocessthatidentiesandmergestheconnectedfacesisneeded.Twoapproachescanbeappliedtogeneratethesetsofcon-nectedfaces.Therstapproachinvolvesselectingthesetsoffacestobemergedbyjudgingtheconnectivitybetweenthememberfacesoutoffacesetsgeneratedarbitrarily.However,inthisapproach,thenumberofsetsgeneratedarbitrarilyincreasesapproximatelybyanorderofnrwhenthetotalnumberoffacesislarge:threesuperoirnrn!r!nr!nn1n2nr1rr1r21XOnrwhereXnumberofcombinationsntotalnumberoffacesFig.18Planardisplayofparticipatingfaces792 KCHUNG,KLEEANDTKIMProcInstnMechEngrsVol216PartB:JEngineeringManufacture B05601IMechE2002rnumberoffacestobemergedForexample,ifthetotalnumberoffacesis200,thenumberofcandidat