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Recognitionofpasfeaturesforautomaticpartingsurfacegenerationininjectionmoulds KChung1,KLee2*andTKim31Ri.e.iftheangle measuredinsideapartissmallerthan180,theedgeisconvex.Likewise,ifitislargerthan180,theedgeisconcave.IfthetwofacesareconnectedsmoothlyasshowninFigs15cord,theedgesareclassiedbythe localcurvature14.Byjudgingtheconvexityoftheedges,themultifaceholeloopscomposedofconcaveorsmoothconcaveedgesareexcludedduringtheprocedureforrecognizingpassagefeatures. Evenifaltheedgessatisfytherstcondition,therearecaseswherepassagefeaturescannotbecomposedbecauseoftherelationshipbetweenthemultifaceholeloopsandthefacescomposingthemodel.Here,thesecond conditioncomesintoplay.Themultifaceholeloopscanbeconsideredasacollectionofedgesthatwilboundthepartingsurfaceslaterforthecorrespondingpassage Fig.14Holeloopthatdoesnotconstituteapassagefeature Fig.15Kyprianousedgeclassication14 790 KCHUNG,KLEEANDTKIM ProcInstnMechEngrsVol216PartB:JEngineeringManufacture B05601IMechE2002 features.Sincethegeneratedpartingsurfacesmustnotoverlapthefacesofapart,multifaceholeloopswhoseinsideregionoverlapsthepartsurfacesmustbeexcludedfromconsideration. AmultifaceholeloopthatsatisessuchaconditionisshowninFig.16,andFig.17showsamultifaceholeloopthatviolatesthecondition.Inotherwords,thepartingsurfacetobegeneratedusingmultifaceholeloopL2 showninFig.16b,whichisidentiedfromthemergedfaceshatchedinFig.16a,doesnotoverlapthefacescom-posingthepart.Mergedfacesareasetofconnectedfaceswithinwhichamultifaceholeloopissearchedfor.How- ever,thepartingsurfacetobegeneratedusingmultifaceholeloopL2inFig.17b,whichissearchedforamongthemergedfaceshatchedinFig.17a,overlapsthepartfaces.Therefore,thecaseinFig.17mustbeexcludedfromcon- siderationinndingthepassagefeatures.Thedetailedconditionforinvalidmultifaceholeloopsisasfollows.Thereadersmaywonderwhyanodsituationlikethisisconsidered.Allpossiblecasesofmultifaceholeloops havetobeconsideredbecausetheyaregeneratedauto-maticallybymergingconnectedfaces.Thefacesthatsharetheedgescomposingamultifaceholeloopanddonotparticipateinthemergingprocess aresidefaces.Ifboththestartingpointandtheend-pointofanedgesharedbytwosidefacesareonthemultifaceholeloop,thisedgecancomposealoopwithseveralotheredgesthatbelongtothemultifacehole loop.Apartingsurfacegeneratedusingthisloopshouldbethesamefaceasoneofthesidefaces,whichmakesthepartingsurfaceoverlapthepartface.Figure18brepresentsatwo-dimensionallayoutofthe partinFig.18a.FacesF1,F2,F3andF4correspondtothemergedfaces,andfacesS1,S2,S3,S4andS5correspondtothesidefaces.Theboundaryedgesofthemultifaceholeloopareindicatedbythicklines. EdgeashowninFig.18bisanedgesharedbythesidefaces,andboththestartingpointandtheend-pointofedgeaareonthemultifaceholeloop.Thus,edgeaformsalooptogetherwithotheredgesofS5thatalso belongtothemultifaceholeloop.ThepartingsurfacegeneratedfromthisloopbecomestheexistingfaceS5,andthusthepartingsurfaceoverlapsS5.Inthisway, Fig.16Exampleofavalidmultifaceholeloop Fig.17Exampleofaninvalidmultifaceholeloop RECOGNITIONOFPASSFEATURESFORAUTOMATICPARTINGSURFACEGENERATION 791 B05601 IMechE2002 ProcInstnMechEngrsVol216PartB:JEngineeringManufacture therecognitionofmultifaceholeloopsyieldinginvalidpartingsurfacescanbeavoidedbyinvestigatingtherelationshipbetweenthemultifaceholeloopsandtheendpointsofedgessharedbythesidefaces. 4.4ProcedureforndingalsetsofconnectedfacesTondthemultifaceholeloopsinapart,aprocessthatidentiesandmergestheconnectedfacesisneeded.Two approachescanbeappliedtogeneratethesetsofcon-nectedfaces.Therstapproachinvolvesselectingthesetsoffacestobemergedbyjudgingtheconnectivity betweenthememberfacesoutoffacesetsgeneratedarbitrarily.However,inthisapproach,thenumberofsetsgeneratedarbitrarilyincreasesapproximatelybyanorderofn rwhenthetotalnumberoffacesislarge:threesuperoirn rn!r!nr!nn1n2nr1rr1r21XOnr whereXnumberofcombinationsntotalnumberoffaces Fig.18Planardisplayofparticipatingfaces 792 KCHUNG,KLEEANDTKIM ProcInstnMechEngrsVol216PartB:JEngineeringManufacture B05601IMechE2002 rnumberoffacestobemergedForexample,ifthetotalnumberoffacesis200,thenumberofcandidatefacesetsis64684950whenfour facesaretobemerged.Thus,thisapproachisnotebullet3-cientingeneratingthesetsofconnectedfacestobemerged.Thesecondapproachinvolvesgeneratingfacesetsby identifyingfacesconnectedtothefacesthathavebeenalreadyidentiedastheelementsofafeasiblefaceset.Inthisapproach,thememberfacesofaregisteredfacesetarestoredinastack.Then,itsearchesfacesconnected tothelastregisteredfaceamongtheregisteredfaces.Iftherearenomorefacesconnectedtothelastregisteredface,thelastregisteredfaceisremovedfromthestackandthesearchingprocesscontinueswiththeregistered facejustbelowtheremovedface.Thisapproachcanebullet3-cientlyshortenthetimeforgeneratingfacesetsbysearch-ingforconnectedfacesonly,whereastherstapproachsearchesallpossiblesetsandcheckstheconnectivity. Thegeneratedsetsoffacestobemergedareusedinthemoduleusedforndingmultifaceholeloops. 5IMPLEMENTATION5.1Programarchitecture Thebasicconceptoftheproposedalgorithmisasfollows.Uptothemomentwhenthenumberofsearchedpassagefeaturesequalsthetotalnumberofpassagefeaturesinamodel,thenumberoffacestobemerged isincreasedstartingfrom2.ThetotalnumberofpassagefeaturesisderivedusingtheEulerequation15.Ineachstep,themultifaceholeloopsarefoundandpassagefeaturesarerecognizedbysearchingfortheconnected multifaceholeloops.Thus,theimplementedprogramiscomposedoffoursubroutines,i.e.routinesforndingthetotalnumberofpassagefeatures,ndingallcom-binationsofconnectedfaces,recognizingmultiface holeloopsandrecognizingpassagefeatures.TheprogramwasdevelopedwithUnigraphicsV15.0APIonWindowsNT. 5.2AnalysisofrunningtimeThealgorithmproposedinthispapersearchesforpassagefeatureswithanincreasingnumberoffacesto bemerged.Thus,therunningtimeforrecognizingallpassagefeaturesinamodelcanbedeterminedbythepassagefeatureinvolvingthemaximumnumberofconnectedfaces.Therefore,therunningtimecanbe representedbythemaximumnumberoffacestobemerged.Asmentionedearlier,theprocedureforgeneratingsetsoffacestobemergedinvolvessearchingforthefaces connectedtoafaceandsearchingagainforthefaces connectedtothesearchedfacesuntilallmembersoftheconnectedfacesetsofthegivennumberoffacesarecollected.Ifthetotalnumberoffacesinapartisn,theaveragenumberoffacesconnectedtoeachfaceism andthenumberoffacestobemergedisr,thenumberoffeasiblefacesetsisoftheorderofnmr1:XOnm r1Generally,theaveragenumberoffacesconnectedtoeachfaceismuchsmallerthanthetotalnumberof facesinapart.ForthepartillustratedinFig.8,thetotalnumberoffacesis286andtheaveragenumberoffacesconnectedtoeachfaceis5.Inthiscase,theexpectednumberof Table1OrderofcombinationsforthepartinFig.8NumberoffacestobemergedExpectednumberofcombinations 2 14303 71504 35750 Fig.19Examplepartwithoorlespocketsandthroughholes RECOGNITIONOFPASSFEATURESFORAUTOMATICPARTINGSURFACEGENERATION 793 B05601 IMechE2002 ProcInstnMechEngrsVol216PartB:JEngineeringManufacture combinationsaccordingtothenumberoffacestobemergedisasshowninTable1. 6CASESTUDY6.1Examplepart TheexamplepartshowninFig.19ahasseveralpockets,holesandpassagefeaturesboundedbytheholeloopsformedoveroneface.Figure19bshowsthesixpassagefeaturesrecognized. 6.2L-shapedpartThesamplepartshowninFig.20aisL-shapedandhasapassagefeaturecomposedofholeloopsformedover multiplefacesinadditiontoasimplepassagefeature.Inthiscase,thenumberoffacesformingthemultifaceholelopsis4.TherecognizedpassagefeaturesareillustratedinFig.20b. 6.3CasingofacellularphoneThesamplepartshowninFig.21aisthefrontcoverofacellularphoneandhas14passagefeatures.Therecog- nizedpassagefeaturesareillustratedinFig.21b.6.4Minicomponentfrontcover ThesamplepartshowninFig.22aisthefrontcoverofaminicomponentandhaspassagefeaturesresidingovermultiplefaces.Thisparthas15passagefeatures.TherecognizedpassagefeaturesareshowninFig.22b. TherunningtimeforthefourcasesillustratedaboveisshowninTable2. 7CONCLUSIONSInthispaper,analgorithmisproposedforautomatic recognitionofpassagefeaturesusingtheconceptofthemultifaceholeloop.Thegenerationofthepartingsurfacesisoneofthemostnaturaltargettaskstobeautomatedinmoulddesignusingathree-dimensional CADsystem.Thepartingsurfacesareeasilygeneratedalongtheboundariesoftheparttobemade.However,iftheparttobemadehaspassagefeatures,theirentranceFig.20L-shapedexamplepart Fig.21Examplepartcoverofacellularphone 794 KCHUNG,KLEEANDTKIM ProcInstnMechEngrsVol216PartB:JEngineeringManufacture B05601IMechE2002 andexitareasshouldalsobecoveredbythepartingsurfaces.Sometimes,itisatediousanderror-pronetasktoidentifyallthepassagefeatureswhentheparthasacomplicatedshape.Thealgorithmproposedin thispapercouldshortenthetimefordesigninginjectionmouldsbyautomaticallyrecognizingpassagefeaturespassingthroughmultiplefaces.Thealgorithmproposedinthispaperrecognizes passagefeatureswithincreaseinthenumberoffacestobemerged.Thus,thetimeforrecognizingpassagefeaturesisinuencedbythemaximumnumberoffaces formingtheholeloopsthatcomposesuchpassagefeatures.Asthenumberoffacestobemergedincreases,thetimeforselectingthefacestobemergedalsoincreasesbecausethenumberoffacesetsincreases. Thus,thealgorithmforgeneratingsetsoffacestobemergedneedstobeimprovedbyexcludingunrealisticcasesinadvancebyexploitingtherelationshipbetweenfacesinapart.Furthermore,analgorithmforautomatic generationofpartingsurfacesbasedontherecognizedpassagefeaturesneedstobedeveloped.Generatingapartingsurfacewouldbeevenmoredibullet3 cultwhenthepartingsurfaceislocatedbetweentheentranceandthe exitofapassage.Thissituationoccurswhenthesidefacesofthepassagehaveaconvexcurvature. 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Table2DatasheetofexamplepartsSimplepart L-shapedpart Housingofcellularphone Minicomponentfrontcover Totalnumberofpassagefeatures 6 2 14 15Runningenvironment PentiumII400MHzCPU,256MbyteRAMTotalnumberofcombinationssearched 48 1335 189 5631Runningtime(s) 1.687 20.625 11.250 163.906 Fig.2Examplepartfrontcoverofanaudiosystem RECOGNITIONOFPASSFEATURESFORAUTOMATICPARTINGSURFACEGENERATION 795 B05601 IMechE2002 ProcInstnMechEngrsVol216PartB:JEngineeringManufacture 10Sakurai,H.andChin,C.Deningandrecognizingcavityandprotrusionbyvolumes.InProceedingsofASMEConferenceonComputersinEngineering,September1993,p.5965. 11Vandenbrande,J.H.Automaticrecognitionofmachinablefeaturesinsolidmodels.PhDdissertion,ElectricalEngi-neeringDepartment,UniversityofRochester,1990.12Joshi,S.andChang,T.C.Graphbasedheuristicsfor recognitionofmachinedfeaturesfroma3-Dsolidmodel.ComputerAidedDes.,1988,20,5866. 13Fu,M.W.,Fuh,J.Y.H.andNee,A.Y.C.Undercutfeaturerecognitioninaninjectionmoulddesignsystem.ComputerAidedDes.,1999,31,777790.14Shah,J.J.andMantyla,M.Featurerecognitiontechnique. 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