STEP-NC based reverse engineering of in-process model
of NC simulation
Shixin Xú, Nabil Anwer, Charyar Mehdi-Souzani, Ramy Harik, Lihong Qiao
To cite this version:
Shixin Xú, Nabil Anwer, Charyar Mehdi-Souzani, Ramy Harik, Lihong Qiao. STEP-NC based
reverse engineering of in-process model of NC simulation. International Journal of Advanced
Manufacturing Technology, Springer Verlag, 2016, .
HAL Id: hal-01363744
https://hal.archives-ouvertes.fr/hal-01363744
Submitted on 11 Sep 2016
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STEP-NCBasedReverseEngineeringofIn-ProcessModelofNCSimulation
ShixinXÚ1,2,NabilANWER1,#,CharyarMEHDI-SOUZANI1,RamyHARIK3andLihongQIAO2
1
LURPA,ENSCachan,Univ.Paris-Sud,61avenueduPrésidentWilson,F-94235Cachan,France
2
SchoolofMechanicalEngineeringandAutomation,BeihangUniversity,Beijing,China,100191
3
DepartmentofMechanicalEngineering,UniversityofSouthCarolina,Columbia,SC,USA
#CorrespondingAuthor/E-mail:[email protected]
Abstract
Thispaperproposesacomprehensiveprocessforreverseengineeringandfeaturerecognitionfroman
in-processmodel(IPM),representedintrianglemesheswhichresultsfromNCsimulation.IPMcanbe
ratherusefulinredesign,processplanning,machininginspection,etc.,inadditiontovisualizing
machiningprocesses.Forexample,wemaycarryoutin-processcorrectionsaccordinglybycomparing
therebuiltmodelfromanIPMwiththeoriginalone.However,untilnowIPMreverseengineering,
especiallymanufacturingfeaturebased,isseldomresearched.First,aftersystematicallysummarizingthe
IPMcharacteristicsandtakingadvantagesofthem,anovelregionsegmentationmethodbasedona
shapedescriptor—calledtheshapeindex,whichisclosetothevisualeffectandiscapabletoidentify
localshapesaccurately,isproposed.Theshapeindex,whichisderivedfromprincipalcurvatures,is
calculatedbydiscretedifferentialgeometrymethods.Thesegmentationiscarriedoutgraduallyfrom
simplesurfacetypes,suchasplanes,cylinders,tomorecomplexsurfacetypes;second,therecognition
ofmanufacturingfeaturesdefinedintheISO14649standardisexplainedindetail.Theapproachisgraph
based,andhighlyreliesonthepresenceofconcaveedgesinthemodel.Intherecognitionalgorithm
Eulercharacteristicandcurvednessofthemodelareapplied,whicharenovelattempts.Casestudiesto
verifytheproposedapproachesareprovided.
Keywords:reverseengineering;regionsegmentation;featurerecognition;in-processmodel;discrete
differentialgeometry;NCsimulation;STEP-NC
1. Introduction
Discretedatageometryprocessinghasgainedmoreattentioninrecentyearsinmanufacturingsinceit
permitssimplerepresentationandyetiscapabletoconsidercomplexshapes.Asaprincipalcomponent
ofvirtualmanufacturing,NCmachiningsimulationdepictsthematerialremovalprocessesbysimulating
themovementsofthemachinetoolandthecuttingtools.Generallymachiningprocessesaresimulated
usingatimeordisplacementdiscretizationofthetoolpath.Correspondingtoeachmachiningprocess,
wecangetanin-processmodel(IPM),asanexample,theIPMshowninFig.1.Thismodelisobtainedby
thegeometricmodelingoftheengagementofthecutterwiththeworkpieceatdiscreteintervalsalong
thetoolpath.Therearevariousmodelingtechniquesforthedescriptionoftheengagement,suchasthe
solid-model-based,thewire-frame-based,thevoxel-/dexel-/z-buffer-based,thepoint-based[1].
Althoughthesolidmodelingtechniques(e.g.B-rep)aremoreprecise,discretemeshes(voxel-,dexel-,
andz-bufferbased)aremostcommonlyusedfortherepresentationofcuttingtoolsandworkpieces
becausethedynamicvisualizationofthematerialremovalonthepartisanessentialfeatureinNC
simulation.Inthecourseofsimulation,thein-processmodelscanbeoutputastrianglemeshes(e.g.in
STL/VRMLfiles).NowadaysthemajorityofcommercialNCsimulators(suchasNCSimul®)providesuch
aninterface.
Fig.1AnIPMoutputafteraroughingprocess
AlthoughresearchonfeaturerecognitionfromregularCADmodelshasbeendoneextensively,feature
recognitionandreverseengineeringfromIPMsarerarelyreportedandstudiedsofar.Anwer,etal[2]
proposea“onesurfacepertrianglemethod”,whichusesaspecialunderlyingdatastructureoffacets.
Thisdatastructureisevaluatedduringthesimulation.Theirmethodisefficientandrobustwhenthe
meshesarenotverylarge.
Untilnow,themajorgoalsofNCsimulationarestillconfinedtocheckanunprovedNCprogramtoavoid
potentialcollisionswithfixtureelements,makingundercuts,orleavingexcessmaterial.However,
ReverseengineeringoftheIPMcanberatherusefulinredesign,processplanning,machininginspection,
etc.Forexample,bycomparingthereconstructedmodelfromanIPMwiththeoriginalCADmodel,we
canknowthepotentialmachiningdeviationofamachiningoperation,thenwemaycarryoutin-process
correction.Inthiswork,bymakinguseofthesimulatedoutput—theIPM,andbyre-establishinga
machiningfeaturebasedmodel,wecanextendtheapplicationsofNCsimulationtobuildthefeedback
linkfromCAM/CNCsystemsorshopflooramendmentsbacktoCAM/CAPP/CADsystems.Thisfeedback
linkisveryusefulbecausethepartprogramisoftenchangedbymachiningengineersaccordingtothe
simulationresultsortheshopfloorsituation.SothecurrentunidirectionalinformationflowfromCAMto
CNCcanbechangedintobidirectionalone[3].There-establishedfeaturemodelcanservefordesign
improvementssincewecancomparethismodelwiththeoriginaldesignedmodel,measuremore
reliableandaccuratedimensionsonthismodel,oruseitforFEA,etc.
Inaddition,insomesituations,theoriginalCADmodelisneitheravailablenorusable,andtheNC
programistheonlydataavailableforproducingapart.ThiscouldhappenwhenoldCADarchivesare
incompatiblewithnewsystemsormachines,ortheyaredamagedorlost,orwhenpartsaredesigned
andmachinedonlyatshopfloors,etc.HencerebuildingthefeaturebasedCADmodelfromtheIPMis
necessaryunderthesecircumstances.Itwouldsavemuchresourcethandesigningafeaturebased
modelfromscratch.
Thesepracticalneedsthusprompttoustodeveloptechniquesforfeaturerecognitionandreverse
engineeringofin-processmodelstopromoteCAM/CNCintegrationandbidirectionalinformation
transferbetweenthem.Theresearchworkreportedinthispaperismotivatedonbasisoftheabove
observationandactualneeds.ItmainlyexplainsonapproachestoIPMsegmentationandthen
recognitionofmanufacturingfeatures(i.e.STEP-NCfeatures).Theremainderofthepaperisorganizedas
follows:Section2presentsbrieflythereviewofliteratureonmeshsegmentation,feature
recognitionandexistingworkonreverseengineeringNCsimulationandG-Code.Section3
describesthecharacteristicsoftheIPMgeometricdata.Section4presentsanoverviewframeworkof
thedevelopedapproach.IPMcoarseandfinesegmentationapproachesareelaboratedinsection5.
IPMcoarsesegmentationapproachiselaboratedinsection5.STEP-NCmanufacturingfeatures
recognitionapproachandclassification-basedrulesarepresentedinsection6.Casestudiesare
presentedinsection7.Finally,conclusionsandperspectivesofthisresearchworkarediscussed
insection8.
2. Relatedworks
Therelatedworksmainlyinvolvemeshsegmentationandfeaturerecognition.Meshsegmentation
partitionstheunorganizedtrianglesetintosubsets,eachofwhichissupposedtocorrespondtoa
particulartypeofsurface.Theresultisregioncollections,likeasurfacemodel.Featurerecognitionisto
furtherextractandorganizesomeregionsintomanufacturingfeatures.Thesourcedataisusuallyasolid
model,butitalsocanbeothertypesofdata,suchaspolygonmeshes,pointcloud,oraG-codeprogram.
2.1Meshsegmentation
Meshsegmentationorregionsegmentationplayanimportantroleinthediscreteshapemodeling
domain.Segmentationmethodstrytoexploitgeometricinformationtoinferadecompositionofthe
surfacethatcorrespondstotheonethatexpertswouldproducemanually[4].Whenobservinga
renderedtrianglemesh,wecaneasilyperceiveadecompositionofthesurfaceintointerestingregions,
suchasprimitiveshapes,whereasitturnsouttobearatherhardtaskforautomation.Segmentation
methodshavebeencomprehensivelysurveyedbyShamiretal[5,6].Segmentationformechanical
engineeringapplicationsaimsatpartitioningthediscretepartmodelintoregionsandeachregioncanbe
fittedbyasinglemathematicallyanalyzableshape.Thesegmentationalgorithmsforamechanicalpart
meshmodelarebroadlyidentifiedintwomaincategories:
Edge-basedapproaches[7-11]–Theytrytodetectboundariesbetweensurfacepatches.Some
derivativeattributes,likenormalvectors,curvatures,arecommonlyusedtofindtheboundaries.Normal
vectorsareusedtodeterminesharpedgesandcurvaturesforsmoothedgedetection.
Face-basedapproaches[12-16]–Theyclusterpoints/verticesintoconnectedregionswithsimilar
propertiesandboundariesarethenderived.Thiscategoryworksontheglobalsizeofpointsetandsoit
ismorerobusttotheedge-basedone.Bénière,etal[12]havepresentedanddevelopeda
comprehensiveprocesstoextractgeometricprimitivesandbuildaB-repmodelfrom3Dmeshes.
Inaddition,therearesomeapproachescombiningedge-basedandface-basedinformationtotryto
overcomelimitationsoftheabovetwocategoriesofapproaches[17,18].Tosegmentmeshesobtained
frompointcloud,Zhao,etal[19]usecurvednesstodetectshapeboundary,anduseshapeindexto
clustervertices.Thispaper’sworkisacontinuationoftheirapproachappliedinIPM.
Mostofthesegmentationapproachesaredirectlybasedonderivativeproperties(normalvectors,
principal/Gaussian/meancurvatures),whicharesensitivetonoise.Theyassumethepolyhedral
surfacesarenoiseless.ButIPMdatahasakindof“noise”—scallopsleftonmachinedsurfaces.Sothereis
noverysuitablesolutionreportedtoregionsegmentationforin-processmodelsyet.
2.2Featurerecognition
Afeature,oraformfeature,tobemorespecificallyinourwork,usuallyreferstoaportionofapartthat
bearscertaingeometricortopologicalproperties,fromwhichwecandeducethemanufacturing
informationformakingthem.Completenessofformfeaturesetisverysubjectiveanddomain
dependent.AfeaturegenerationmodelproposedbyNallurietal[20]attemptstodefinethe
completenessofafeatureset.Theydefinedomainindependentformfeatureasasetoffaceswith
distincttopologicalandgeometriccharacteristics.Theymodelcreationofaformfeatureasadditionor
subtractionoffeature-solidto/frombased-solid.Theydefinefeature“type”basedonthelocaltopology
ofparticipatingbase-solidfacesand“shape”basedonshapeofthefeature-solid.Basedonthese
definitionstheyenumerateandclassifyformfeatures.Theyenumerate94sweepformfeaturesand
provideproofthatthose94typesarecompleteforsweepfeature-solid.
Inthispaperweareinterestedinmachiningfeatures,whichareconcernedwithboththegeometric
shapesandmanufacturingoperations,needingmoreparametersintheirdefinition.Forexample,we
mayeitherusethename“pocket”torefertoasweptcutontheboundaryofapartmodel,ortoatrace
leftonthepartboundarybyaspecificmachiningoperation.Machiningfeatures,asanimportantsubset
ofmanufacturingfeatures,canberegardedasthevolumesweptbyacuttingtool,whichisalwaysa
negative(subtracted)volume.Workonfeaturescanbedividedintotworoughcategories:design-byfeatures[21]andfeaturerecognition[22].Indesign-by-featuresfeaturestructuresareintroduced
directlyintoamodelusingparticularoperationsorbysewinginshapes.Ontheotherhand,thegoalof
featurerecognitionistoextractautomaticallyhigherlevelentities(e.g.machiningfeatures)fromlower
levelelements(e.g.surfaces,edges,etc.)ofaCADmodel.
Automaticfeaturerecognitionisregardedasanidealsolutiontoautomatedesignandmanufacturing
processes.Thisisthepartoftheresearchthathasattractedmuchoftheattention.Anotherimportant
applicationoffeaturerecognitionisformanufacturabilityevaluation.Afeaturerecognitionsystem
shouldbeabletointerpretthedesigndifferentlybasedonalternativefeaturesandfeedbackthe
manufacturabilityandcostofthoseinterpretationstothedesigner.
TherearedifferentfeaturerecognitiontechniquesthathavebeenproposedforCAD/CAMintegration
andprocessplanning.Hanetal[22]providesadetailedanalysisofsomeoftheexistingapproaches.The
mostcommonmethodsrangefromgraph-basedalgorithms[23]tohint-basedandvolumetric
decompositiontechniques.Inthegraph-basedfeaturerecognition,agraphshowingthetopologyofthe
part(connectionoffaces)iscreated.Thegraphisoftenattributed(e.g.,theedgesaremarkedas
concaveorconvex),itisthenanalyzedtoextractsubsetsofnodesandarcsthatmatchwithapredefined
template.
Graph-basedapproachesarecriticizedforseveralshortcomings.Theyfailtoaccountfor
manufacturabilityoftherecognizedfeaturesduetotheirstrongrelianceontopologicalpatternsrather
thangeometry.Theintersectionoffeaturescausesanexplosioninthenumberofpossiblefeature
patternsthatspoilsattemptstoformulatefeaturepatterns.Toaddressthesedifficulties,Vandenbrande
etal[24]proposedtosearchfor“minimumindispensableportionofafeature’sboundary”,calledhints,
ratherthancompletefeaturepatterns.Forexample,presenceoftwooppositeplanarfacesisahintfor
potentialexistenceofaslotfeature.Hintsarenotnecessarilyrestrictedtothepartgeometry.Theycan
beextractedfromdesignattributesaswell.Forexample,“athreadattributemaybetakenasahole
hint”.Thisapproachhasbeenmoresuccessfulinrecognizingintersectingfeatures.Someauthors[25,26]
areinfavorofusingahybridofgraph-basedandhint-basedfeaturerecognitiontoimprovethe
efficiencyofhint-basedreasoning.Inthehybridapproach,graph-basedreasoningisusedtofindout
thoseareasofthepartthatcertainlyleadtovalidfeatureswhenusedbythehint-basedreasoner.
However,buildingfeaturerecognitionsystemsthatfunctioneffectivelyonrealindustrialproductshas
beenelusive.Arealproductwiththousandsoffacesandedgesbringsalmostalltheaboveapproaches
toahaltduetocomputationalcomplexity.Furthermore,thefeaturesstudiedintheseapproachesare
usuallyoversimplified.Themajorityoffeaturerecognitionliteraturenormallyhandles2½Dfeatures.The
workdonebySundararajan[27]isfocusedonfreeformsurfaces,butitislimitedinapplication.Some
issuessuchasthepresenceoffilletededgesandfreeformsurfacesinthemodelarestudiedbyRahmani
andArezoo[25].
Fewcommercialfeaturerecognitionsystemsarealsoavailable.Theyhaveeffectivelyadoptedfeature
recognitiontechnologyforrecreatingthefeaturetreefromimportedmodelssothateventheimported
modelscanbeeditedasifitwereanativemodel.Major3DCADmodelershavefeaturerecognitionto
convertimported3Dmodelsintonativefeaturebasedmodels.CAMsoftwareanddesignfor
manufacturingsoftwarearealsobuiltusingthistechnology.FewCAD/CAMsoftwarehaveused
commerciallyavailablethird-partyfeaturerecognitionlibrary,whichrecognizesvariousfeaturesfromBrepmodels[28].Separatelibrariesareavailablefordesign,manufacturingandsheetmetalapplications
[28].However,manufacturingfeaturessuchas3/4/5-axisfeaturerecognitionaregenerallyunavailable
insuchcommercialsystems.
ManyresearchesfocusedonreconstructionofsurfacesorB-Repsolidmodelfromtriangularmeshes,but
onlyfewwentfurthertorecognizefeatures.TheworkdonebySuniletal[29]enablestoperform
featurerecognitionfromameshmodelofsheetmetalparts.Kiswantoetal[30]discussedfeature
identificationbyemployinginformationfromnormalvectorsoffacetedmodel.Thisinformation
togetherwithcurvatureinformationareusedtodetectflat,saddle,concave,convexandclosedbounded
featuresonasculpturedsurface.Extractingfeatures,especiallySTEP-NCfeatures,fromafacetedmodel
stillneedstobeinvestigatedfurther.
Verylimitedworkshasbeenreportedonrecognitionmanufacturing/machiningfeaturesfromaninprocessmodelofNCsimulation[2],toourknowledge.Inparticular,noregionsegmentationworkthat
usesshape-indexhasbeenreported.IfdevelopedtheNCsimulationfunctionscanbeextended.The
emphasisofourpresentworkisonthereverseengineeringandfeaturerecognitionofin-processmodels.
Variousdesignandrealizationissuesareaddressedinthesectionstofollow.
2.3ReverseengineeringofNCsimulationandG-code
TheNCsimulationgeometricresult,thein-processmodel,canbeusedtorebuildapart’sCADmodel.To
ourknowledge,reportedworkonthisproblemisscarce.Karunakaran,etal[31]proposedanalgorithm
foroctree-to-B-repconversion,whichcandealwiththereverseengineeringofthesimulationwhose
geometricoutputisoctreerepresentation.Anwer,etal[2]proposedtwomethods:“onesurfaceper
triangle”methodanddiscreteshapesegmentationmethodforprocessingmesh-outputofNCsimulation.
TheformeroneturnsthemeshintoapolygonalB-repmodel,byattachingsuchinformationascolor
indicatingatool,cutnumber,surfaceindextotrianglemeshesinthecourseofsimulation.Eachtriangle
isturnedintoafaceoftheB-repmodel.ThismethodwasrealizedincooperationwithadeveloperofNC
simulationsoftware.Thelatteroneisbasedondifferentialgeometryandthepairshapeindex,
curvedness.Thismethoddecomposeverticesintoagroupofregionsthatcanberepresentedbyprimary
shapes.Xu,etal[32]continuedtheaboveworktobuildamachiningfeaturebasedmodelfromtheIPM.
ApartprogramG-codecanalsobeusedtorebuildthepart’sCADmodelbysupplementingcuttingtool
andrawpieceinformation.Cioană,etal[33]developedanadd-onapplicationforSolidWorks®toimport
toolpathdatafromGcode,togetherwithcuttingtooldata,tobuildaCADmodelinteractively.Yanetal
[34]developedamethodforfeaturerecognitionfromG-codebasedonZ-maprepresentationofforms
(workpieceandtools).Foreachcuttingoperation,theirsystemcreatesandupdatestheZ-mapofthe
machinedareaandextractscutcontours,cuttingparametersandmillingfeature.Millingfeature
recognitionisdonebycomparingZlevelsandcheckingthecontinuityofthecutcontours.Shinetal[35]
developedasystemcalledG2STEPtoconvertG-codeintoSTEP-NC.IntheirapproachturningG-code
programsarehandledindetail,andturningfeaturerecognitionarementioned.Zhangetal[3]proposed
amethodtore-usetheprocessknowledgeembeddedinG-codepartprogramswithdifferent
manufacturingresources.Theirmethodcanrecognize2½DfeaturesfrommillingG-codemainlybytool
types,toolpathboundaryandtherawpiecegeometry.
3. In-processmodelcharacteristics
Anin-processmodelisthegeometricoutputdataofanNCsimulation.Invirtualmachiningitisusedfor
visualizationofthemachiningprocess.Thein-processmodelcanbeoutputbythesimulationsystemasa
collectionofunorderedsetoftriangles,whichareusuallyinSTLfileformat.Intermsoftriangleshapes
withinatrianglemesh,therearetwodistincttypesoftrianglemeshes.OnetypeisasshowninFig.2a
(typeI).Withinarequiredsurfacedeviation,thistype,whichisusuallyusedforvisualizationpurpose,
usesasfewtrianglesaspossibletodiscretizeapart’ssurfacesinordertopresentrapidlythedynamic
variationsoftheworkpiecebeingmachined.Thesize,shapeanddistributiondensityoftrianglesare
quitedifferent.TheothertypeisshownasinFig.2b(typeII).Theshapesoftrianglesareroughlysimilar,
butthesizesoftrianglescanbequitedifferent,andtrianglesareusuallydenselydistributedinsurface
zonesoralongcurvedboundaries,whichmeansthenumberoftrianglesperunitareaismorethanother
zones.Thistypeoftriangulationisusuallyusedforanalysis,suchasFEA.Thefactorstocontrolthesizes
anddistributionsoftrianglesarethemaximumtriangle’sedgelengths,elementnumberpercurvature
radiusofthepart’ssurface,etc.OnecommonmethodtogettypeIItriangulationistheDelaunay
triangulation,whichmaximizetheminimumangleofalltheanglesofthetriangles,tendingtoavoid
skinnytriangles.Intermsofthequalityofthetrianglemeshdata,typeIIisgenerallybetterthantypeI.
Besides,thetrianglemeshobtainedaftertheprocessingofscannedcloudpointsinreverseengineering
belongstothistypesinceahugenumberofthedensepointsareusedtoconstructthemesh.TheNC
simulationrequiresrapiddisplayandupdateofthegeometricvariationoftheworkpiecebeingcut,so
theIPMadoptstheformertypeoftrianglemesh.Ittriestousetheleastnumberoftrianglesforbetter
performance.
ByobservingtypeItrianglemesh,wecanfindthat,exceptfortheplanar/cylindricalzones,the
characteristicsoftriangleswithinthesurfacezonearequitesimilartothoseoftypeII.Thereforewe
havetodeviseanIPM-basedregionsegmentationmethodthatcanefficientlyhandletrianglemeshtype
IaswellastypeIIconsideringthatageneralmechanicalpartiscomposedofplanarandcylindrical
surfacesandpossiblymanyothertypesofsurfaces.
ab
Fig.2Twotypesoftrianglemesh:a)typeI;b)typeII
OnedistinctivecharacteristicsofIPMisthatthereareoftenscallopsandstepovertraceslefton
machinedsurfaces,asseenonthewallfacesinFig.3.Thepartismachinedbyanendmillcutter.These
scallopsandtraces,whichwilldisturbthetrueunderlyingsurfacetyperecognition,canbeconsideredas
akindofnoise.
AnothercharacteristicoftheIPMofNCsimulationisthatitoftenhasoffcutcomponents,someofwhich
areevenconnectedtothefinishedpartthruathinslice,liketheoffcutcoloredinredasshowninFig.3.
Fig.3AnIPM(Theconnectedoffcutisindicatedbyredcolor.)
AnothercharacteristicofIPMisthatitusuallyhasplentyofclustersofnarrowtrianglesinplanarand
cylindricalregions(Fig.2a).Thesenarrowtrianglesresultfromthediscretizationofcylindershapesor
ruledsurfacesonthemechanicalpart,andtheirconnectionshavecertainregularpatterns.Large
trianglesarepresentinplanarfaceswhoselineboundaryedgesarenotdiscretized.
Hence,anin-processmodelofNCsimulationisamodelwithnon-uniformvertex/triangledistributions.It
ismainlycomposedofthreetypesoftriangles:narrowtriangles,relativelysmalluniformtrianglesand
largetriangles.
4. Overviewofthemethod
Infacttheworkistoestablishahigh-levelgeometricstructurebasedontheunstructuredtrianglemesh.
ConsideringthesecharacteristicsofNCsimulation,andtakingadvantageofthem,wehavedevisedan
efficientmethodforsegmentationandfeaturerecognition,whichisuniquelyadaptedtoin-process
model.Fig.4showstheoverallstrategyofthemethodwhichconsistsofthefollowingsteps:(1)
PolyhedralB-repmodelconstruction:thisisthepre-processingoftheIPM,includingoffcutremoval,IPM
dataerrorcorrection,thebuildingofamanifoldpolyhedralB-repmodel;Computationofvertexnormal
vectors,vertexcurvatures,edge-xities,someattributesoftrianglemesh,etc.Thesewillbeusedfor
subsequentprocessingandfordeterminingsomethresholds.(2)Coarsesegmentation:identificationof
sharpedgesonthepart’sboundary,identificationofnarrowtriangleclusters,segmentationofplanar
andmostofcylindricalfaces;(3)Shapeindexbasedsegmentationandrefinement:segmentationofnonruledfaces.Ninesurfacetypesaredefinedbasedonshapeindex.Everyvertexoftheshapeisassigneda
surfacetypelabelduringlocalsurfacetyperecognition.Thenconnectedregionsaregeneratedfrom
theseclusteredvertices;(4)STEP-NCfeaturerecognition:featureclassidentificationanditsdefining
components,suchasitsprofile(s),parameters.
Fig.4Flowchartofthemethod
Thepre-processingstepincludesremovingoffcuts,buildingapolyhedralB-repmodelandcomputesome
geometricvalues(likefacetnormalvectors,dihedralanglesbetweentwofacets).TheNCsimulation
software,suchasNCSimul®,generallyoutputsIPMasanSTLfile.Thisoriginalmeshdatausuallycontains
offcuts,isolatedvertices/edgesusuallyresultingzero-areatriangles,incorrectlyorientedtriangles,holes,
etc.Forexample,theIPMshowninFig.3hasapartoftheoffcutsthatisstillconnectedtothefinished
part.
ForamendingthevariousdefectsoftheIPM,approachesarebriefedasfollows:Isolatedornonmanifoldvertices/edges/facesaredetectedandcorrectedautomatically(Forexample,ifazero-area
triangleisfound,anisolatedvertexoredgeisdetected,thenthistrianglecanberemoved.);incorrectly
orientedtrianglesarereversedautomaticallyaccordingtotheorientationoftheirneighboringtriangles;
holesarefilledinteractivelyinconsiderationthatthemodelcanbeanon-solidmesh,andareal
boundaryandahole’sboundarycannotbeidentifiedautomatically;theoffcutsarecleanedinteractively
sinceitiseasytomakeoutthemforauser.Ifanoffcutisconnectedtothepart,theremightbesome
newholesleftontheIPMafterauserdeletesittocleanthemodel,ameshsplittingoperationwitha
polygonsectionisusedandmakesuretheholeshealed.
Thereforeafterrepairingthemodel,inourcase,webuildawatertightpolyhedralB-repmodel,inwhich
eachtriangleisbuiltasanorientedface,andmeanwhiletheIPMdataiscorrected[2].Weadoptthe
half-edgedatastructurefortheB-repmodel.Thisprocedureincludeeliminationofoffcutdata,
constructing/healingmodeltopology,computinggeometricvaluesofthemodelandstoringthemtothe
extendedattributesoftherelevantentities(faces/edges/vertices).Thepre-processedIPMcanbesaved
asanalternativemeshfileformat,OFF,whichisindexbased,andhencemuchsmallerinsizecompared
withthecorrespondingSTLfile.AfterfinishingthissteptheIPMdatahasnoduplicatedvertices,no
wronglyorientednormalvectors,nodegeneratedfaces,nonon-manifoldentities,andnoinvalidface
indices.
5. In-processmodelsegmentation
Inthissection,anewsegmentationmethodisdevelopedtoidentifymachiningregionfromtriangular
meshesofthein-processmodelofNCSimulation.Aftertheidentificationofsharpedgesandgrouping
narrowtriangles,thensmallregulartrianglesarealsogrouped.Fromthesegroups,regionboundaries
areidentified.Torecognizethesurfacetypesforthegroupsofsmallregulartriangles,shapeindexbased
segmentationisapplied.
5.1Identificationofsharpedges
Theedge-xity,whichisameasureofanedge’sconcavity/convexity,isusedtodecidewhetheranedgeis
anobviouslysharpedgeornot.Forasharededgeoftwosurfaces,theedge-xitymisdefinedas(Fig.5)
[36]:
m=(n1×n2)‧a1(1)
Where,n1,n2areunitnormalvectorsofthetwosurfacesF1andF2,a1istheirsharededgee’sdirection,
representedasaunitvector.
ab
Fig.5Definitionoftheedge-xity:a)smoothmodel;b)discretemodel
Herewesupposethatif|m|≥ε1(Whereε1isasmallvalue,whichcanbeadjustedbyusers.),thenthe
edgeisconsideredasasharpedge.Thisconstraintcorrespondstothedihedralangleofthetwofacets.
Forexample,whenε1=0.5,itisequivalenttohaveaconstraintonthedihedralanglebetween30°and
150°.Fig.6showstheobviouslysharpedgesfilteredoutingreen.
Fig.6Sharpedgesfilteredbyedge-xities
5.2Identificationandgroupingofnarrowtriangles
Firstwedefinetheshapeattributeofanarrowtriangle.Inatriangle,ifoneofitsangleα<ε2,andno
otheranglegreaterthan(90°+ε2),thenthetriangleisconsideredasanarrowtriangle.Hereitiscalleda
pintriangle.Besidesthetriangle’sshape,thegroupingcriteriaalsotakesaccounttheadjacency
relationshipandthesizeofthetriangles.Thisstepistogrouptheconnectedpintrianglesinthemesh
intoregions.Wehavenoticedthatapintriangle’sheadedge(i.e.theoppositeedgeofthetriangle’s
smallestangle,theshortestedgeinthetriangle)isusuallyresultedfromthediscretizationofacurved
edge.
Thegroupingoperationisperformedasfollows:Forapintriangle,ifoneofitssideedges,whichform
thesmallestangle,isnotasharpedge,andtheadjacenttriangleisanaxetriangle,thenaddtheadjacent
triangletothisgroup.Dothesameforthepintriangle’sanothersideadjacenttriangle.Repeatthe
groupingoperationforthenewlyaddedtriangle(s).Inthegrouppintrianglesareconnectedonlybytheir
sideedges,andtheirheadedges’lengthsalongacertaindirectionaresimilar.Bytheendofgrouping
operation,iftherearelessthan3pintrianglesinagroup,wedropthisgroupsincetheyareunlikely
resultedfromacylinder.Fig.7showsaresultaftergroupingpintriangles.(Herewesetε2=15°inthe
experiments.)
Nexttodeterminetheunderlyingsurfacetypesofthegroupregionsofthepintriangles.Thesurface
typeshouldbeplanarorcylindricalinmostcases.First,usethelinearleastsquaremethodtodetermine
whetheragroupregioncanbefittedbyaplaneornotwithinagiventolerance.Ifthegroupregion
cannotbefittedbyaplane,thenusetheGaussimagefeatureofacylinder(whichismappingfroma
pointonasurfacetotheunitnormalofthesurfaceatthispoint)todeterminewhethertheregionisa
cylinderornot.TheGaussianimageofacylinderisagreatcircleontheGaussiansphere,i.e.thenormal
ofthefacetsformingthecylinderformapartofthegreatcircleontheGaussiansphere.Take3
connectedfacetstostart,if(1)thereisaconstrainedplanepossiblepassingthrutheoriginofGauss
spheresuchthatthedistanceofthe3normalpointsfromtheconstrainedplaneisbelowathreshold
valueand(2)thecirclefittedonthese3pointsformsapartofgreatcircleonGausssphere(i.e.center=
(0,0),radius=1),thenthe3connectedfacetsformacylinder.Addadjacentfacetifitsatisfiestherules.
Markidentifiedcylindricalfacetsasconvex(ridge)orconcave(valley)dependingonwhetherthefacet
normalsaredivergingorconverging.Iftheregionisnotacylinder,thensettheregionasundetermined
surfacetype.Forthiscase,theregionprobablybeothertypeofruledsurface,orapartofatorus,ora
partofasurface.Theregion’ssurfacetypewillbedeterminedbythesubsequentcurvature-based
segmentationmethod.
Fig.7Narrowtriangleidentificationandgrouping
5.3Groupingsmallregulartriangles
SmallregulartrianglesareusuallydiscretizedbyageneralsurfaceinanIPM.Theyhaverelatively
uniformsizesandshapes,andtheyaredenseinaregion.Thegroupingpurposeistocontrolthesizeof
sub-components,whichpossiblymakesthesegmentationlesscomplicated.Thegroupingoperationtries
tostartfromboundarytrianglesofaregionbeingformed,andisperformedasfollows:selectaseed
trianglethatisnotyetgroupedandsharesanedgewithapintriangle'sheadedge.Ifthereisnopin
triangleintheIPM,fromtheungroupedtriangles,selectaseedtrianglethathasasharpedge.Checkthe
seed’sadjacenttriangle,iftheadjacenttriangleissimilartotheseedintermsofshapeandarea,then
addittothegroup.Againcheckthenewly-addedtriangle,graduallyexpandthegroupwithtrianglesthat
aresimilartotheiradjacentonesuntilnomorecanbeadded.Thegroupingoperationsshouldnotcross
sharpedgeboundaries.
Inthesegroups,thereareprobablystillsomeplanarand/orcylindricalregionsleft,usethesame
methodsin4.2toidentifythem.TheresultforthisstepisshowninFig.8.
Fig.8Smallregulartrianglegrouping
5.4Groupmergingandidentificationofregionboundaries
Thisstepistomergeadjacentregionsofthesametypestoreducethenumberofregionsobtainedinthe
previoussteps.Forplanartypeofregions,ifseveralgroupsandtheirsurroundingungroupedtriangles
arecoplanar,theycanbemergedintooneregion.Iftwoadjacentcylindricaltypeofregionshavesame
axisandradius,theycanbemergedintooneregionaswell.Ifseveralungroupedbigtrianglesare
coplanar,theycanbegroupedasaregion.Aftertheseexpansionandmergeoperations,thereprobably
arestillsomeisolatedtriangles(liketheonesinthebottomsofthesurfacesasshowninFig.8).Ifthe
adjacenttrianglesoftheisolatedonebelongtoasmallregulartrianglegroup,addtheisolatedtriangle
tothisgroup.
Aftertheaboveoperations,eachtrianglebelongstoaplanarorcylindricalregion,oraregulartriangle
group.Inaregionitsexternaledgesformitsboundary.Aregion’sboundary,likeaface,possiblyconsists
ofoneormoreedgeloops.Aloop’sdirectionkeepsthedirectionofhalfedgesinboundarytriangles.Ina
planarregion,theloopscanbemarkedasouterorinnerloops.Ifaloop’snormalvectorconformstothe
region’snormalvector,thenitisanouterloop;ifaloop’snormalvectorisoppositetotheregion’s
normalvector,thenitisaninnerloop.Inordertofacilitatesubsequentapplications,ifseveral
consecutiveboundaryedgescanformacircle/arc,theyarelabeled.Fig.9showstheparts’regionsafter
coarsesegmentation.Regionsaredemarcatedbyblueboundaries.Theunderlyingsurfacetypesofthose
groupsinorangecolorwillbedecidedinthenextfurthersegmentationprocedureusingdiscrete
differentialgeometrymethods.
Fig.9Resultsofcoarsesegmentation
5.5Shapeindexbasedregionsegmentation
Aregulartrianglegroupobtainedabovemightbecomposedbyseveralsurfacepatchesunderneath.This
phaseistoidentifythetrianglesetofthesepatches.Thesegmentationisperformedontheregular
trianglegroups.Specifically,itisoperatedonthesetofverticesoftriangleswithinagroup.Avaluecould
beassociatedwitheachvertexinthevertexsetwhichsomehowencapsulatesthecharacteristicsofthe
localityofthevertex.Thedefinitionofsegmentationisthepartitionofverticessuchthateachregion
consistsofconnectedverticeswhichhavethesamevaluewithinatolerance.
Inthisphasethefirststepistoidentifyflat(planar)typeofverticesbasedonthenormalvectorsof
triangles.Themethodisasfollows:foravertexofatriangleintheregulartrianglegroup,computethe
normalvectorsofthevertex’sone-ringtriangles,comparethesevectors,iftheirdirectionsareequal
withinatolerance,thenmarkvertex’stypeasflat.Thissimpleyeteffectivemethodbypassescurvature
sincecurvaturecalculationneedsnormalvectorinformationaswell.
Thesecondstepistocomputethecurvatures.Theprincipalcurvaturesandprincipaldirectionsfor3D
meshesarecomputedfromthevertex’sneighborhoodvertices[37-39].Themethodadoptedhereis
basedontheworkreportedin[37],whichwasimprovedbyaddingweightstothediscreteshape
operatormatrixandmodifyingneighborregion[2].Specialattentionshouldbepaidtoverticesonthe
modelboundary.Theboundaryistheintersectionofadjacentsurfaces,whichimpliesthatthegeometric
propertyofeachvertexonaboundaryshouldbecalculatedfromitssurroundingneighborhoodwithin
onesurface.Iftheneighborhoodverticesarechosenacrosstheboundary,highdeviationoftheprincipal
curvaturesofthevertexwouldoccur.Tolowerthedeviation,theanisotropicneighborhoodisadvised
here.Basedonthecoarsesegmentationresult,whichhasmarkedtheregion’sboundaryedges,we
choosethetwo-ringneighborhoodtrianglesofavertexexclusivelywithintheregion(whereas,foran
innervertex,chooseonlyone-ringneighborhoodtriangles.),andthereforemoreaccuratecurvatures
wouldbeobtained.Forexample,inFig.10,tocomputethecurvaturesofvertexV,onlythe7neighboring
verticesofVintheorangeregionareused,theother4verticesinthelightorangeregionarenotused.
Thefirstringverticesareindicatedbybluecolor,andthesecondringverticesareindicatedbylightblue
color.Whentherearescallopnoisesusuallycausedbyaball-endcuttingtoolmachiningintheIPMdata,
wecanchoosetwoormoreneighborhoodtrianglesofavertextocomputethevertex’scurvatures.This
caneasethedisturbanceofthescallops.
Fig.10Neighborhoodvertexselectionforcomputingcurvaturesofavertexonregionboundary
Thethirdstepistocomputetheshapeindexvalueforthenon-flattypeverticesandclassifythem
accordingly.Shapeindex,asinglevaluefordescribinglocalshape,isselectedasthemathematicalbasis
forregionsegmentation[40].Theshapeindex,ranged[-1,1],iscalculatedbytheprincipalcurvatures.
Shapeindexisdefinedas:
(2)
Where,kmaxandkminarethemaximumandminimumprincipalcurvaturesofavertex,respectively.
Thenforthenon-flattypesofvertices,ninesurfacetypes(sphericalcup,trough,rut,saddlerut,saddle,
sphericalcap,dome,ridgeandsaddleridge)aredefinedbasedontheirshapeindexvalues(Fig.11).Note:
weaddanisolatevalue2,whichisnotcalculatedbytheshapeindexformulaanddoesnotbelongtothe
shapeindexinterval,forlabelingflatvertices.Everyvertexoftheshapeisassignedasurfacetypelabel
duringlocalsurfacetyperecognition.
Fig.11Surfacetypes,shapeindexscalesandcolorscales
Thefourthstepistogenerateconnectedregionsbyclusteringverticeswhichhavethesamesurfacetype.
Thentwooperationsareperformed[19]:connectedregiongrowingtogenerateinitialsegmentation
result,andregionrefining,whichaimstoreduceover-segmentedregionsandtoimprovethe
segmentationresult.Whenavertexyetunassignedwitharegionlabelismet,thevertexismarkedwith
aregionlabelbyitsneighborcondition.Withthisassociatedregionlabel,thevertexisaddedtoan
existingregionorcreatesanewregion.
ThestepsfortheregionsegmentationofaregulartrianglegroupareillustratedinFig.12.
Setofverticesofaregulartrianglegroup
Identifyflattypeofvertices
Identifysurfacetypesofnon-flatverticesbyshapeindices
Vertexclusteringandconnectedregionlabeling
Partitionsatisfying?
N
Regionmergingandrefining
Y
Regionsegmentationresults
Fig.12Stepsfortheregionsegmentationofaregulartrianglegroup
TheIPMregionsegmentationestablishedahigherstructureonthetrianglemesh.Theresultisalistof
regions,andeachregionisgiventhefollowinginformation:allfacets(triangles)oftheregion,itssurface
type,anditsboundaryedgesanditstype(line,arc…).
6. Manufacturingfeaturerecognition
ThissectionelucidatesSTEP-NCmanufacturingfeaturesrecognitionapproachandclassification-based
rules.AfterabriefintroductionofSTEP-NCfeatures,wepresentsrulesonlybasedontopological
characteristicstoclassifyfourbasictypesofformfeatures,whichcoversthemajorityofSTEP-NC
features.ThendetailedexplanationtorecognizevarioustypesofSTEP-NCfeaturesaregiven.
6.1STEP-NCfeatures
ThemanufacturingfeaturesdefinedintheISO14649(STEPDataModelforComputerizedNumerical
Controllers)standardareoftencalledSTEP-NCfeatures.ISO14649isamodelofdatatransferbetween
CAD/CAMsystemsandCNCmachines[41,42].Itaimsatstandardizingthedataformatsusedatthe
machinelevel,onekeylinkintheentireprocesschaininmanufacturingenterprises.Itspecifies
machiningprocessesratherthanmachinetoolmotion,usinganobject-orienteddatastructure.The
essentialentityofthestandard,“machining_workingstep”,specifiestheassociationbetweena
manufacturingfeatureandamachiningoperationcompletedtothatfeature.Itencapsulatesdesign
information(i.e.manufacturingfeature)andmanufacturinginformation,suchascuttingtool,feedrate,
cuttingspeed,coolantstatus.STEP-NCcreatesanexchangeable,workpiece-orienteddatamodelforCNC
machinetools,supportsthedirectuseofproductdatafromISO10303.Thedatamodeloftherecent
STEPAP242[43]formachiningformfeatureisconsistentwithSTEPAP214andSTEP-NC.
Fig.13showstheSTEP-NCmanufacturingfeature,whichisanabstractsupertypeofregion,transition
featureand2½Dmanufacturingfeature.ThisfigureindicatesthataSTEP-NCfeatureisdefinedimplicitly
byasetofparameters.Afeaturewithaprofile,likepocket,slot,step,isdefinedusinganopen/closed
boundarywithadepthoratravelpath.Forexample,informationoffeature’sdepth,placement,‘feature
boundary’and‘bottomcondition’isusedtodefineaclosedpocket.The‘featureboundary’(aclosedand
non-self-intersectingprofile)ofaclosedpocketisdefinedintheXYplaneofthefeaturecoordinate
system.ThepocketisformedbymovingtheprofileadistanceofthedepthalongthenegativeZ-axis
direction.The‘bottomcondition’specifiesthepocket’spossiblebottomshape.Onthepocket’sbottom
theremightexistislands(bosses),whicharenotcutduringthemillingofthepocket.Apocketmayhave
otherparameters:slope(definingtheanglebetweensidefacesandZ-axis),‘planarradius’(definingthe
edgefilletbetweensidefacesandthebottom)and‘orthogonalradius’(definingtheedgefilletamong
sidefaces).Holes,slots,steps,profilefeatures,etc.aredefinedsimilarly.
Atransitionfeatures,describingthetypeofconnectionbetweenadjacentmachiningfeatures,canbe
definedonlyontheborderofthetwofeatures.Chamfer(definedbytheangleandadimension)and
‘edgeround’(definedbyaradiusandoptionally2dimensions)aretwotypesoftransitionfeaturesin
STEP-NC.Acompoundfeatureisagroupofconnectedtwoormorefeatures.‘Counterbore’consistingof
2holeswithdifferentdiameters,and‘countersunk’consistingofataperedholeandacylindricalhole,
aretwotypesofcompoundfeatures.Theirbottomsofthenon-thruholeswithlargerdiametersarethe
startingsurfacesforthethruholeswithsmallerdiameters.
Fig.13STEP-NCfeatures[41]
6.2Featureclassification
Weclassifyformfeaturesbasedonthepurelytopologicalcharacteristicsandweusegraphtheoryto
analyzethem[36].Formfeaturesimplypotentialmachininginformationthatmakestheirforms.Their
geometricscopeisgenerallylargerthanthoseofmachiningfeatures.Foreachdefinedcategorythe
correspondingSTEP-NCfeaturesaregiven.Sothesubsequentfeatureextractionalgorithmscanexploit
andmatchthegraphpropertiesofeachcategory.
Hereformfeaturesarerepresentedbytheadjacencygraphs,whosenodesdenotefaces,andarcswith
concavity/convexityvaluesdenoteedges[36].Forexample,theformfeatureshowningrayinFig.14ais
representedbytheadjacencygraphGshowninFig.14b.RemovingtheconvexedgesinG,wegetthe
graphG+,asshowninFig.14c.
0
f1
1
0
f4
1
0
f0
1
f2
1
1
0
1
f0
f3
1
f3
f2
1——concavity
f4
1
f1
1——concavity
0——convexity
abc
Fig.14Adjacencygraphofafeature:a)aformfeature;b)graphG;c)graphG+
(1)Passage.Apassagehasnobottom,andconsistsofasetoffacesformingawall.Thewallfacesare
connectedbyconcaveorconvexedges.Aconcaveedgeistheonewhoseedge-xitym<0;whereasa
convexedgeistheonewhoseedge-xitym>0.Ifthereareconvexedges,theirnumberaregenerallyless
thanthenumberofconcaveedges.
Apassagehasthefollowingproperties(iorii)(Fig.15&16):
i)
ThegraphG+isacycleandG=G+;
ii)
ThegraphG+isoneorseveralchainsandgraphGisacycle.
Where,Gistheadjacencygraph,G+isthegraphafterremovingtheconvexedgesinG.
TheSTEP-NCfeaturesthatbelongtothepassageclassarethruroundholesandthruclosedpockets
(Fig.17).
ab
Fig.15Exampleofapassage:a)thepassage;b)G/G+
abc
Fig.16Anotherexampleofapassage:a)thepassage;b)G;c)G+
ab
Fig.17STEP-NCpassagefeatures:a)thruholes;b)thruclosedpocket
(2)Depression.Adepressionhasoneaccessofentryandonebottomfaceconnectingitswallfaces
viaconcaveedges.Ithasthefollowingproperties(iandii)(Fig.18):
i)GraphG+hasavertexvwhosedegreedeg(v)=λ(G+),whereλ(G+)isthenumberofcocylcles(i.e.
numberofverticesminusnumberofconnectedcomponents,whichis1inthispaper.);
ii)GraphG-vobtainedbysuppressionvertexvofG,isacycle,whoseconcaveedgesismorethanthe
convexedgesinnumber.
TheSTEP-NCdepressionfeaturesareblindroundholes,blindclosedpockets,andslotswithtwoends.
abc
def
Fig.18STEP-NCdepressionfeatures:a)blindclosedpocket,planarbottom;b)G+;c)G-v;d)blindclosed
pocket,radiusedbottom;e)blindclosedpocket,generalbottom;f)slotwith2radiusedends
Adegenerateddepressionistheonewhosebottomfacedegeneratestoanedgeoravertex.Likethe
depressioninFig.19,itsbottomisvertex.Inthiscase,wecanaddanisolatedelementvtothegraph.If
thegraphG+vhastheaboveproperties,thenthefeatureisadepression.
v
v
Fig.19Adegenerateddepression:a)thefeature;b)G+v
(3)K-protrusion.Ak-protrusionhasoneorseveralaccessesofentry,andhasonebasefaceonwhich
protrusionsareattachedviaconcaveedges.Ithasthefollowingproperties(iandiiandiii)(Fig.20):
i)GraphG+hasavertexvwhosedegreedeg(v)=λ(G+);
ii)GraphG-vcontainskdisjointcomponents.
iii)Acomponent(G-v)i,(1≤i≤k),itisacyclewhoseconcaveedgesislessthantheconvexedgesin
number.
TheSTEP-NCk-protrusionfeaturesarebosses,profilefeaturesandsphericalcap.
ab
cde
Fig.20Exampleofk-protrusion:a)thek-protrusion;b)G;c)G+;d)(G-v)1;e)(G-v)2
(4)K-slot.Ak-slothasoneorseveralaccessesofentry,andhasonebasefaceconnectingoneor
severalopenwallfaces.Ithasthefollowingproperties(iandii)(Fig.21):
i)GraphG+hasavertexvwhosedegreedeg(v)=λ(G+);
ii)GraphG-vcontainskdisjointchains(G-v)1,…,(G-v)j,and/orisolatedverticess1,…,sk.
TheSTEP-NCk-slotfeaturesareblindopenpockets,slotsthathasatleastoneendisopen,andsteps.
ab
cde
Fig.21Exampleofk-slot:a)thek-slot;b)G;c)G+;d)(G-v)1;e)(G-v)2
(5)Compoundclass.Thistypeofformfeatureiscomposedbyseveralsimplefeaturesdefinedabove.For
example,adepressionwithanislandonitsbottomisacompoundfeature.Thebasicprocessing
approachisdecompositionthegraph.Fig.22showsacompoundandthegraphdecomposition.
abcde
Fig.22Exampleofacompound:a)thefeature;b)G+;c)G-v;d)(G-v)1(depression);e)(G-v)2(k-protrusion)
6.3STEP-NCfeaturerecognition
6.3.1Flowchartofthealgorithm
Generallyspeaking,thefeaturerecognitionisdoneintwophases.Onephaseistoidentifytheform
featureclass(passage,depression,k-protrusion,ork-slot),andthendeterminethecorrespondingSTEPNCfeatureclass;theotherphaseistoextracttheSTEP-NCfeatureparametersaccordingtothe
standard’sspecifications.Fig.23showstheflowchartofthefeaturerecognitionalgorithm.
Input: regions & shape types
Process region borders
Generate region adjacency matrix
Identify thru holes/closed_pockets
Identify blind holes/closed_pockets
Identify bosses, profile features
Identify open pockets, slots, steps
Identify transition features
Group into compound features
End
Fig.23.Flowchartofthefeatureextractionalgorithm
6.3.2Processofregionborders
Afterregionsegmentation,mostofregionbordersaresmooth,butinthesmallregulartriangleregions,
therearesomesegmentswhosebordersarejagged.Tokeepthetopologicalrelationshipofmesh
unchanged,weadoptthemethodin[44],tofindtheshortestpathbetweentwoborderverticesthatare
currentlyconnectedwithjaggededges.InFig.24thejaggedborderedgesofsegmentSconsistofe1-e2,
e3-e4.Bysearchingtheshortestpathontheborder,thealternativeedgesarefoundase’1,e’3-e’4,
respectively.
Fig.24Regionboundarysmoothing
Determineouter/innerloopsofregionborders.Iftwotrianglessharinganedgearenotinsameregion,
thesharededgeisaborderedge.Theborder’sdirectionisinconformancetotheedgedirectionofthe
bordertriangle.Foraplanarregion,thenormalvectorofaborderiscalculatedaccordingtoitsdirection.
Iftheborder’svectorisinthesamedirectionastheregion’s,thentheborderistheouterloopofthe
region;Iftheborder’svectorisintheoppositedirectiontotheregion’s,thentheborderisaninnerloop
theregion.
Fitregionborderswithlines,arcsorsplinecurves.TheprofilesofaSTEP-NCfeatureconsistoflines,arcs
andsplinecurves.Thisfittingprocesswillfacilitatetoextractamachiningfeatureanddecideitstypeand
itsparameters.
6.3.3Regionadjacencymatrix
Inordertoimprovetheefficiencyofthealgorithm,adataschemeoriginallyusedinimagesegmentation
[45]—regionadjacencygraph(RAG)isadopted.Thisalgebraicstructurecontainsasetofnodesanda
setofedges.Eachnodesrepresentsaconnectedregion(i.e.aconnectedsubsetofthemesh),andeach
edgerepresentsanadjacencybetweentworegions.Thealgorithminputistheregionsegmentation
resultofanin-processmodel,whichareregionsrepresentedbyacollectionoftrianglesandtheir
respectiveshapetypes.HeretheinputisstructuredasaRAG.Thenafterfinishingsomerelevant
calculations(suchastheconvexity/concavityforregionborders.),theRAGaretransformedasaregion
adjacencymatrix(whichissimilartoafaceadjacencymatrix).Theadjacencymatrixisasquare
symmetricmatrixanditsdimensionisequaltothenumberofregions.Theelementsaijofthismatrix
describethedependenciesbetweenregions:
0:regioniandregionjarenotincontact
type:diagonalelementsindicatearegiontype
aij= 1:regionsiandjshareaconcaveedge
-1:regionsiandjshareaconvexedge
-2:regionsiandjshareatangentedge
Theextractionalgorithmcheckstheserelationsfrequently,sothecreationofthismatrixacceleratethe
calculations.
6.3.4Extractionofthruholesandthru,closedpockets
Thesefeaturesbelongtothepassageclass.Hereweproposeanovelapproachtorecognizethem.First
wecalculatethenumberofpassagesinthein-processmodelbyusingEulercharacteristic(alsocalled
Eulernumber).TheniftheEulernumberindicatesthattherearepassagesinthemodel,normal
searchingproceduresareperformed.Thiswillcertainlyincreasetheefficiencyofthealgorithm.
HereistheexplanationonhowtocalculatetheEulercharacteristic,whichisatopologicalinvariant,a
numberthatdescribesatopologicalspace'sshaperegardlessofthewayitisbent.TheEuler
characteristic,commonlydenotedbyχ,wasclassicallydefinedforthesurfacesofpolyhedra,according
totheformula[46]
χ=V–E+F(3)
WhereV,E,andFarerespectivelythenumbersofvertices,edgesandfacesinthegivenpolyhedron.
Ontheotherhand,theEulercharacteristicofaclosedmanifoldshapecanbecalculatedfromits
genusg,whichisnumberofpassages,intuitively.
χ=2–2g(4)
Afterpre-processing,theIPMbecomesamanifoldpolyhedralB-reptrianglemeshmodel.Moreover
itsfacenumberandedgenumberhasthefollowingrelationship.
E=3F/2(5)
Combining(1),(2)and(3),thenumberofpassagesisasunder:
g=1+F/4–V/2(6)
ThenumberoftrianglesFandthenumberofverticesVcanbeeasilygotfromthepre-processedIPM.
Ifg>0thenperformthefollowingdetections.
Ausualapproachtoextractthruholesandthru,closedpocketsistoanalyzeregion’sinnerloopswith
convexedgesonly[47].Suchaloopindicatestheexistenceofaholeoraclosedpocket.Startingfrom
suchaloop,thefeature’ssides(wallfaces)arecollected.Thecollectionendswhensideregions
encounteracommonregionhavinganinnerloopwithconvexedges.Thetwoinnerloopsconfirmthat
theholeorthepocketisbottomless.Ifthetypeofsideregionsis“rut”,thenthefeatureisathruhole;
otherwiseitisathruclosedpocket.ButasFig.15shows,thethrupocketisnotoriginatedfromaninner
loop.Inthiscasetheabove“loop”hintcannotbeused,butwecanbesurethatthereisapassageinthe
partbyapplyingformula(6),thenthegraphmatchingofthetopologicalpropertiesofapassagecanbe
usedtosearchthepassage.SotheEulernumbercanhelpfindpassagesinsomesituation.
Nextdeterminethefeature’sparameters.Thelocationoftheregioncontainingtheinnerloopwith
biggerz-valueisusedtodeterminethelocation(x,y,z)andtwovectorsdescribingtheorientationofthe
feature.ThefirstvectornormaltotheregiondecidesZ-axis,whilethevectorlayingontheregiondecide
X-axis.Theregionwiththisinnerloopisthestartingfaceofthefeature.Ifthefeatureisaholeas
decidedabove,theinnerloopisinfactacircle,andthehole’sradiusequalstothecircle’s.Ifthereare
arcsbetweentwoadjacentloopedgesformingconcaveangle,theradiusofthearcsisusedtostorethe
valueoforthogonal_radiusparameter(Fig.17b).
6.3.5Extractionofblindholesandblind,closedpockets
Extractingblindholesandblind,closedpocketsisalsodonebyanalyzingregion’sinnerloopswith
convexedges.Thesedepressionfeatureshavebottomregionswithconcaveborderedges.Asidewallof
thefeaturestartsfromtheinnerloopsandendsatthebottomregionthruaconcaveedge.Thefeature’s
location,orthogonal_radiusofthefeaturecanbedecidedinthesamewayasthru,closedpockets.To
findthebottom,thesideregionhavingthegreatestlengthinthedirectionofthevectornormaltothe
regionwiththeinnerloopisselected.Ifsuchdeterminedsideregioncontactswiththeregionwhose
typeiscylindrical(rut),orsaddle,orsphericalcup,andthesetworegionsformaconcaveangle,the
radiusofsuchcylindricalorcupregionsisselectedasthevalueofplanar_radiusparameterandalso
pocket/holedepthisrevised.Notethatthefeature’sbottomregioncanbeinclined.Afterthebottom
regionisselected,thepocket/holebottomtypemustbedetermined.Forexample,ablindholecanhave
4bottomtypes:flat,conical,flatwithradius,orsphericalbottom(Fig.25).Thebottomtypecanbeeasily
decidedbythebottomregion’ssurfacetype.Iftheregionrepresentingthebottomhasinnerloopswith
concaveedgesonly,thepockethasbosses.Bossisthepartofthematerialwhichmustbenotcutduring
themachining.Thepocketbottomregionalsocanhaveinnerloopwithconvexedges,determiningother
concavefeature,forexamplenextpocketlyingonthisbottom.Allthesideregionsandthebottom
regionformingthefeaturearemarkedasrecognized.Suchregionsarenolongeranalyzedbythe
extractingprocedure.Thestartingregionforthepocketorholeisnotmarkedasrecognizedbecause
suchregionscanbethepartofotherfeature.
AccordingtoSTEP-NCfeaturespecifications,someslotscanbeconsideredasthespecialtypesofpockets.
Iftheappropriateconditionsaresatisfied,thepocketisclassifiedasslot.Forexample,ifthepocket
profile(theinnerloop)consistsoftwoparallellinesandtwoarcs,likearunningtrack,andwidthofthe
pocketistwicethevalueoftheradiusonthepocketends,thenthepocketisaslotwithtworadiused
ends(Fig.18f).
Fig.25STEP-NCblindholetypes
6.3.6Extractionofbosses,profilefeatures,sphericalcap
InISO14649aboss,asadependentmachiningfeature,havingnoseparateworkingstepassignedtoit,
canoccuronfeaturesofplanarface,blindclosed/openpocket,andstep.Anoutsideprofile(Fig.26a)is
theremovalvolumeofarbitraryshapefromtheoutsideshapeofaworkpiece.Thesetypesoffeatures
canbeextractedbyanalyzingaregion’sinnerloopwithconcaveedgesonly,andtheregionisthebase
face.Foraprofilefeaturethisloopisthe“feature_boundary”;forabossfromthisloopitsboundary,
whichisdefinedatthetopoftheboss,canbeinferred.Basedonthelengthofthesideregionsofthe
bossorprofilefeature,measuredinthedirectionofthevectornormaltothebasefaceofthefeature,
determinestheparameterofHeightofabossorDepthofaprofilefeature.Regionsformingthebossor
profilefeaturearemarkedasrecognized.
Asphericalcapiscircularaboutanaxisofrotation.Itconsistsofallpointsatagivendistancefroma
pointconstitutingitscenter.Thecenterisdefinedbyitsplacement,whichisinthesphere'scenter.Fig.
26bshowsasphericalcapsittingonaboss.Whenwefoundoutalltheconnectedregionsoriginating
fromaninnerloopwithconcaveedges,weidentifyaregionwhosesurfacetypeis“sphericalcap”
(surfaceindex≈1),thenthisregionisobviouslyaspherical_capfeature.Thefeature’sparameters,radius
andinternal_anglecanbeobtainedbyfittingtheregionwithaspheresurface.
ab
Fig26.a)Profilefeature;b)sphericalcap
6.3.7Extractionofopenpockets,slotsandsteps
Searcharegionwhoseouterborderhasmostnumberofconnectedconcaveedges.Thenumbershould
beequalorgreaterthan2.Thisregionisselectedasthebottomfaceofthenewblindfeature(pocketor
slot).Theconnectedregionssharingtheconcaveedgeswiththebottomisincludedasthesidefaces.The
sidefacewiththegreatestdimensioninthedirectionofthevectornormaltothebottomisusedto
decidethepocketdepth.Sideregionsaremarkedasrecognized.Againsearcharegionwhoseouter
borderhasmostnumberofconnectedconcaveedges,andrepeattheoperation.Thisregionmightbe
sameastheonepreviouslyselectedsincetheremightexistseveraldisconnectedopenpocketsbasedon
sameface.
Slotisregardedasaspecialpockettypeundercertaingeometricconstraints.Theaboveoperationshave
extractedblindopenpockets.Amongthemtheremightexistsuchaslotwhoseoneendisopenandthe
otherendiswoodruffed,orradiused,orflat,asdefinedbyISO14649(Fig.21a).Thespecificslottypecan
bedeterminedbycheckingtherelevantgeometricconstraints.Notethatslotswithtwoendsbeing
woodruffed/radiused/flat,orslotswithloopendtypes,havealreadybeenextractedin7.5sincetheyare
infactblindclosepockets.
Thetopologyofathru,openpocketsisfacechainconnectedbyconcaveedges.Soregionchains
connectedbyconcaveborderedgesaresearchedamongunrecognizedregions.Theseregionsformthe
sidefacesofathru,openpocket,andfromthemtheopen_boundaryparametercanbeinferred.This
methodcanonlyextractautomaticallythru,openpocketswhosesidefaceshaveconcaveedges.For
thosewhosesidefaceswithoutconcaveedges,userinterventionisneeded.
Thruslotsandsteps(Fig.21a)arespecialthru,openpocketssatisfyingcertaingeometricconstraints.A
stepfeatureisavolumeofmaterialremovedfromthetopandthesidesoftheworkpiece.Astephas
twoplanarfacesdefinedbyaV-profile,andconnectedbyaconcaveedge.Asforthethruslot,one
commonshapehasabottomfaceandtwoparallelsidefaces,connectedbytwoconcaveedges.Inthe
extractedthru,openpocketstheremightincludesomethruslotsand/orsteps.Wecanusethese
geometriccharacteristicstosortoutthruslotsandstepsfromtheextractedthru,openpockets.
6.3.8Extractionoftransitionfeatures
ISO14649definestwotypesoftransitions:chamfersandedgerounds.Theruleforextractingchamfers
isachamfer’sgeometrictraitsplusitsmanufacturingknowledge.Achamferisalwaysanouterchamfer,
whichmeansallitsedgesareconvex,asonlythiscanbegeneratedinaseparatemachiningoperation.
Itslength/widthratioishighandithasthenormalvectornorparallelorperpendiculartoZ-axisofthe
partcoordinatesystemingeneral.Checkingthesepropertiesonunmarkedplanarregions,chamferscan
beselected.Thechamfer’sparameterangle_to_planeistheanglebetweenoneofitsadjacentregions
andthechamferregionusuallywithvalueof45°or30°frommanufacturingpointofview.
Rounding/blendingfeaturesincludingedgeroundsareextractedhereusingauniqueapproach
developedbytheauthors.Curvednessmapofthemodelisfirstcomputed,andthenunmarkedregions
withhighcurvednessareidentifiedasroundingfeatures.
Curvednessisapositivevaluethatspecifiestheamountorintensityofthesurfacecurvature[40].Itis
definedas:
(7)
Wherekmaxandkminarethemaximumandminimumprincipalcurvaturesofavertex,respectively.
Weusethecurvednessvaluetodetectroundingregion.Verticesonsmoothedgesandtransitionregions
havehighercurvednessvalue,asthusathresholdcanbegiventodetectthem.Thismethodiseasytobe
realizedandtooperate.Thecurvednessrangeofadiscretemodelisdependentonitsshapesize.The
thresholdcanbegivenastheaverageofthemodel’smaximumcurvednessandminimumcurvedness.
Fig.27bshowstheresultsofaroundedpocket’scurvednessmap.Inmostcasestheidentifiedrounding
regionshavesurfacetypesofrut/ridge/spherical_cup/spherical_cap.AsfortheISOedgeroundfeature,
accordingtothedefinition,itisalwaysanouterfillet,whichcanbemanufacturedinanextramachining
operation.Thismeansthatonlytheroundingregionfilteredbythecurvednesswithsurfacetype‘ridge’
canbeanedgeroundfeature.Theedgeroundfeature’sparameter‘radius’canbecalculatedbyfitting
the‘ridge’regionwithacylindricalsurface.
ab
Fig.27a)Roundedpocket;b)Curvedness
6.3.9Groupingintocompoundfeatures
Acompoundfeatureisafeaturecomposedoftwoorseveralsimplefeatures.Unlikeareplicatefeature,
thereisnoregularspacingbetweentheelementsofacompoundfeature.Twoexamplesofcompound
featuresinSTEP-NCarecounterbore_holeandcountersunk_holeasshowninFig.28.
Aftersimplefeaturesinthepartmodelareextracted,groupingsimplefeaturesintocompoundfeatures
canbedonebycheckingtheirgeometricpatterns.Forexample,acounterborefeatureconsistsoftwo
co-axialholes.Oneblindholehasalargerdiameterthantheother.Thelargerhole’sbottomconnects
thesmallhole.Toextractacounterbore,firstselect2co-axialholes:oneisblindandtheotheristhru,
thencomparetheirdiametersandconnectionrelationship.Ifthetwofitthepattern,thentheyare
groupedintoacounterborefeature.
Fig.28Counterboreandcountersunkholes
Insomesituationafeatureisbrokenduetoitsintersectionwithotherfeature(s).Anexampleisshown
asinFig.29.Thethruholeintersectswiththethrupocketonthesidefaces.Becauseofthis,twoseparate
holesareextracted.Thelinkingapproachissimilartotheoneforcompoundfeaturegrouping.During
linkingofbrokenholes,theco-axialrelationshipandthesamevalueofselectedparameters(thehole
diameterinthiscase)isusedasthelinkingcriteria.
Inaddition,theapproachtogroupsimplefeaturesintoreplicatefeaturesissimilar.
Fig.29Linkingbrokenfeatures
7. Casestudy
TheproposedmethodsforfeaturerecognitionandreverseengineeringofIPMwereverifiedby
developingthesoftware.Theinputdata,thepart’sIPM,wasgeneratedbyNCSimul9.0,whichusesaGcodeprogramrunningontheSiemens840DCNCcontrollers.TheIPMwasoutputaftertheNC
simulationasanSTLfile,andthenwasconvertedintoanOFFfile,whichunifiedduplicatedverticesand
thereforewasmuchsmallerinsize.ThesoftwarewasdevelopedwithMicrosoftVisualStudio2012(C++).
ItsinterfacewascreatedwithQt,andOpenGLgraphiclibrarywasusedforthevisualization.For
processingthetrianglemesh,OpenMeshandCGALdevelopinglibrarieswereused.Thesoftwarewasrun
onacomputerwithanIntelCoreCPU2.4GHzand4GbRAM.
FortheexamplepartshowninFigures6-9,itsIPMhas631verticesand1256triangles.Thetotal
processingtimeafterfeaturerecognitionis23ms,andtheresultisdisplayedinFig.30.
ab
Fig.30Resultfortheexamplepart:a)segmentationresult;b)featuresgotfromtherecognition
Thetestsoftware’sinterfacesandanothertestpartareshowninFig.31.TheIPMtreatmentfunctions
areundermenu“Meshes”.Themachiningfeaturerecognitionfunctionsareundermenu“NC-Features”.
Thispart’sIPMshowninFig.2ahas1556verticesand3112triangles.Thetotalprocessingtimeis57ms.
TheregionsegmentationresultforthetestcaseisshowninFig.31.Themeshsegmentsofthepart
“Pièce_test”include1sphericalcap,1ridge,2saddles,9sphericalcups,28rutsand19planes.
Fig.31Screenshotofthesoftwareforregionsegmentationofthetestpart
Afterthefeaturerecognition,wecanknowthatthemodelhas20featuresintotal,presentedontheleft
treelist(Fig.32)—1squarepocketwith1boss(sphericalcap);1three-axispocket;3counterboreholes;1
planarface(i.e.thepart’stopface)with2bosses;1chamferonthesquarepocket’sentranceborder;9
holeswithdifferentbottomconditionsonthepart’sinclinedfaces;and1slotwithwoodruffendsona
sideface.Whenthefeature’snameintreelistisclicked,thefeature’sparametersareshowninthe
bottom-righttable.
Chamfer13
RoundHole1
Boss1ofPlanarface17
Pocket16
CounterBoreHole10
Planarface17
Boss1ofPocket16(sphericalcap)
Pocket14
Fig.32Screenshotofthesoftwareforfeaturerecognitionofthetestpart(annotationsaddedmanually)
Aquantitativeanalysistothereconstructionwasperformed.Wechosesomeparametersfromthispart’s
CADmodelasastandardreferenceandcomparedthemwiththerecoveredonesbytheproposed
approach.ThreefeaturesintheCADmodelshowninFig.33areselectedforthecomparison.FromTable
1,wecanseetherecoveredvaluesareveryclosetothoseoftheCADmodel,especiallyforfeatures
placedhorizontallyorvertically.Incolumn“Error”ofTable1,theerroriscomputedasthedistanceof
twopositions;andfortwovectors,theerroriscomputedastheirangleinradian.Theseerrorsare
deemedtoberesultedmainlyfromthesimulationdiscretization,andnotfromthereverseapproach.
Planarface17
RoundHole1
Boss1ofPocket16
Fig.33CADmodelofthetestpart
Table1:Quantitativecomparisontothereconstruction
Features
Checkedvalues
Valuesgotfrom
CADmodel
ValuesgotbyREofIPM
Theerror
Boss1of
Pocket16
Center(x,y,z)
(-34,-16.5,20)
(-34.000,-16.501,20.000)
0.001
Radius
16
16.000
0.000
Planarface17
(nx,ny,nz)－normalvector
(0,0,1)
(0.000,0.000,-1.000)
0.000
p－distancefromorigintoplane
(xnx+yny+znz=p)
36
36.000
0.000
Axisvector(nx,ny,nz)
(0,0.5,0.866)
(0.000,0.498,0.867)
0.014rad
Axisposition(x,y,z)
(12,46.8,31.5)
(12.000,46.789,31.504)
0.012
Diameter
10.3
10.369
0.069
Depth
32
31.886
0.114
RoundHole1
8. Conclusions
Thepresentedmethodinthisresearchforfeaturerecognitionandreverseengineeringofanin-process
modelhasthefollowingfeatures:(1)Itusesshapeindextosegmentameshforthefirsttime,toourbest
knowledge.Todecidethelocalsurfacetypeofamesh,onlyonevalue,theshapeindex,issufficient,
whereasothermethodsusuallyuseacombinationoftwoormoretypesofcurvatures.(2)Itadoptsa
progressivesegmentationmethodaccordingtotheIPMcharacteristics.Inthiswayeachregionofthe
IPMcanbepartitionedusingthemosteffectivealgorithm.(3)Theproposedformfeatureclassification
approachisonlydependedonthesolid’stopology,anditcancoveraratherlargescopeofforms.
Degeneratedandcompoundformfeaturescanalsobehandled.Basedontheclassifiedforms,STEP-NC
featurescaneasilyberecognized.(4)Twonoveltiesarepresentedinthefeaturerecognitionapproach:
EulercharacteristicisappliedtoaidtheextractionSTEP-NCpassagefeatures(thruholesandclosed
pockets,etc.),andthemodel’scurvedness,ashapedescriptor,isusedtoextracttransitionfeaturesand
edgerounds.Therecognitioninputdataisthesegmentationresult－regionswiththeirshapetypes.The
outputisSTEP-NCfeatures,includingthefeaturetypes,theirdefiningcomponents,suchasprofiles,
placements,scalarparameters.
The key advantage of our method comes from the adoption of the shape index derived from the two
principal curvatures for mesh segmentation. Other curvature based methods usually use the Gaussian and
mean curvatures, or the principal curvatures, or combination of them. Some problems of other methods
are: size and local shape are coupled; rules to classify the local shape is complex; surface shape variation
is hard to be shown by only one type of curvature in a color scale. Whereas, the shape index is scale
invariant, and is quite consistent to the intuitively distinct shapes, which may facilitates a user interface
design by this single parameter instead of two. Besides, parabolic curves on a surface can neatly be
distinguished, but the Gaussian or mean curvatures cannot.
Thefutureworkforimprovementsofthemethodmayimplythefollowing:(1)improvingcurvature
accuracyofverticesonboundaries.Verticesofthemeshshouldbefirstclassifiedasverticesoftheform,
verticesonedgesandverticesinsidefacesbyapplyingtensorvotingtheory[13];(2)regionboundary
smoothingapproach.Bothglobaldirectionandlocaldirectionoftheboundaryshouldbeconsidered,
especiallyattheintersectingpointofseveralboundaries.Currentlyonlylocaldirectionishandled;(3)
refiningclassificationrulesofformfeatures,anddetailingthegraph’stopologicalpropertiesfor
degeneratedandcompoundformfeatures,aswellastherelevantgraphoperationmethods.For
example,thenumberofconcaveorconvexedgesofgraphG-vdecidesadepressionorprotrusion,which
isnotpreciseinsomerarecases.Considerusingedge-xityinsteadofnumberofconcaveedges;(4)
refiningapproachestoextractopenpocketsandprofilefeatures,andemploymentofmanufacturing
knowledgetosupporttheextractionalgorithm.Anopenpocketcanberathercomplex,needingfurther
manufacturinginformationtodecideitsexactSTEP-NCfeaturetype.Similarsituationexistsfortransition
features.
ACKNOWLEDGEMENT
ThisworkisapartoftheANGELFUIprojectfundedbytheFrenchInter-ministerialFundand
endorsedbytopFrenchcompetivenessclusters(SYSTEMATICPARISREGION,VIAMECAandASTECH).
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