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ORIGINALARTICLEFASTCOLLISIONDETECTIONAPPROACHTOFACILITATEINTERACTIVEMODULARFIXTUREASSEMBLYDESIGNINAVIRTUALENVIRONMENTGAOLIANGPENGTHEOBJECTSNOTINTJADVMANUFTECHNOL201046315328DOI101007/S0017000920730GPENGXHOUTJINXZHANGSCHOOLOFMECHANICALANDELECTRICALENGINEERING,HARBININSTITUTEOFTECHNOLOGY,HARBIN,CHINAEMAILPGL7782HITEDUCNCWUSCHOOLOFMANAGEMENT,HARBININSTITUTEOFTECHNOLOGY,HARBIN,CHINAPENETRATINGINTOOTHERSMUSTBEGUARANTEEDTHEREFORE,AFASTINTERACTIVECOLLISIONDETECTIONCDALGORITHMISFUNDAMENTALINSUCHAVRSYSTEMHOWEVER,COLLISIONCHECKINGFORACOMPLEXVEISCOMPUTATIONALLYINTENSIVERESEARCHERSHAVEADDRESSEDSOME“UNIVERSAL”ALGORITHMSTOREDUCETHECOMPUTATIONALCOSTSBUTTHESEALGORITHMSOFTENNEEDAUXILIARYDATASTRUCTURESANDREQUIREINTENSIVEPREPROCESSINGTIMECOSTINADDITION,THEIMPLEMENTATIONOFSUCHALGORITHMISVERYCOMPLICATEDTHEREFORE,BASEDONTHEWELLSTUDYOFMODULARFIXTURECHARACTERISTICSANDPRACTICALREQUIREMENTS,WEDEVELOPA“SPECIAL”CDALGORITHMTOKEEPTHEASSOCIATEDCOSTSASLOWASPOSSIBLEFORVRBASEDMODULARFIXTUREASSEMBLYDESIGNTHEPAPERISORGANIZEDASFOLLOWSAREVIEWOFRELATEDWORKOFTHEEXISTINGCDALGORITHMSISPRESENTEDINSECTION2SECTION3GIVESANOVERVIEWOFOURPROPOSEDALGORITHMINSECTION4,WEDESCRIBETHESPACESUBDIVISIONMODELUSEDINOURALGORITHMSECTION5PROVIDESTHEDETAILSABOUTTHEBROADPHASEOFOURPROPOSEDALGORITHM,INWHICHIRRELEVANTOBJECTSAREDISCARDEDANDASETOFOBJECTSTHATCANPOSSIBLYCOLLIDEAREDETERMINEDTHENARROWPHASEFOREXACTPOLYGONBASEDOVERLAPTESTSISDESCRIBEDINSECTION6SECTION7PRESENTSSOMEEXPERIMENTALRESULTSOFOURALGORITHM,ANDFINALLY,INSECTION8,WEGIVECONCLUDINGREMARKSANDOUTLINEDIRECTIONSFORFUTUREEXTENSIONSOFTHISWORK2RELATEDWORKDURINGTHEPASTFEWYEARS,AGREATDEALOFEFFORTHASBEENMADETOSOLVETHECDPROBLEMFORVARIOUSTYPESOFINTERACTIVE3DGRAPHICSANDSCENARIOSFORAWORKSPACEFILLEDWITHNOBJECTS,THEMOSTOBVIOUSPROBLEMISTHEON2PROBLEMOFDETECTINGCOLLISIONSBETWEENALLOBJECTS,WHICHISTIMECONSUMINGANDNOTBEARABLEIFTHENUMBERNISLARGETHUS,SOMENECESSARYTECHNIQUESARENEEDEDTOREDUCETHECOMPUTATIONALCOSTSGENERALLY,ACDALGORITHMCONSISTSOFTWOMAINSTEPS,NAMELYBROADPHASEANDNARROWPHASE9THEFIRSTPHASEAIMSTOFILTEROUTPAIRSOFOBJECTSWHICHAREIMPOSSIBLETOINTERACTANDDETERMINEWHICHOBJECTSINTHEENTIREWORKSPACEPOTENTIALLYINTERACTTHESECONDPHASEISTOPERFORMAMOREACCURATETESTTOIDENTIFYCOLLISIONBETWEENTHOSESELECTEDOBJECTPARTSINTHEFIRSTPHASE,MOREOVERIFNECESSARY,TOFINDTHEPAIRSOFCONTACTINGPRIMITIVEGEOMETRICELEMENTSPOLYGONS,ANDTOCALCULATETHEOVERLAPPINGDISTANCEFORACDALGORITHM,ITISCRITICALTOREDUCETHENUMBEROFPAIRSOFOBJECTSORPRIMITIVESTHATNEEDTOBECHECKEDTHEREFORE,ANUMBEROFDIFFERENTTECHNIQUESHAVEBEENUSEDTOMAKECOARSEGRAINDETECTION,AMONGWHICHSPACEDECOMPOSITIONANDBOUNDINGVOLUMESISMOSTPOPULARINSPACEDECOMPOSITIONMETHODS,THEENVIRONMENTISSUBDIVIDEDINTOSPACEGRIDSUSINGHIERARCHICALSPACESUBDIVISIONOBJECTSINTHEENVIRONMENTARECLUSTEREDHIERARCHICALLYACCORDINGTOTHEREGIONSTHATTHEYFALLINTOTHESEOBJECTSARETHENCHECKEDFORINTERSECTIONBYTESTINGFOROVERLAPPINGGRIDCELLSEXPLOITINGSPATIALPARTITIONINGMETHODSLIKEOCTREES10,11,BSPTREES12,KDTREES13,ETCUSINGSUCHDECOMPOSITIONSINAHIERARCHICALMANNERCANFURTHERSPEEDUPTHECOLLISIONDETECTIONPROCESSBUTLEADSTOEXTREMELYHIGHSTORAGEREQUIREMENTSBOUNDINGVOLUMEBVAPPROACHISUSEDINPREVIOUSCOMPUTERGRAPHICSALGORITHMSTOSPEEDUPCOMPUTATIONANDRENDERINGPROCESSTHEBVOFAGEOMETRICOBJECTISASIMPLEVOLUMEENCLOSINGTHEOBJECTTYPICALLY,BVTYPESAREAXISALIGNEDBOXESAABBS14,SPHERES15,ANDORIENTEDBOUNDINGBOXESOBB16SINCEAABBSMETHODISSIMPLETOCOMPUTEANDALLOWSEFFICIENTOVERLAPQUERIES,ITISOFTENUSEDINHIERARCHY,BUTITALSOMAYBEAPARTICULARLYPOORAPPROXIMATIONOFTHESETTHATTHEYBOUND,LEAVINGLARGE“EMPTYCORNERS”THESYSTEMSUTILIZINGAABBSINCLUDEICOLLIDE17,QCOLLIDE18,ANDSOLID19,ETCBOUNDINGSPHEREISANOTHERNATURALCHOICETOAPPROXIMATEANOBJECTASITISPARTICULARLYSIMPLETOTESTPAIRSFOROVERLAP,ANDTHEUPDATEFORAMOVINGOBJECTISTRIVIALHOWEVER,SPHERESARESIMILARTOAABBSASTHEYCANBEPOORAPPROXIMATIONSTOTHECONVEXHULLOFCONTAINEDOBJECTSINCOMPARISON,ANOBBISARECTANGULARBOUNDINGBOXATARBITRARYORIENTATIONSIN3DSPACEINANIDEALCASE,THEOBBCANBEREPOSITIONEDSUCHTHATITISABLETOENCLOSEANOBJECTASTIGHTLYASPOSSIBLEINOTHERWORDS,THEOBBISTHESMALLESTPOSSIBLEBOUNDINGBOXOFARBITRARYORIENTATIONTHATCANENCLOSETHEGEOMETRYINQUESTIONTHISAPPROACHISVERYGOODATPERFORMINGFASTREJECTIONTESTSASYSTEMCALLEDRAPID20FORINTERFERENCEDETECTIONBASEDONOBBHASBEENBUILT,WHICHAPPROXIMATESGEOMETRYBETTERTHANAABBSTHESHORTCOMINGSOFOBBTREEAGAINSTSPHERETREELIEINITSSLOWNESSTOUPDATEANDORIENTATIONSENSITIVE9MOSTCDRELATEDRESEARCHESAREINVOLVEDIN“UNIVERSAL”ALGORITHMS,ANDFEWLITERATURESAREFOUNDTODEVELOPCDAPPROACHINASPECIALAPPLICATIONLIKEVIRTUALASSEMBLYACTUALLY,AFASTANDINTERACTIVECOLLISIONDETECTIONALGORITHMISFUNDAMENTALTOAVIRTUALASSEMBLYENVIRONMENT,WHICHALLOWSDESIGNERSTOMOVEPARTSORCOMPONENTSTOPERFORMASSEMBLYANDDISASSEMBLYOPERATIONSFIGUEIREDO21PRESENTEDAFASTERALGORITHMFORTHEBROADANDNARROWPHASESOFTHECOLLISIONDETECTIONALGORITHMOFDETERMININGPRECISECOLLISIONSBETWEENSURFACESOF3DASSEMBLYMODELSINVIRTUALPROTOTYPEENVIRONMENTSTHEALGORITHMUSEDTHEOVERLAPPINGAABBANDTHERTREEDATASTRUCTURETOIMPROVEPERFORMANCEINBOTHTHEBROADANDNARROWPHASESOFTHECOLLISIONDETECTIONTHISAPPROACHISFORSUCHAVEWITHOBJECTSDISPERSEDINTHE316INTJADVMANUFTECHNOL201046315328SPACEINADDITION,THERTREEDATASTRUCTUREISVERYMEMORYINTENSIVESTEPHANE22WORKEDONCONTINUOUSCOLLISIONDETECTIONMETHODSANDCONSTRAINTSTODEALWITHRIGIDPOLYHEDRALOBJECTSFORDESKTOPVIRTUALPROTOTYPINGWHEREASSUCHA4DMETHODISONLYUSEFULFORHANDLINGTHEPATHOFKNOWNMOVINGOBJECTSESPECIALLY,THEALGORITHMISSOCOMPUTATIONALLYINTENSIVETHATITHASTORUNONHIGHENDCOMPUTERSCOLLISIONDETECTIONISACRITICALPROBLEMINMULTIAXISNUMERICALCONTROLNCMACHININGWITHCOMPLEXMACHININGENVIRONMENTSTHEREHASBEENMUCHPREVIOUSWORKONINTERFERENCEDETECTIONANDAVOIDANCEINNCMACHININGSIMULATIONWANG23DEVELOPEDAGRAPHICSASSISTEDCOLLISIONDETECTIONAPPROACHFORMULTIAXISNCMACHININGINTHISMETHOD,ACOMBINATIONOFMACHININGENVIRONMENTCULLINGANDATWOPHASECOLLISIONDETECTIONSTRATEGYWASUSEDRESEARCHESSURVEYEDABOVEPROVIDEDVARIOUSEFFICIENTTECHNIQUESTOCARRYOUTCOLLISIONDETECTIONFORPOLYGONALMODELSHOWEVER,THESEPOPULARALGORITHMSAIMEDATGENERALPOLYGONALMODELS,MOSTOFWHICHNEEDEXPENSIVEPRETREATMENTSORLARGESYSTEMMEMORYORBOTHOFTHEMINORDERTOIMPROVETHEPERFORMANCEANDMEETREALTIMEREQUIREMENTSTHEREFORE,WHENTHESEALGORITHMSAREUTILIZEDINDESKTOPVRAPPLICATIONSYSTEMSUCHASMODULARFIXTUREDESIGN,THEREQUIREMENTOFREALTIMECANNOTBEWELLGUARANTEEDFEWCDRESEARCHESCANBEFOUNDINTHEAREAOFCOMPUTERAIDEDFIXTUREDESIGNHU24PRESENTEDANALGORITHMOFFASTINTERFERENCECHECKINGBETWEENTHEMACHININGTOOLANDFIXTUREUNITS,ASWELLASBETWEENFIXTUREUNITS,TOREPLACETHEVISUALLYCHECKEDMETHODMOREOVER,INKUMARSWORK25,INORDERTOAUTOMATEINTERFERENCEFREEMODULARFIXTUREASSEMBLYDESIGN,THEMACHININGINTERFERENCEDETECTIONISACCOMPLISHEDTHROUGHTHEUSEOFCUTTERSWEPTSOLIDBASEDONCUTTERSWEPTVOLUMEAPPROACHHOWEVER,THESEALGORITHMSAREONLYCAPABLEOFSTATICINTERFERENCECHECKINGANDAPPLIEDINCADSOFTWAREPACKAGESTHERESEARCHPRESENTEDINTHISPAPERMAKESASOLUTIONTOTHESEISSUESBYADDRESSINGA“SPECIAL”COLLISIONDETECTIONALGORITHMFORVRBASEDMODULARFIXTUREDESIGNTHEPROPOSEDALGORITHMUSESTHEHYBRIDAPPROACHOFSPACEDECOMPOSITIONANDBOUNDINGVOLUMEMETHODTOGETHIGHPERFORMANCE3ALGORITHMOVERVIEW31REQUIREMENTSFORPROPOSEDALGORITHMWEAIMEDTODEVELOPADESKTOPVRBASEDMODULARFIXTUREASSEMBLYDESIGNSYSTEM,INWHICHTHEDESIGNERCANSELECTSUITABLEFIXTUREELEMENTSANDPUTTHEMTOGETHERTOGENERATEAFIXTURESTRUCTURE,LIKE“BUILDINGBLOCKS”WITHOUTPHYSICALFIXTUREELEMENTS,HE/SHECANTESTDIFFERENTSTRUCTURESCHEMESANDFINALLYDESIGNAFEASIBLEFIXTURECONFIGURATIONTHATMEETSTHEFIXTURINGFUNCTIONREQUIREMENTSINORDERTORETAINHIGHDEGREEOF“REALITY”INENGINEERINGAPPLICATION,THEREARETHREEMAINREQUIREMENTSFORACDALGORITHMTOPERFORMMODULARFIXTURECONFIGURATIONDESIGN1PRECISEANDFASTDURINGTHESIMULATIONOFASSEMBLYANDDISASSEMBLYOPERATIONS,FINDINGPRECISECOLLISIONSISANIMPORTANTTASKFORACHIEVINGREALISTICBEHAVIOR26WHENTHEUSERINTERACTIVELYASSEMBLESAPARTORACOMPONENT,THE“FLYING”OBJECTMAYCOLLIDEWITHSTATICMODELS,THUSTHESYSTEMMUSTFINDOUTTHE“COLLIDING”EVENTIMMEDIATELYTHEINTERVALBETWEENTWOCHECKINGPOINTSSHOULDBENEARENOUGHTOACHIEVEBETTERPERFORMANCEOTHERWISE,WHENOBJECTSMOVEVERYFAST,THEYMAYAPPEARBEFORECHECKING,WHICHWILLREDUCETHEIMMERSIVEFEELINGSTHEREFORE,THEPROPOSEDSYSTEMCARRIESOUTACDCHECKINGTASKINEACHRENDERINGLOOPOFVEINADDITION,INMODULARFIXTUREASSEMBLYDESIGNPROCESS,THEDESIGNERSELECTSELEMENTSANDASSEMBLESTHEMTORIGHTPOSITIONORDISASSEMBLESTHEMTOCHANGETHEFIXTURECONFIGURATIONONCEANELEMENTISASSEMBLEDORDISASSEMBLED,THE“STATIC”ENVIRONMENTMODELSAREUPDATEDACCORDINGLY,THECDCHECKINGMODELNEEDSRESTRUCTURESOTHEPREPROCESSSHOULDNOTTAKETOOLONGOTHERWISE,THEPERFORMANCEOFPROPOSEDSYSTEMWILLBEIMPAIREDSEVERELYFORCERTAIN“SMOOTHFEEL”CANNOTBEACHIEVED2LOWSYSTEMREQUIREMENTSFINDINGCOLLISIONSINA3DENVIRONMENTISTIMECONSUMINGINSOMECASES,ITCANEASILYCONSUMEUPTO50OFTHETOTALRUNTIME21HOWEVER,INMODULARFIXTUREDESIGNWORKSPACE,THEREARESOMEOTHERTIMECONSUMINGTASKS,SUCHASDESIGNPROCESSCONTROLANDREASONING,AUTOMATICGEOMETRICCONSTRAINTSRECOGNITIONANDSOLVING,ETCINSPITEOFTHECOMPLEXITYOFTHE3DVIRTUALPROTOTYPESDUETOTHOUSANDSOFPOLYGONS,THEDESIGNEDCDCHECKINGPROCEDUREMUSTBEDONEINREALTIMEWITHRELATIVELYLOWSYSTEMRESOURCEDEMANDS3LOWHARDWARECOSTINORDERTOACHIEVEWIDERENGINEERINGAPPLICATIONS,THEPROPOSEDMODULARFIXTUREASSEMBLYSYSTEMISDESIGNEDTORUNONCOMMONPCLIKEPOPULARCADCOMMERCIALSOFTWAREALTHOUGHMUCHRESEARCHHASENGAGEDINDEVELOPINGHARDWAREACCELERATEDCDALGORITHMS,WHICHUTILIZESPECIALGRAPHICHARDWARE,LIKEGRAPHICSPROCESSINGUNIT,TODEALWITHTHECOMPUTINGCOLLISIONS,THUSTHESYSTEMSCPUCANBEFREEDNEVERTHELESS,WEDIDNOTPLANTOADOPTTHISKINDOFMETHODANDOPTIMIZEPERFORMANCEONLYFROMSOFTWAREIMPLEMENTATIONTHEOBJECTIVEOFTHISRESEARCHISTODEVELOPACDALGORITHMINTJADVMANUFTECHNOL201046315328317TAKINGINTOACCOUNTALLABOVEREQUIREMENTS,UNFORTUNATELY,THESEOBJECTIVESUSUALLYAREINCONFLICTTOMEETTHEPRECISEDEMAND,WEMUSTINCREASECHECKINGFREQUENCYWHICHWILLENORMOUSLYINCREASETHECOMPUTATIONALCOMPLEXITYANDTHEMEMORYBANDWIDTHREQUIREMENTSO,HOWCANABALANCEBEREACHEDWITHREGARDTOTHESEINOTHERWORDS,HOWCANTHEUTILIZATIONOFSYSTEMRESOURCESBEMINIMIZEDYETTHEPERFORMANCEOPTIMIZEDWITHOUTTHEHELPOFEXTRAHARDWAREITISTHESTARTPOINTOFOURALGORITHM32MODULARFIXTUREANALYSISTHEOBJECTIVEOFTHISRESEARCHISTODEVELOPACDALGORITHMFORASSISTINGINMODULARFIXTUREASSEMBLYDESIGNOPERATIONSINVETOSIMPLIFYTHEALGORITHMANDTOGAINHIGHPERFORMANCE,THECHARACTERISTICSOFMODULARF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