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INTJADVMANUFTECHNOL200016635–6422000SPRINGERVERLAGLONDONLIMITEDTHEPREPROCESSINGOFDATAPOINTSFORCURVEFITTINGINREVERSEENGINEERINGMINGCHIHHUANGANDCHINGCHIHTAIDEPARTMENTOFMECHANICALENGINEERING,TATUNGUNIVERSITY,TAIPEI,TAIWANREVERSEENGINEERINGHASBECOMEANIMPORTANTTOOLFORCADMODELCONSTRUCTIONFROMTHEDATAPOINTS,MEASUREDBYACOORDINATEMEASURINGMACHINECMM,OFANEXISTINGPARTAMAJORPROBLEMINREVERSEENGINEERINGISTHATTHEMEASUREDPOINTSHAVINGANIRREGULARFORMATANDUNEQUALDISTRIBUTIONAREDIFFICULTTOFITINTOABSPLINECURVEORSURFACETHEPAPERPRESENTSAMETHODFORPREPROCESSINGDATAPOINTSFORCURVEFITTINGINREVERSEENGINEERINGTHEPROPOSEDMETHODHASBEENDEVELOPEDTOPROCESSTHEMEASUREDDATAPOINTSBEFOREFITTINGINTOABSPLINEFORMTHEFORMATOFTHENEWDATAPOINTSREGENERATEDBYTHEPROPOSEDMETHODISSUITABLEFORTHEREQUIREMENTSFORFITTINGINTOASMOOTHBSPLINECURVEWITHAGOODSHAPETHEENTIREPROCEDUREOFTHISMETHODINVOLVESFILTERING,CURVATUREANALYSIS,SEGMENTATION,REGRESSING,ANDREGENERATINGSTEPSTHEMETHODISIMPLEMENTEDANDUSEDFORAPRACTICALAPPLICATIONINREVERSEENGINEERINGTHERESULTOFTHERECONSTRUCTIONPROVESTHEVIABILITYOFTHEPROPOSEDMETHODFORINTEGRATIONWITHCURRENTCOMMERCIALCADSYSTEMSKEYWORDSCURVEFITTING;PREPROCESSINGOFDATAPOINTS;REVERSEENGINEERING1INTRODUCTIONWITHTHEPROGRESSINTHEDEVELOPMENTOFCOMPUTERHARDWAREANDSOFTWARETECHNOLOGY,THECONCEPTOFCOMPUTERAIDEDTECHNOLOGYFORPRODUCTDEVELOPMENTHASBECOMEMOREWIDELYACCEPTEDBYINDUSTRYTHEGAPBETWEENDESIGNANDMANUFACTURINGISNOWBEINGGRADUALLYNARROWEDTHROUGHTHEDEVELOPMENTOFNEWCADTECHNOLOGYINANORMALAUTOMATEDMANUFACTURINGENVIRONMENT,THEOPERATIONSEQUENCEUSUALLYSTARTSFROMPRODUCTDESIGNVIAGEOMETRICMODELSCREATEDINCADSYSTEMS,ANDENDSWITHTHEGENERATIONOFMACHININGINSTRUCTIONSREQUIREDTOCONVERTRAWMATERIALINTOAFINISHEDPRODUCT,BASEDONTHEGEOMETRICMODELTOREALISETHEADVANTAGESOFMODERNCOMCORRESPONDENCEANDOFFPRINTREQUESTSTOMINGCHIHHUANG,DEPARTMENTOFMECHANICALENGINEERING,TATUNGUNIVERSITY,40CHUNGSHANNROAD,3RDSECTION,TAIPEI104,TAIWANEMAILMINDYKMGHERTTITEDUTWPUTERAIDEDTECHNOLOGYINTHEPRODUCTDEVELOPMENTANDMANUFACTURINGPROCESS,AGEOMETRICMODELOFTHEPARTTOBECREATEDINTHECADSYSTEMISREQUIREDHOWEVER,THEREARESOMESITUATIONSINPRODUCTDEVELOPMENTINWHICHAPHYSICALMODELORSAMPLEISPRODUCEDBEFORECREATINGTHECADMODEL1WHEREACLAYMODEL,FOREXAMPLE,INDESIGNINGAUTOMOBILEBODYPANELS,ISMADEBYTHEDESIGNERORARTISTBASEDONCONCEPTUALSKETCHESOFWHATTHEPANELSHOULDLOOKLIKE2WHEREASAMPLEEXISTSWITHOUTTHEORIGINALDRAWINGORDOCUMENTATIONDEFINITION3WHERETHECADMODELREPRESENTINGTHEPARTHASTOBEREVISEDOWINGTODESIGNCHANGEDURINGMANUFACTURINGINALLOFTHESESITUATIONS,THEPHYSICALMODELORSAMPLEMUSTBEREVERSEENGINEEREDTOCREATEORREFINETHECADMODELINCONTRASTTOTHISCONVENTIONALMANUFACTURINGSEQUENCE,REVERSEENGINEERINGTYPICALLYSTARTSWITHMEASURINGANEXISTINGPHYSICALOBJECTSOTHATACADMODELCANBEDEDUCEDINORDERTOEXPLOITTHEADVANTAGESOFCADTECHNOLOGIESTHEPROCESSOFREVERSEENGINEERINGCANUSUALLYBESUBDIVIDEDINTOTHREESTAGES,IEDATACAPTURE,DATASEGMENTATIONANDCADMODELLINGAND/ORUPDATING1,2APHYSICALMOCKUPORPROTOTYPEISFIRSTMEASUREDBYACOORDINATEMEASURINGMACHINEORALASERSCANNERTOACQUIRETHEGEOMETRICINFORMATIONINTHEFORMOF3DPOINTSTHEMEASUREDRESULTSARETHENSEGMENTEDINTOTOPOLOGICALREGIONSFORFURTHERPROCESSINGEACHREGIONREPRESENTSASINGLEGEOMETRICFEATURETHATCANBEREPRESENTEDMATHEMATICALLYBYASIMPLESURFACEINTHECASEOFMODELRECONSTRUCTIONCADMODELLINGRECONSTRUCTSTHESURFACEOFAREGIONANDCOMBINESTHESESURFACESINTOACOMPLETEMODELREPRESENTINGTHEMEASUREDPARTORPROTOTYPE3INPRACTICALMEASURINGCASES,HOWEVER,THEREAREMANYSITUATIONSWHERETHEGEOMETRICINFORMATIONOFAPHYSICALPROTOTYPEORSAMPLECANNOTBEMEASUREDCOMPLETELYANDACCURATELYTORECONSTRUCTAGOODCADMODELSOMEDATAPOINTSOFTHEMEASUREDSURFACEMAYBEIRREGULAR,HAVEMEASUREMENTERRORS,ORCANNOTBEACQUIREDASSHOWNINFIG1,THEMAINSURFACEOFMEASUREDOBJECTMAYHAVEFEATURESSUCHASHOLES,ISLANDS,ORROUGHNESSCAUSEDBYMANUFACTURINGINACCURACY,CONSEQUENTLYTHECMMPROBECANNOTCAPTURETHECOMPLETESETOFDATAPOINTSTORECONSTRUCTTHEENTIRESURFACE636MCHUANGANDCCTAIFIG1THEGENERALPROBLEMSINAPRACTICALMEASURINGCASEMEASUREMENTOFANEXISTINGOBJECTSURFACEINREVERSEENGINEERINGCANBEACHIEVEDBYUSINGEITHERCONTACTPROBINGORNONCONTACTSENSINGPROBINGTECHNIQUESWHATEVERTECHNIQUEISAPPLIED,THEREAREMANYPRACTICALPROBLEMSWITHACQUIRINGDATAPOINTS,FOREXAMPLES,NOISE,ANDINCOMPLETEDATAWITHOUTEXTENSIVEPROCESSINGTOADJUSTTHEDATAPOINTS,THESEPROBLEMSWILLCAUSETHECADMODELTOBERECONSTRUCTEDWITHANUNDESIREDSHAPEINORDERTOREBUILDTHECADMODELCORRECTLYANDSATISFACTORILY,THISPAPERPRESENTSAUSEFULANDEFFECTIVEMETHODTOPREPROCESSTHEDATAPOINTSFORCURVEFITTINGUSINGTHEPROPOSEDMETHOD,THEDATAPOINTSAREREGENERATEDINASPECIFIEDFORMAT,WHICHISSUITABLEFORFITTINGINTOACURVEREPRESENTEDINBSPLINEFORMWITHOUTTHEPROBLEMSPREVIOUSLYMENTIONEDAFTERFITTINGALLOFTHECURVES,THESURFACEMODELCANBECOMPLETEDBYCONNECTINGTHECURVES2THETHEORYOFBSPLINEMOSTOFTHESURFACEBASEDCADSYSTEMSEXPRESSSHAPESREQUIREDFORMODELLINGBYPARAMETRICEQUATIONS,SUCHASINBEZIERORBSPLINEFORMSTHEMOSTUSEDISTHEBSPLINEFORMBSPLINESARETHESTANDARDFORREPRESENTINGFREEFORMCURVESANDSURFACESINCURRENTCOMMERCIALCADSYSTEMSBSPLINECURVESANDBEZIERCURVESHAVEMANYADVANTAGESINCOMMON4CONTROLPOINTSINFLUENCETHECURVESHAPEINAPREDICTABLE,NATURALWAY,MAKINGTHEMGOODCANDIDATESFORUSEI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
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