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TotalReviewofComputer-aidedDesignandManufacturingScoreAssessmentAttendance(10%)Rollcall5times(2markseachtime)courseerercises(15%)Coursee

xercises3times(5markseachtime)Termpaper(25%)Examination(50%)2-houropenbookpaper(CAD90%plusCAM10%),Calculationproblemsa

ndnounsexplainExaminationMaterialLecturenotesTutorialsandexercisesTeachingMaterial(MECHANICALENGINEERINGCAD/CAM)ReferencesbooksSurfacemod

ellingforCAD/CAM,Chapter1-5,7Geometricmodelling,chapter9-10.TheCNCWorkshop(ver2),chapter1Chapter1:InstructionWhatisCAD/CAM/

CAE/CAPP?Howistherelationshipamongthem?)WhatistheHISTORYofCAD/CAM?HardwareandsoftwareofCAD/CAMsystem?Wh

atisGeometricModellinganditstypicalapplications?Chapter2:CurvesFourcurvemodelsStandardpolynomialcurveFergusoncurveBez

iercurveB-splinecurveCurvefittingPolynomialCurveModelsCurveSegmentDefinition:Acubicpolynomialcurvemodel:r(u)=a+bu+cu2+du3usedinrepresentingacurves

egmentisspecifiedbyitsendconditions,e.g.,(a)4points(P0,P1,P2andP3)or(b)twoendpointsP0andP1;twoendtangentst0andt1.P0P1P2

P3niiiar0u(u)Ingeneral,adegree-npolynomialcurvecanbeusedtofit(n+1)datapoints.FergusonCurveModelConstructing

acurvesegment:JoiningtwoendpointsP0andP1;Havingspecifiedendtangentst0andt1i.e.,P0=r(0);P1=r(1);t0=r

’(0);t1=r’(1)P1P0t1t0r(u)r(u)=UA=UMVwith0u1BezierCurveModelwith0u1OnevaluatingtheBezierequationanditsderivativeatu=0,1r(0)=V0r

(1)=Vnr’(0)=n(V1–V0)r’(1)=n(Vn–Vn-1)BezierfoundafamilyoffunctionscalledBernsteinPolynomialsthatsatisfytheseconditions:BezierCurveModelCubic(n=3)Bez

iercurvemodelV0V1V2V3V3V2V1V0V2V1V0V3r(u)=(1–u)3V0+3u(1–u)2V1+3u2(1–u)V2+u3V3r(u)==UMRr(0)=V0r’(0)=3(V1–V0)r(1)=V3r’(1)=3(V3

–V2)Theshapeofthecurveresemblesthatofthecontrolpolygon.B-splineModelwith0u1Ni,n(u)=TheprimaryfunctionB-splineModeldefinedbyn+1pointsViisgivenbyth

eWhereB-splineModelQuadraticuniformB-splinemodelwithcontrolpointsV0,V1,andV2r(t)=½[t2t1]=U3M3P30≤t≤1CubicuniformB-splinemodelwithc

ontrolpointsV0,V1,V2,andV3r(t)=1/6[u3u2u1]=U4M4P40≤t≤1ParametricContinuityConditionTwocurvesegmentsra(u)andrb(u)ra(1

)=P1=rb(0)(C0-continuous)ra’(1)=t1=rb’(0)(C1-continuous)ra’’(1)=rb’’(0)(C2-continuous)CollectivelycalledaparametricC2-condi

tion.ThecompositecurvetopassthroughP0,P1,P2,andthetangentst0andt2areassumedtobegiven.Thus,theproblemhereistodeterminetheunknownt1sothatthetw

ocurvesegmentsareC2-continuousatthecommonjoinP1.P0P1P2t2t0t1=?ra(u)rb(u)CubicSplineFitting(FergusonModel)EmployingFergusoncurvemodelra(

u)=UCSarb(u)=UCSbwith0u1U=[u3u2u1]C=1122123301000001Sa=[P0P1t0t1]TSb=[P1P2t1t2]TApplyingC2c

ontinuity:ra’’(1)=6P0–6P1+2t0+4t1rb’’(0)=-6P1+6P2-4t1-2t2C0-continuityandC1-continuityalreadyappliedCubic

SplineFitting（FergusonModel)ApplyingparametricC2-conditiont0+4t1+t2=3(P2–P0)Now,considerconstructingaC2-continuouscurvepassingthrough

asequenceofn+1(P0toPn)pointsEndtangentst0andtnaregiven,inadditiontothe(n+1)points{Pi}.(Howmanycurvesegments???)Therearetotallyncurve

segments.Foreachpairofneighbouringcurvesegmentsri-1(u)andri(u),wehaveti-1+4ti+ti+1=3(Pi+1–Pi-1)fori=1,2,…,n–1B-splineModelOnevalua

tingthecubicB-spline(k=4)anditsderivativeatt=1,0,r(0)=[4V1+(V0+V2)]/6r(1)=[4V2+(V1+V3)]/6r’(0)=(V2–V0)/2r’(1)=(V3–V1)/2B-splinecurvesandBezie

rcurveshavemanyadvantagesincommonControlpointsinfluencecurvesegmentshapeinapredictable,naturalway,makingthemgoodcandidatesforus

einaninteractivedesignenvironment.Bothtypesofcurveareaxisindependent,multivalued,andbothexhibittheconvexhullproperty.B-splinecurv

eshaveadvantagesoverBeziercurves:Localcontrolofcurveshape.Theabilitytoaddcontrolpointswithoutincreasingthedegreeof

thecurve.V0V1V3V2CubicSplineFittingEstimationofendtangents,t0andtnCircularendconditionPolynomialendconditionFreeendc

onditionChapter3:SurfacesFoursurfacepatchmodelsStandardpolynomialsurfacepatchFergusonsurfacepatchBeziersur

facepatchB-splinesurfacepatchThreeSurfaceConstructionMethodsTheFMILLmethodFergusonfittingmethodB-splinefittingmethodCurvedBoundaryInterpol

atingSurfacePatchesStandardPolynomialPatchModelConsideravector-valuedpolynomialfunctionr(u,v)whosedegreesarecubicinbothuandvwit

hcoefficientsdijfor(ui,vj).Thatisabi-cubic(standard)polynomialpatchdefinedasr(u,v)=with0u,v1whichcanbeexpressedinamatrixformasr(u,v)=

UDVTwhere,U=[u3u2u1],V=[v3v2v1],andthecoefficientsmatrixD=FergusonSurfacePatchModelSolvingthe16linearequationsfortheunknownco

efficientsdijgivesusaFergusonpatchequation:r(u,v)=UDVT=UCQCTVTfor0u,v1C=Q=BezierSurfacePatchModelr(u,v)

==UMBMTVT0u,v1WhereM=B=ThematrixMiscalleda(cubic)Beziercoefficientmatrix,andBiscalledaBeziercontrolp

ointnetwhichformsacharacteristicpolyhedron.BezierSurfacePatchModelBezierpatchvs.FergusonPatchByevaluatingthecornerconditionsoftheBezierp

atch,wehavethefollowingrelationships:Atu=0,v=0,r(0,0)=V00s00=3(V10–V00)t00=3(V01–V00)x00=9(V00–V01–V10+

V11)B-splineSurfacePatchModelConsidera44arrayofcontrolvertices{Vij}.r(u,v)==UNBNTVTfor0u,v1N=SurfaceConstructi

onMethodsItisdesiredtouselowdegree(usuallycubic)polynomialpatchmodeltoformacompositesurface.Threemethodstobeintroduced:TheFMI

LLmethodFergusonfittingmethodB-splinefittingmethodB-SplineSurfaceFittingComparisonbetweenFergusonfittingandB-sp

linefittingSamecompositesurfaceresultedWhenmakingfurtherchanges,localchangeforB-splinesurface,globalchangeforFergusonsurfa

ce.Question:Whenonecontrolpointischanged,howmanypatchesareaffected?CurvedBoundaryInterpolatingSurfacePatchesMethodsofconstructingasurfacep

atchinterpolatingtoasetofboundarycurves:RuledsurfacesLoftedsurfacesCoonssurfacesTwotypesofsweepsurfacepatches:Translational

sweeppatchesRotationalsweeppatchesRuledSurfacesConsidertwoparametriccurves,r0(u)andr1(u)with0u1(seefigure).Alinearble

ndingofthe2curvesdefinesasurfacepatchcalledaruledsurfacer(u,v)=r0(u)+v(r1(u)-r0(u));0u,v1Avectorinthedirectionofr

1(u)-r0(u)iscalledarulingvectort(u).TranslationalSweepSurfacePatchesInputSummaryTwoparametricspacecurves,g(u)andd(v).A

translationalsweepsurfaceisdefinedbythetrajectoryofthecurveg(u)sweptalongthesecondcurved(v).Themovingcurveg(

u)iscalledageneratorcurveTheguidingcurved(v)iscalledadirectorcurver(u,v)=g(u)+d(v)-d(0)0u,v1r(u,v)g(u)RotationalSweepSurf

acePatchesAlsoknownassurfaceofrevolutionConsiderasectioncurves(u)onthex-zplanes(u)=x(u)i+z(u)k=(x(u),0,z(u))Rotatethesectioncurves(u)aboutthez-ax

is,theresultingsweepsurfacecanbeexpressedasanparametricequationas:r(u,)=(x(u)cos,x(u)sin,z(u))r(u,)Chapter4:SolidM

odellingTwosolidmodelrepresentationschemesGraph-basedmodel(B-reps)Booleanmodel(CSG)EulerFormulaGraph-BasedModelsForsolidsrepresentedas

planar-facedpolyhedron,manysimplerepresentationschemesareavailable,e.g.,connectivitymatrixforpolyhedron.Connectivitymatrix(oradjacen

cymatrix):Abinarymatrix0-elementindicatesnoconnectivityexists1-elementsindicateconnectivityexistsbetweenthepairofelements(vertices,edges,orfac

es).BooleanModelsThebinarytreeforthismodelTheleafnodesaretheprimitivesolids,withBooleanoperatorsateachinternalnodeandtheroot.Eachinternalnod

ecombinesthetwoobjectsimmediatelybelowitinthetree,and,ifnecessary,transformstheresultinreadinessforthenextoperation.BasicConceptsofSoli

dModelEuler’slaw(orEuler’sformula)Foravalidsolid(polyhedron),thefollowingrelationshipmustbesatisfied:V–E+F-(L–

F)=2–2HV=NumberofverticesE=NumberofedgesF=NumberoffacesL=NumberofedgeloopsH=NumberofthroughholesThisexpressioncanalsobere-writ

tenas:V–E+F-R=2–2HWhereR=L–Fisthenumberofinterioredgeloops.ExternaledgeloopInterioredgeloopChapter7:PartProgrammingandManufacturingWhati

sCNC/NC?Howabouttheircharacteristics?)WhatisCNC/MC/FMS/CIMS?Howistherelationshipamongthem?)WhatisthebasicconstructionforNCprogramming?Howtode

terminethecocrdinatesystemsofNCmachinetools?WhatisRP/RE?Howabouttheircharacteristics?)TipYoushouldpreparesufficientmaterials.Yousho

uldbringyourscientificcalculator,notyouriPhone.Youmayneedaruler.Alloftheseformthescopeoftestinthefinalexam.Thefina

ltipPractice,practice,andpractice…ThankyouWishyouforthebestgrades!