重庆大学机自实验班计算机辅助设计与制造总复习PPT.ppt

TotalReviewofComputer aidedDesignandManufacturing ScoreAssessment Attendance 10 Rollcall5times 2markseachtime courseerercises 15 Courseexercises3times 5markseachtime Termpaper 25 Examination 50 2 houropenbookpaper CAD90 plusCAM10 Calculationproblemsandnounsexplain ExaminationMaterial LecturenotesTutorialsandexercisesTeachingMaterial MECHANICALENGINEERINGCAD CAM ReferencesbooksSurfacemodellingforCAD CAM Chapter1 5 7Geometricmodelling chapter9 10 TheCNCWorkshop ver2 chapter1 Chapter1 Instruction WhatisCAD CAM CAE CAPP Howistherelationshipamongthem WhatistheHISTORYofCAD CAM HardwareandsoftwareofCAD CAMsystem WhatisGeometricModellinganditstypicalapplications Chapter2 Curves FourcurvemodelsStandardpolynomialcurveFergusoncurveBeziercurveB splinecurveCurvefitting PolynomialCurveModels CurveSegmentDefinition Acubicpolynomialcurvemodel r u a bu cu2 du3usedinrepresentingacurvesegmentisspecifiedbyitsendconditions e g a 4points P0 P1 P2andP3 or b twoendpointsP0andP1 twoendtangentst0andt1 Ingeneral adegree npolynomialcurvecanbeusedtofit n 1 datapoints FergusonCurveModel Constructingacurvesegment JoiningtwoendpointsP0andP1 Havingspecifiedendtangentst0andt1i e P0 r 0 P1 r 1 t0 r 0 t1 r 1 r u UA UMVwith0 u 1 BezierCurveModel with0 u 1 OnevaluatingtheBezierequationanditsderivativeatu 0 1 r 0 V0r 1 Vnr 0 n V1 V0 r 1 n Vn Vn 1 BezierfoundafamilyoffunctionscalledBernsteinPolynomialsthatsatisfytheseconditions BezierCurveModel Cubic n 3 Beziercurvemodel r u 1 u 3V0 3u 1 u 2V1 3u2 1 u V2 u3V3 r u UMR r 0 V0r 0 3 V1 V0 r 1 V3r 1 3 V3 V2 Theshapeofthecurveresemblesthatofthecontrolpolygon B splineModel with0 u 1 Ni n u Theprimaryfunction B splineModeldefinedbyn 1pointsViisgivenbythe Where B splineModel QuadraticuniformB splinemodelwithcontrolpointsV0 V1 andV2 r t t2t1 U3M3P30 t 1 CubicuniformB splinemodelwithcontrolpointsV0 V1 V2 andV3 r t 1 6 u3u2u1 U4M4P40 t 1 ParametricContinuityCondition Twocurvesegmentsra u andrb u ra 1 P1 rb 0 C0 continuous ra 1 t1 rb 0 C1 continuous ra 1 rb 0 C2 continuous CollectivelycalledaparametricC2 condition ThecompositecurvetopassthroughP0 P1 P2 andthetangentst0andt2areassumedtobegiven Thus theproblemhereistodeterminetheunknownt1sothatthetwocurvesegmentsareC2 continuousatthecommonjoinP1 CubicSplineFitting FergusonModel EmployingFergusoncurvemodelra u UCSarb u UCSbwith0 u 1U u3u2u1 C Sa P0P1t0t1 TSb P1P2t1t2 TApplyingC2continuity ra 1 6P0 6P1 2t0 4t1rb 0 6P1 6P2 4t1 2t2 C0 continuityandC1 continuityalreadyapplied CubicSplineFitting FergusonModel ApplyingparametricC2 conditiont0 4t1 t2 3 P2 P0 Now considerconstructingaC2 continuouscurvepassingthroughasequenceofn 1 P0toPn pointsEndtangentst0andtnaregiven inadditiontothe n 1 points Pi Howmanycurvesegments Therearetotallyncurvesegments Foreachpairofneighbouringcurvesegmentsri 1 u andri u wehaveti 1 4ti ti 1 3 Pi 1 Pi 1 fori 1 2 n 1 B splineModel OnevaluatingthecubicB spline k 4 anditsderivativeatt 1 0 r 0 4V1 V0 V2 6r 1 4V2 V1 V3 6r 0 V2 V0 2r 1 V3 V1 2B splinecurvesandBeziercurveshavemanyadvantagesincommonControlpointsinfluencecurvesegmentshapeinapredictable naturalway makingthemgoodcandidatesforuseinaninteractivedesignenvironment Bothtypesofcurveareaxisindependent multivalued andbothexhibittheconvexhullproperty B splinecurveshaveadvantagesoverBeziercurves Localcontrolofcurveshape Theabilitytoaddcontrolpointswithoutincreasingthedegreeofthecurve V0 V1 V3 V2 CubicSplineFitting Estimationofendtangents t0andtnCircularendconditionPolynomialendconditionFreeendcondition Chapter3 Surfaces FoursurfacepatchmodelsStandardpolynomialsurfacepatchFergusonsurfacepatchBeziersurfacepatchB splinesurfacepatchThreeSurfaceConstructionMethodsTheFMILLmethodFergusonfittingmethodB splinefittingmethodCurvedBoundaryInterpolatingSurfacePatches StandardPolynomialPatchModel Consideravector valuedpolynomialfunctionr u v whosedegreesarecubicinbothuandvwithcoefficientsdijfor ui vj Thatisabi cubic standard polynomialpatchdefinedasr u v with0 u v 1whichcanbeexpressedinamatrixformasr u v UDVTwhere U u3u2u1 V v3v2v1 andthecoefficientsmatrixD FergusonSurfacePatchModel Solvingthe16linearequationsfortheunknowncoefficientsdijgivesusaFergusonpatchequation r u v UDVT UCQCTVTfor0 u v 1C Q BezierSurfacePatchModel r u v UMBMTVT0 u v 1WhereM B ThematrixMiscalleda cubic Beziercoefficientmatrix andBiscalledaBeziercontrolpointnetwhichformsacharacteristicpolyhedron BezierSurfacePatchModel Bezierpatchvs FergusonPatchByevaluatingthecornerconditionsoftheBezierpatch 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 SurfaceConstructionMethods Itisdesiredtouselowdegree usuallycubic polynomialpatchmodeltoformacompositesurface Threemethodstobeintroduced TheFMILLmethodFergusonfittingmethodB splinefittingmethod B SplineSurfaceFitting ComparisonbetweenFergusonfittingandB splinefittingSamecompositesurfaceresultedWhenmakingfurtherchanges localchangeforB splinesurface globalchangeforFergusonsurface Question Whenonecontrolpointischanged howmanypatchesareaffected CurvedBoundaryInterpolatingSurfacePatches Methodsofconstructingasurfacepatchinterpolatingtoasetofboundarycurves RuledsurfacesLoftedsurfacesCoonssurfacesTwotypesofsweepsurfacepatches TranslationalsweeppatchesRotationalsweeppatches RuledSurfaces Considertwoparametriccurves r0 u andr1 u with0 u 1 seefigure Alinearblendingofthe2curvesdefinesasurfacepatchcalledaruledsurfacer u v r0 u v r1 u r0 u 0 u v 1Avectorinthedirectionofr1 u r0 u iscalledarulingvectort u TranslationalSweepSurfacePatches InputSummaryTwoparametricspacecurves g u andd v Atranslationalsweepsurfaceisdefinedbythetrajectoryofthecurveg u sweptalongthesecondcurved v Themovingcurveg u iscalledageneratorcurveTheguidingcurved v iscalledadirectorcurver u v g u d v d 0 0 u v 1 RotationalSweepSurfacePatches AlsoknownassurfaceofrevolutionConsiderasectioncurves u onthex zplanes u x u i z u k x u 0 z u Rotatethesectioncurves u aboutthez axis theresultingsweepsurfacecanbeexpressedasanparametricequationas r u x u cos x u sin z u Chapter4 SolidModelling TwosolidmodelrepresentationschemesGraph basedmodel B reps Booleanmodel CSG EulerFormula Graph BasedModels Forsolidsrepresentedasplanar facedpolyhedron manysimplerepresentationschemesareavailable e g connectivitymatrixforpolyhedron Connectivitymatrix oradjacencymatrix Abinarymatrix0 elementindicatesnoconnectivityexists1 elementsindicateconnectivityexistsbetweenthepairofelements vertices edges orfaces BooleanModels ThebinarytreeforthismodelTheleafnodesaretheprimitivesolids withBooleanoperatorsateachinternalnodeandtheroot Eachinternalnodecombinesthetwoobjectsimmediatelybelowitinthetree and ifnecessary transformstheresultinreadinessforthenextoperation BasicConceptsofSolidModel Euler slaw orEuler sformula