完整和不完整缓和曲线在AutoCAD中的精确表示

©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(2007)01-61-05:P209:AAutoCAD3,3:20060429:(1963),,,GPS(,450052):Simpson,nn1,:;;;;;1AutoCAD,:()CAD,CAD,CAD[1],[2][4],,01/R;(RR),,1/R1/R,1/R1/R,,()[5],,,,3Au2toCAD,,AutoCAD,AutoCADAutoCAD,,CADAutoCAD,plinespline,plineSF[1],S,,;F,,;spline,,,,,,spline2AutoCAD2111,ZH,ZHx,ZHy,[6]:x=0lcosdly=0lsindl(1)1161AutoCAD©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(1),=l2/2RlS(1),(1)[6]:x=l-l540R2l2S+l93456R4l4S-y=l36RlS-l7336R3l3S+l1142240R5l5S-(2)(1)Simpson,Simpson[7]:x=16m1+cosS+2m-1j=1cos(L2j)+4mj=1cos(L2j-1)y=16msinS+2m-1j=1sin(L2j)+4mj=1sin(L2j-1)(3):S=lS2R,mSimpson,n=2m,[0,l];(Li)=i2l28m2RlS,i(3)2j()2j-1()212AutoCAD(1),;(2),;Simpson(3),,,mnnsplinen,AutoCAD,,,AutoCAD213n[8],(3)(1):E=-l5180n4f(4)()[0,l](4),,|E|(5)(4)(5):n01273-14l54|f(4)()|14(6)x,:f(l)=cosl22C(7)[7]:f(4)(l)=6l2C3sinl22C+l4-3C2C4cosl22C(8),C=RlS[7]n,lS3R,,(8):|f(4)()|=62C3sin22C+4-3C2C4cos22C364C6+(4-3C2)2C812(9)[0,l],l[0,lS],,[0,lS](9),=lS,|f(4)()|:|f(4)()|max=1R4l2S(l4S+9R4+30R2l2S)12(10)(6),K=lS/R,:n01273-14l14S(K8+30K6+9K4)18(11)(11):n,,n1n:n1/m0.010.0050.0010.00050.0001n(-14)3.163.765.626.6910.00,1,n1n,,RlSKlS,n;R,n,lSR,K,n(24);,,lSR,lS2R,K,lS,n(1015)214n(11),,,Q=(K8+30K6+9K4)18(12)QK,2Q,K=011,012215Q,:^Q=014+111K(13)26©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=019985,(13)(12)2(13)(12),KK=011[9],K215,K011215,(13)(11):n(0111+013K)14l14S(14)=01001m,:n(0162+1169K)l14S(15)(14)(15)n215AutoCADAutoCAD,:RlS,(15)(11)n,lS/n,n+1;,[2][7][9]ZHHY;,spline,(ZH)(HY);ListArea,lS,,,,1,,,[10];Simpson,nn2;Gauss-Legendre,[9]3AutoCAD,3,AB,RR,l0,ZHR:C=RlSC=R(lS-l0)(16):lS=RR-Rl0(17),nlS,,n1:n1=l0lSn(18)(17),:n1=(1-RR)n(19)(19)n1,AutoCAD,,[7][9]344111lS=250m,R=2000m(15)n=313,n=4,5250/4=6215m(3),AutoCAD,1mm011mm,n6,ZH,1215mID,(),,2361AutoCAD©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=4n=2n=1x/mmy/mmx/mmy/mmx/mmy/mmK0+00000000+12.500+0.10000+25.00000-0.100+37.500+0.10-0.100+50.000+0.10-0.200+62.500+0.10-0.300+75.000+0.10-0.500+87.500+0.10-0.600+100.000+0.10-0.600+112.500+0.10-0.700+125.00000-0.700+137.50000-0.700+150.0+0.1000-0.500+162.500-0.10-0.500+175.000-0.20-0.500+187.500-0.10-0.300+200.000-0.10-0.200+212.5-0.10-0.10-0.100+2250000-0.100+237.50000000+250.0000000,(14)(15)n,,2n=2n=1,2,n,;n,n=2;n=1,(1mm)4122l0=611435m,R=126m,R=60m,(17)lS=1171285m(15)(18)(19)n16,AutoCAD,,215m,3n16,n1=4,33,n=6,1mm,n=4,HY,1mm,;nn1,,n1,HY,lS(),n1,,n13n=6n=4x/mmy/mmx/mmy/mmK0+000000+2.500000+5.000000+7.5-0.10-0.100+10.000000+12.5-0.10000+15.000000+17.5-0.10-0.2-0.10+20.000-0.400+22.5-0.10-0.500+25.000-0.400+27.500-0.200+30.000000+32.5-0.10+0.2+0.10+35.0-0.10+0.4+0.20+37.5-0.10+0.6+0.20+40.000+0.6+0.30+42.5+0.1+0.1+0.5+0.30+45.0+0.2+0.1000+47.5+0.2+0.1-0.8-0.50+50.000-1.6-1.00+52.5-0.3-0.1-1.8-1.10+55.0-0.5-0.3-1.6-0.90+57.5-0.3-0.2-0.9-0.40+60.0-0.1-0.1-0.400+61.43500005,,Simpson,,nn1nn1,AutoCAD,l0lS,n1nl0/lS,n1,,,(14)(19)nn1,n23,AutoCAD,n,,n,,,,,46©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[7],nn2;,5Gauss-Legendre[9],,,[1].AutoCAD2000[M].:,1999[2].[J].,2005(1)[3],.[J].,2002(1)[4].[J].,2004(1)[5],.[J].,2005(1)[6].[M].:,1982[7].Simpson[J].,2001(3)[8].[M].:,1999[9].Gauss-Legendre[J].,2004(2)[10].[J].,2001(1)PreciseDisplayingofCompleteandIncompleteEasementonAutoCADLiQuanXin,YeGang(ZhengzhouPlanning&SurveyResearchInstitute,Zhengzhou450052,China)Abstract:ThedisplayingmethodofeasementinAutoCADisproposedbyusingcubicsplineinthispaper.ConsideringthefactthattheparametricequationsofeasementcanbeexpressedbycompoundSimpsonformulae,therigorousorsimplefor2mulaefordeterminingthenumberofequal-arcforfittingcompleteeasement,andfordeterminingtheoneforincompleteease2mentarederived.Finally,thetwoexamplesaregivenouttoillustratethefeasibilityandValidityofthedisplayingmethod.Keywords:Completeeasement;incompleteeasement;mathematicmodel;splinecurve;displaying;node()2007278,,11:,,,2005,,,:1953,;,,,,,,28,,,,,30,,;()561AutoCAD