利用CASIO编程计算器的积分功能进行缓和曲线上点位坐标的精确计算

:1009-2269(2010)01-0010-03CASIO3(,730046):,,.,,,.,.:;;;:U212.24:B0,,RR1R2,,.,,.,,.CASIOfx24800Pfx25800P,.1():rL=A2(1)rP;LP(r=);A.H,P(r=).:d=LRHdL(2):=L22RH(rad)(3)(ZH)(HZ),x,y,Pxy:dx=dLcos,dy=dLsin(4):x=cosdL=cosL22RHdL,y=sindL=sinL22RHdL(5),cossin:cos=1-22!+44!+(-1)n-12n-2(2n-2)!3:2009210226:(19712),,,.cos=-33!+55!+(-1)n-12n-1(2n-2)!(6)(3)(6)(5):x=L-L540R2H2+L93456R4H4-L13599040R6H6+(-1)n-1L13(2RH)2n-2(2n-2)!(4n-3)y=L36RH-L7336R3H3+L11442240R5H5-L159676800R7H7+(-1)n-1L4n-1(2RH)2n-1(2n-1)!(4n-1)(7).,.,,x,y,:x=L-L540R2H2,y=L36RH(8)([1][2][3])(8).[6],.,cossin,x12,y8.,.2CASIO,(3)(rad).(deg),,:=L22RH180=90L2RH(deg)(9)(5):x=cos(90L2RH)dL,x=sin(90L2RH)dL(10)(10).CASIO,baf(x)dx=limx0nni=1f(i)xi,.baf(x)dxfx24800P(f(x),a,b,n);fx25800P(f(x),a,b,tol).f(x),x,a,b.n,tol.ntol,.,CASIOfx24800P,KLMNabnbaf(x)dx.,,.,(10):x=L0cos(90L2RH)dL,y=L0sin(90L2RH)dL.(11)CASIOfx24800Pfx25800P,x,x.,(11)Lx.,PZH(HZ)L,ZH(HZ),x,y,xy:X=(cos(90X2(RH)),0,LY=(sin(90X2(RH)),0,L.3,,R=30;H=30,ZH=5+100.(ZH)111:CASIO,x,y,1.1(8)(7)4xiyixiyixiyiZH5+1000.0000.0000.0000.0000.0000.0005+1109.9970.1859.9970.1859.9970.1855+12019.9011.48119.9011.47619.9011.4765+13029.2505.00029.2594.91129.2594.911:(8),y.5+130,(8)5.000-4.911=0.089.,(7)4,.,CASIO,,.:CASIOfx25800P:ZH=?Q:H=?H:R=?R:Lbl1:P=?P:P2QL:X=:(cos(90X2(RH)),0,L)Y=:(sin(90X2(RH)),0,L)Goto1,ZHHR.P,.4,,..:[1].[M].:,2002.[2],,,.[M].:,2003.[3].[M].:,2000.[4],.CASIOfx25800P[M].:,2008.[5],.[J].,2009(1):57259.[6],,,.CASIO[J].,2008(3):44246.PreciseCalculationforPointCoordinatesofEasementCurvebyUsingIntegralFunctionofCasioCalculatorHEYu2xin(LanzhouCityConstructionSchool,Lanzhou730046,China)Abstract:Becausethecurveradiusofeasementcurvegraduallychanges,theformulaforcalculatingthecoordinatescannotbeobtainedwiththemethodofintegration.Onlywithseriesexpansionmethodcanapproximativeresultsbeobtained,butthismethodhassomedisadvantages,suchascomplex,greatcal2culation,lowspeed,lowaccuracy.TheexactvalueofpointcoordinatesontheeasementcurvecaneasilybeobtainedthroughusingthedefiniteintegralfunctionofCasiocalculator.Keywords:programmedCasiocalculator;integralfunction;easementcurve;coordinatescalculationforcoordinates2117