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高斯投影坐标正反算-1-高斯投影坐标正反算学院：班级：学号：姓名：课程名称:指导老师：高斯投影坐标正反算-2-实验目的：1.了解高斯投影坐标正反算的基本思想；2.学会编写高斯正反算程序，加深了解。实验原理：高斯投影正算公式中应满足的三个条件：1.中央子午线投影后为直线；2.中央子午线投影后长度不变；3.投影具有正形性质，即正形投影条件。高斯投影反算公式中应满足的三个条件：1.x坐标轴投影成中央子午线，是投影的对称轴；2.x轴上的长度投影保持不变；3.正形投影条件，即高斯面上的角度投影到椭球面上后角度没有变形，仍然相等。操作工具：计算机中的VB6.0代码：DimaAsDouble,bAsDouble,xAsDouble,yAsDouble,y_#Diml_AsDouble,b_AsDouble,a0#,a2#,a4#,a6#,a8#,m2#,m4#,高斯投影坐标正反算-3-m6#,m8#,m0#,l0#,e#,e1#Dimdeg1AsDouble,min1AsDouble,sec1AsDouble,deg2AsDouble,min2AsDouble,sec2AsDoublePrivateSubCommand1_Click()Dimx_AsDouble,t#,eta#,N#,W#,k1#,k2#,ik1%,ik2%,dh%deg1=Val(Text1.Text)min1=Val(Text2.Text)sec1=Val(Text3.Text)deg2=Val(Text4.Text)min2=Val(Text5.Text)sec2=Val(Text6.Text)l_=(deg1*3600+min1*60+sec1)/206265b_=(deg2*3600+min2*60+sec2)/206265dh=Val(Text9.Text)k1=((l_*180/3.14159+3)/6)k2=(l_*180/3.14159/3)ik1=Round(k1,0)ik2=Round(k2,0)Ifdh=6Thenl0=6*ik1-3ElseIfdh=3Then高斯投影坐标正反算-4-l0=3*ik2ElseMsgBoxerror,48,error:ExitSubEndIfEndIfl=l_-l0*3.14159/180e=Sqr(a*a-b*b)/am0=a*(1-e*e)m2=e*e*m0*3/2m4=e*e*m2*5/4m6=m4*e*e*7/6m8=e*e*m6*9/8a0=m0+m2/2+m4*3/8+m6*5/16+m8*35/128a2=m2/2+m4/2+m6*15/32+m8*7/16a4=m4/8+m6*3/16+m8*7/32a6=m6/32+m8/16a8=m8/128x_=a0*b_-a2*Sin(2*b_)/2+a4*Sin(4*b_)/4-Sin(6*b_)*a6/6+Sin(8*b_)*a8/8t=Tan(b_)e1=Sqr((a*a-b*b)/(b*b))eta=Sqr(e1*e1*Cos(b)*Cos(b))高斯投影坐标正反算-5-W=Sqr(1-e*e*Sin(b_)*Sin(b_))N=a/Wx=x_+N*Sin(b_)*Cos(b_)*l*l/2+N*Sin(b_)*Cos(b_)^3*(5-t*t+9*eta*eta+4*eta^4)*l^4/24+N*Sin(b_)*Cos(b_)^5*(61-58*t*t+t^4)*l^6/720y=N*Cos(b_)*l+N*Cos(b_)^3*(1-t*t+eta*eta)*l*l*l/6+N*Cos(b_)^5*(5-18*t*t+t^4+14*eta*eta-58*eta*eta*t*t)*l^5/120Text7=xIfdh=6Theny_=y+500000+1000000*ik1ElseIfdh=3Theny_=y+500000+1000000*ik2ElseMsgBoxerror,48,error:ExitSubEndIfEndIfText8=y_EndSubPrivateSubCommand2_Click()高斯投影坐标正反算-6-Dimbf#,j%,Wf#,Vf#,Nf#,Mf#,c#,tf#,etaf#,dh%,ik%x=Val(Text7.Text)y_=Val(Text8.Text)e=Sqr((a*a-b*b)/(a*a))m0=a*(1-e*e)m2=e*e*m0*3/2m4=e*e*m2*5/4m6=m4*e*e*7/6m8=e*e*m6*9/8a0=m0+m2/2+m4*3/8+m6*5/16+m8*35/128a2=m2/2+m4/2+m6*15/32+m8*7/16a4=m4/8+m6*3/16+m8*7/32a6=m6/32+m8/16a8=m8/128bf=x/a0Forj=1To10bf=(x+a2/2*Sin(2*bf)-a4*Sin(4*bf)/4+a6*Sin(6*bf)/6-a8*Sin(8*bf)/8)/a0Nextje1=Sqr(a*a-b*b)/bVf=Sqr(1+e1*e1*Cos(bf)*Cos(bf))Wf=Sqr(1-e*e*Sin(bf)*Sin(bf))高斯投影坐标正反算-7-Nf=a/Wfc=a*a/bMf=c/Vf^3tf=Tan(bf)e1=Sqr((a*a-b*b)/(b*b))etaf=Sqr(e1*e1*Cos(bf)*Cos(bf))ik=Int(y_/1000000)y=y_-ik*1000000-500000b_=bf-tf*y*y/(2*Mf*Nf)+tf*(5+3*tf*tf+etaf*etaf-9*etaf*etaf*tf*tf)*y*y*y*y/(24*Mf*Nf*Nf*Nf)+tf*(61+90*tf*tf+45*tf*tf*tf*tf)*y*y*y*y*y*y/(720*Mf*Nf*Nf*Nf*Nf*Nf)l=y/(Nf*Cos(bf))-(1+2*tf*tf+etaf*etaf)*y*y*y/(6*Nf*Nf*Nf*Cos(bf))+(5+28*tf*tf+24*tf*tf*tf*tf+6*etaf*etaf+8*etaf*etaf*tf*tf)*y*y*y*y*y/(120*Nf*Nf*Nf*Nf*Nf*Cos(bf))dh=Val(Text9.Text)Ifdh=6Thenl0=6*ik-3ElseIfdh=3Thenl0=3*ik高斯投影坐标正反算-8-ElseMsgBoxerror,48,error:ExitSubEndIfEndIfl_=l0*3.14159/180+lsec1=l_*206265deg1=Int(sec1/3600)min1=Int((sec1-deg1*3600)/60)sec1=sec1-deg1*3600-min1*60sec2=b_*206265deg2=Int(sec2/3600)min2=Int((sec2-deg2*3600)/60)sec2=sec2-deg2*3600-min2*60Text1=deg1Text2=min1Text3=Round(sec1,5)Text4=deg2Text5=min2Text6=Round(sec2,5)EndSubPrivateSubCommand3_Click()高斯投影坐标正反算-9-EndEndSubPrivateSubCommand4_Click()Text1.Text=Text2.Text=Text3.Text=Text4.Text=Text5.Text=Text6.Text=Text7.Text=Text8.Text=Text9.Text=Text10.Text=EndSubPrivateSubOption1_Click()a=6378245b=6356863.01877305EndSubPrivateSubOption2_Click()高斯投影坐标正反算-10-a=6378140b=6356755.28815753EndSubPrivateSubOption3_Click()a=6378137b=6356752.3142EndSubPrivateSubOption4_Click()a=6378137b=6356752.3141EndSubPrivateSubOption5_Click()a=Val(InputBox(a,plsaseinput))b=Val(InputBox(b,pleaseinput))EndSub高斯投影坐标正反算-11-界面截图如下：使用方法：1.如下所示，高斯投影坐标正算时，在经度纬度相应的文本框里输入经纬度，再在度号对应的文本框里输入是六度带还是三度带，最后按坐标正算按钮即可，答案会显示在X，Y相应的文本框里；2.如果要进行坐标反算，则输入X，Y与度号，最后按坐标反算按钮即可得到所需的大地经纬度；3.注意选择需要的椭球。高斯投影坐标正反算-12-