高斯正反算

大地坐标向笛卡尔坐标转换

高斯正反算
采用不同椭球实现高斯克里格投影，将经纬度坐标转换为高斯平面坐标：正算
高斯平面坐标转换为不同椭球下的经纬度坐标：反算

http://robekeane.iteye.com/blog/1441566

http://blog.163.com/superliuwhu@126/blog/static/68557075200992654039167/

 1 void GaussProjectDirect(double a,double efang,double B,double L,double L0,double& x,double &y,double& R)//高斯投影正算克氏
 2 {   
 3 
 4 double b=aefangtob(a,efang);
 5 double e2=seconde(a,b);
 6 double W=sqrt(1-efang*sin(B)*sin(B));printf("W=%f",W);
 7 double N=a/W;printf("N=%f",N);
 8 double M=a*(1-efang)/pow(W,3);printf("M=%f",M);
 9 double t=tee(B);
10 double eitef=eitefang(a,b,B);
11 double l=L-L0;
12 //主曲率半径计算
13 double m0,m2,m4,m6,m8,n0,n2,n4,n6,n8;
14 m0=a*(1-efang);     n0=a;
15 m2=3.0/2.0*efang*m0;   n2=1.0/2.0*efang*n0;
16 m4=5.0/4.0*efang*m2;   n4=3.0/4.0*efang*n2;
17 m6=7.0/6.0*efang*m4;   n6=5.0/6.0*efang*n4;
18 m8=9.0/8.0*efang*m6;   n8=7.0/8.0*efang*n6;
19 //子午线曲率半径
20 double a0,a2,a4,a6,a8;
21 a0=m0+m2/2+3*m4/8+5*m6/16+35*m8/128;
22 a2=m2/2+m4/2+15*m6/32+7.0/16.0*m8;
23 a4=m4/8.0+3.0/16.0*m6+7.0/32.0*m8;
24 a6=m6/32+m8/16;
25 a8=m8/128;
26 
27 double X=a0*B-a2/2*sin(2*B)+a4/4*sin(4*B)-a6/6*sin(6*B)+a8/8*sin(8*B);
28 x=X+N/2*t*cos(B)*cos(B)*l*l+N/24*t*(5-t*t+9*eitef+4*pow(eitef,2))*pow(cos(B),4)*pow(l,4)+N/720*t*(61-58*t*t+pow(t,4))*pow(cos(B),6)*pow(l,6);
29 y=N*cos(B)*l+N/6*(1-t*t+eitef)*pow(cos(B),3)*pow(l,3)+N/120*(5-18*t*t+pow(t,4)+14*eitef-58*eitef*t*t)*pow(cos(B),5)*pow(l,5);
30      R=sqrt(M*N);
31 }
32 
33 
34 //高斯投影反算
35 
36 
37 void GaussProjectInvert(double a,double efang,double x,double y,double L0,double &B,double& L,double& R)
38 {
39    double b=aefangtob(a,efang);
40 
41 
42 double m0,m2,m4,m6,m8,n0,n2,n4,n6,n8;
43 m0=a*(1-efang);     n0=a;
44 m2=3.0/2.0*efang*m0;   n2=1.0/2.0*efang*n0;
45 m4=5.0/4.0*efang*m2;   n4=3.0/4.0*efang*n2;
46 m6=7.0/6.0*efang*m4;   n6=5.0/6.0*efang*n4;
47 m8=9.0/8.0*efang*m6;   n8=7.0/8.0*efang*n6;
48 
49 
50 //子午线曲率半径
51 double a0,a2,a4,a6,a8;
52 a0=m0+m2/2+3*m4/8+5*m6/16+35*m8/128;
53 a2=m2/2+m4/2+15*m6/32+7.0/16.0*m8;
54 a4=m4/8.0+3.0/16.0*m6+7.0/32.0*m8;
55 a6=m6/32+m8/16;
56 a8=m8/128;
57 
58 
59 double X=x;
60     double FBf=0;
61 double Bf0=X/a0,Bf1=0;
62 while((Bf0-Bf1)>=0.0001)
63 {   Bf1=Bf0;
64    FBf=a0*Bf0-a2/2*sin(2*Bf0)+a4/4*sin(4*Bf0)-a6/6*sin(6*Bf0)+a8/8*sin(8*Bf0);
65    Bf0=(X-FBf)/a0;
66 }
67 double Bf=Bf0;
68 double Vf=bigv(a,b,Bf);
69 double tf=tee(Bf);
70 double Nf=bign(a,b,Bf);
71 double eiteffang=eitefang(a,b,Bf);
72 double Bdu=rad_deg(Bf)-1/2.0*Vf*Vf*tf*(pow((y/Nf),2)-1.0/12*(5+3*tf*tf+eiteffang-9*eiteffang*tf*tf)*pow((y/Nf),4)+1.0/360.0*(61+90*tf*tf+45*tf*tf)*pow((y/Nf),6))*180/PI;
73 double ldu=1.0/cos(Bf)*(y/Nf+1.0/6.0*(1+2*tf*tf+eiteffang)*pow((y/Nf),3)+1.0/120.0*(5+28*tf*tf+24*tf*tf+6*eiteffang+8*eiteffang*tf*tf)*pow((y/Nf),5))*180.0/PI;
74     
75 
76 B=deg_int(Bdu);
77 L=L0+deg_int(ldu);
78 double W=sqrt(1-efang*sin(B)*sin(B));printf("W=%f\n",W);
79 double N=a/W;printf("N=%f\n",N);
80 double M=a*(1-efang)/pow(W,3);printf("M=%f\n",M);
81 R=sqrt(M*N);
82 
83 
84 }