高斯克吕格投影换带计算(高斯正反算公式)

//高斯投影正、反算 
//6度带宽 54年北京坐标系 
//高斯投影由经纬度(UnitD)反算大地坐标(含带号，Unit:Metres) 
void GaussProjCal(double longitude, double latitude, double *X, double *Y) 
{
int ProjNo=0; int ZoneWide; 带宽 
double longitude1,latitude1, longitude0,latitude0, X0,Y0, xval,yval;
double a,f, e2,ee, NN, T,C,A, M, iPI;
iPI = 0.0174532925199433; 3.1415926535898/180.0; 
ZoneWide = 6; 6度带宽 
a=6378245.0; f=1.0/298.3; //54年北京坐标系参数 
a=6378140.0; f=1/298.257; //80年西安坐标系参数 
ProjNo = (int)(longitude / ZoneWide) ; 
longitude0 = ProjNo * ZoneWide + ZoneWide / 2; 
longitude0 = longitude0 * iPI ;
latitude0=0; 
longitude1 = longitude * iPI ; //经度转换为弧度
latitude1 = latitude * iPI ; //纬度转换为弧度
e2=2*f-f*f;
ee=e2*(1.0-e2);
NN=a/sqrt(1.0-e2*sin(latitude1)*sin(latitude1));
T=tan(latitude1)*tan(latitude1);
C=ee*cos(latitude1)*cos(latitude1);
A=(longitude1-longitude0)*cos(latitude1);
M=a*((1-e2/4-3*e2*e2/64-5*e2*e2*e2/256)*latitude1-(3*e2/8+3*e2*e2/32+45*e2*e2
*e2/1024)*sin(2*latitude1)+(15*e2*e2/256+45*e2*e2*e2/1024)*sin(4*latitude1)-(35*e2*e2*e2/3072)*sin(6*l
atitude1));
xval = NN*(A+(1-T+C)*A*A*A/6+(5-18*T+T*T+72*C-58*ee)*A*A*A*A*A/120);
yval = M+NN*tan(latitude1)*(A*A/2+(5-T+9*C+4*C*C)*A*A*A*A/24
+(61-58*T+T*T+600*C-330*ee)*A*A*A*A*A*A/720);
X0 = 1000000L*(ProjNo+1)+500000L; 
Y0 = 0; 
xval = xval+X0; yval = yval+Y0; 
*X = xval;
*Y = yval;
}


//高斯投影由大地坐标(Unit:Metres)反算经纬度(UnitD)
void GaussProjInvCal(double X, double Y, double *longitude, double *latitude) 

{
int ProjNo; int ZoneWide; 带宽 
double longitude1,latitude1, longitude0,latitude0, X0,Y0, xval,yval;
double e1,e2,f,a, ee, NN, T,C, M, D,R,u,fai, iPI;
iPI = 0.0174532925199433; 3.1415926535898/180.0; 
a = 6378245.0; f = 1.0/298.3; //54年北京坐标系参数 
a=6378140.0; f=1/298.257; //80年西安坐标系参数 
ZoneWide = 6; 6度带宽 
ProjNo = (int)(X/1000000L) ; //查找带号
longitude0 = (ProjNo-1) * ZoneWide + ZoneWide / 2; 
longitude0 = longitude0 * iPI ; //中央经线
X0 = ProjNo*1000000L+500000L; 
Y0 = 0; 
xval = X-X0; yval = Y-Y0; //带内大地坐标
e2 = 2*f-f*f;
e1 = (1.0-sqrt(1-e2))/(1.0+sqrt(1-e2));
ee = e2/(1-e2);
M = yval;
u = M/(a*(1-e2/4-3*e2*e2/64-5*e2*e2*e2/256));
fai = u+(3*e1/2-27*e1*e1*e1/32)*sin(2*u)+(21*e1*e1/16-55*e1*e1*e1*e1/32)*sin(
4*u)+(151*e1*e1*e1/96)*sin(6*u)+(1097*e1*e1*e1*e1/512)*sin(8*u);
C = ee*cos(fai)*cos(fai);
T = tan(fai)*tan(fai);
NN = a/sqrt(1.0-e2*sin(fai)*sin(fai));
R = a*(1-e2)/sqrt((1-e2*sin(fai)*sin(fai))*(1-e2*sin(fai)*sin(fai))*(1-e2*sin
(fai)*sin(fai)));
D = xval/NN;
//计算经度(Longitude) 纬度(Latitude)
longitude1 = longitude0+(D-(1+2*T+C)*D*D*D/6+(5-2*C+28*T-3*C*C+8*ee+24*T*T)*D
*D*D*D*D/120)/cos(fai);
latitude1 = fai -(NN*tan(fai)/R)*(D*D/2-(5+3*T+10*C-4*C*C-9*ee)*D*D*D*D/24
+(61+90*T+298*C+45*T*T-256*ee-3*C*C)*D*D*D*D*D*D/720); 
//转换为度 DD
*longitude = longitude1 / iPI; 
*latitude = latitude1 / iPI;
}

几个重要参数的意义：

NN卯酉圈曲率半径，测量学里面用N表示 

M为子午线弧长，测量学里用大X表示 

fai为底点纬度，由子午弧长反算公式得到，测量学里用Bf表示

R为底点所对的曲率半径，测量学里用Nf表示