GPS定位（五）-高斯投影正反算C程序

基本思想

斯投影正算公式就是由大地坐标（L，B）求解高斯平面坐标（x，y），而高斯投影反算公式则是由高斯平面坐标（x，y）求解大地坐标（L，B）。

计算模型

高斯投影正算

这里输入的经纬度应该转化为度，而不是度分秒或者度分的格式

int LongLat2XY(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 = 3;////3度带宽
	//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 
	a = 6378137.0; f = 1.0/298.257223563;//WGS84坐标系参数
	//ProjNo = (int)(longitude / ZoneWide) ;      //6度带
	//longitude0 = ProjNo * ZoneWide + ZoneWide / 2; //6度带
	ProjNo = (int)(longitude / ZoneWide+0.5) ; 
       // ProjNo = (int)(longitude / ZoneWide) ; //--带号
	longitude0 = ProjNo * ZoneWide ; //--中央子午线
	longitude0 = longitude0 * iPI ;//--中央子午线转化未弧度
	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*latitude1));
	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; //6度带
	X0 = 1000000L*ProjNo+500000L;  //3度带
	Y0 = 0; 
	xval = xval+X0; yval = yval+Y0; 

	*X= xval;
	*Y= yval;
        printf("%lf   %lf\r\n",xval,yval);
	return 1;
}

高斯投影反算

int XY2LongLat(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
	a = 6378137.0; f = 1.0/298.257223563;//WGS84坐标系参数
	ProjNo = (int)(X/1000000L) ; //查找带号
	// 	ZoneWide = 6; ////6度带宽 
	// 	longitude0 = (ProjNo-1) * ZoneWide + ZoneWide / 2; //计算每带中央子午线经度
	ZoneWide=3;   ////3度带宽
	longitude0 =  ProjNo * ZoneWide;
	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));// 字串1 
	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); 
	int g=0;
	//转换为度 DD
	*longitude = longitude1 / iPI; 
	*latitude = latitude1 / iPI;

	return 1;
}

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