高斯投影的正算反算C++源代码
一、 设计目的：
加深理解高斯—克吕格投影的实质，掌握高斯—克吕格投影直角坐标的运用，理解通用坐标和自然坐标值的关系。
二、 设计内容：
1、编程实现由经纬度到直角坐标的转换；
2、正确计算点所在的分度带；
3、准确计算出点的通用坐标值。
三、 方法与步骤：
1、理解公式中每个字母的含义；
2、编程。
3、编程的程序如下：
// 高斯投影正反算公式.cpp : Defines the entry point for the console application.
//#include "iostream.h"
#include "math.h"
int main(int argc, char* argv[])
{
int n,a,d,c;
int L[4],B[4],C[3],D[3],L0;
double l,N,a0,a4,a6,a3,a5,x,y,BB,P,b,Z,Bf,b2,b3,b4,b5,Nf,LL,xx,yy;
cout<<"1----正算(L,B-->x,y) 2----反算(x,y-->L,B)"<<endl;
cout<<"请选择正算（1）或反算（2）:"<<endl;
cin>>n;
/////////////////正算
if(n==1)
{
cout<<"请按顺序输入L,B:"<<endl;
cout<<"输入L(度,分,秒):"<<endl;
cin>>L[1]>>L[2]>>L[3];
cout<<"请输入B(度,分,秒):"<<endl;
cin>>B[1]>>B[2]>>B[3];
BB=3.141592654*(B[1]+B[2]/60.0+B[3]/3600.0)/180;
P=3.141592654*(B[1]*3600+B[2]*60+B[3])/(180*3600);
////////////////计算点所在投影带的中央子午线
L[0]=6*(int((L[1]+L[2]/60.0+L[3]/3600.0)/6)+1)-3;
cout<<"点所在投影带的中央子午线为:"<<endl;
cout<<L[0]<<"度"<<endl;
l=3.141592654*(L[1]+L[2]/60.0+L[3]/3600-L[0])/180;
N=6399698.902-(21562.267-(108.973-0.612*cos(BB)*cos(BB))*cos(BB)*cos(BB))*cos(BB)*cos(BB);
a0=32140.404-(135.3302-(0.7092-0.0040*cos(BB)*cos(BB))*cos(BB)*cos(BB))*cos(BB)*cos(BB);
a4=(0.25+0.00252*cos(BB)*cos(BB))*cos(BB)*cos(BB)-0.04166;
a6=(0.166*cos(BB)*cos(BB)-0.084)*cos(BB)*cos(BB);
a3=(0.3333333+0.001123*cos(BB)*cos(BB))*cos(BB)*cos(BB)-0.1666667;
a5=0.0083-(0.1667-(0.1968+0.0040*cos(BB)*cos(BB))*cos(BB)*cos(BB))*cos(BB)*cos(BB);
///////////代号计算
a=L[0]/6+1;
d=L[0]-1.5;
c=d/3+1;///////////////计算坐标
x=6367558.4969*P-(a0-(0.5+(a4+a6*l*l)*l*l)*l*l*N)*sin(BB)*cos(BB);
y=(1+(a3+a5*l*l)*l*l)*l*N*cos(BB);
/////////////格式控制
cout.setf(ios::fixed);
cout.setf(ios::showpoint);
cout.precision(3);
cout<<"正算结果为:"<<endl;
cout<<"平面坐标:"<<endl;
cout<<"x="<<x<<endl;
cout<<"y="<<y<<endl;
cout<<"分度带号为："<<endl;
cout<<"辣度带号为："<<a<<endl;
cout<<"三度带号为："<<c<<endl;
cout<<"通用坐标为（米）："<<endl;
cout<<"x="<<x<<endl;
cout<<"y="<<y+500000<<endl; //通用坐标计算
}
else if(n==2) /////////////////////反算
{
cout<<"请依次输入坐标x,y(m):"<<endl;
cin>>xx>>yy;
cout<<"请输入点所在投影带的中央子午线(度):"<<endl;
cin>>L0;
b=xx/6367558.4969;
Bf=b+(50221746+(293622+(2350+22*cos(b)*cos(b))*cos(b)*cos(b))*cos(b)*cos(b))*(1.0E-10)*sin(b)*cos(b);
Nf=6399698.902-(21562.267-(108.973-0.612*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf);
Z=yy/(Nf*cos(Bf));
b2=(0.5+0.00336975*cos(Bf)*cos(Bf))*sin(Bf)*cos(Bf);
b3=0.333333-(0.1666667-0.001123*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf);
b4=0.25+(0.161612+0.005617*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf);
b5=0.2-(0.1667-0.00878*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf);
BB=Bf*3600*180/3.141592654-(1-(b4-0.147*Z*Z)*Z*Z)*Z*Z*b2*180*3600/3.141592654;
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C[1]=int((BB-C[0]*3600)/60);
C[2]=int(BB-C[0]*3600-C[1]*60);
cout<<"B="<<C[0]<<"度"<<C[1]<<"分"<<C[2]<<"秒"<<endl;
D[0]=int(LL/3600);
D[1]=int((LL-D[0]*3600)/60);
D[2]=int(LL-D[0]*3600-D[1]*60);
cout<<"L="<<D[0]<<"度"<<D[1]<<"分"<<D[2]<<"秒"<<endl;
}
return 0;
}四、成果：
1、程序运行结果如下图：1260