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O2/30+(4*K2+5)*M2-L2)*O2/12+1)*N2*I2*O2/2
计算结果X
T2
=((((L2-18)*L2-(58*L2-14)*K2+5)*O2/20+M2-L2)*O2/6+1)*N2*(H2*J2)
计算结果Y
表中公式的来源及EXCEL软件的操作方法，请参阅有关资料，这里不再赘述。按上面表格中的公式输入到相应单元格后，就可方便地由经纬度求得平面直角坐标。当输入完所有的经纬度后，用鼠标下拉即可得到所有的计算结果。表中的许多单元格公式为中间过程，可以用EXCEL的列隐藏功能把这些没有必要显示的列隐藏起来，表面上形成标准的计算报表，使整个计算表简单明了。从理论上讲，可计算的数据量是无限的，当第一次输入公式后，相当于自己完成了一软件的编制，可另存起来供今后重复使用，一劳永逸。
二、GPS坐标转换方法与面积计算
GPS所采用的坐标系是美国国防部1984世界坐标系，简称WGS-84，它是一个协议地球参考系，坐标系原点在地球质心。GPS的测量结果与我国的54 系或80系坐标相差几十米至一百多米，随区域不同，差别也不同，经粗落统计，我国西部相差70米左右，东北部140米左右，南部75米左右，中部45米左右。由此可见，必须将WGS-84坐标进行坐标系转换才能供标图使用。坐标系之间的转换一般采用七参数法或三参数法，其中七参数为X平移、Y平移、Z平移、X旋转、Y旋转、Z旋转以及尺度比参数，若忽略旋转参数和尺度比参数则为三参数方法，三参数法为七参数法的特例。这里的Z、Y、Z是空间大地直角坐标系坐标，为转换过程的中间值。在实际工作中我们常用的是平面直角坐标，是否可以跳过空间直角坐标系，省略复杂的运算，进行简单转换呢？为此，笔者进行了长期的实践，证明是可行的。其在原理是：不把GPS所测定的WGS-84坐标当作WGS-84坐标，而是当作具有一定系统性误差的54系坐标值，然后通过国家已知点纠正，消除该系统误差。我们暂把该方法称作坐标改正法，下面以WGS-84坐标转换成54系坐标为例，介绍数据处理方法：
首先，在测区附近选择一国家已知点，在该已知点上用GPS测定WGPS-84坐标系经纬度B和L，把此坐标视为有误差的54系坐标，利用54系EXCEL将经纬度BL转换成平面直角坐标X’Y’，然后与已知坐标比较则可计算出偏移量：
△X=X－X’
△Y=Y－Y’
式中的X、Y为国家控制点的已知坐标，X’、Y’为测定坐标，△X和△Y为偏移量。
求得偏移量后，就可以用此偏移量纠正测区内的其他测量点了。把其他GPS测量点的经纬度测量值，转换成平面坐标X’Y’，在此XY坐标值上直接加上偏移值就得到了转换后的54系坐标：
X=X’+△X
Y=Y’+△Y
在上述EXCEL计算表的最后两列，附加上求得的改正数并分别与计算出来的XY相加后，即得到转换结果。若测量路线是一闭合区域的话，可把计算结果按路线顺序排列起来，再输入相应的计算公式，即可计算出该区域的面积。有关用坐标计算面积的原理与公式，这里不再叙述，读者可参阅有关资料。需要说明的是，面积的计算精度基本上不受坐标转换精度的影响，若只需要求算面积的话，可不进行坐标系转换这一步，只需要把BL化成XY就行了。
就1：1万比例尺成图而言，在一般的县行政区范围内（如40Km×40Km），用此简单的坐标改正法进行转换与较复杂的七参数法没有多大差别。能否满足 1：1万比例尺变更调查的要求，主要取决于GPS接收机本身的精度，与转换方法的选择关系不大。当面积较大时，使用该方法可能会使误差增大，这时可考虑分区域转换。
#include <windows.h>
#include <math.h>
#include <stdio.h>
#include "CoorTrans.h"
////////////////////////////////////////////
// Common functions
////////////////////////////////////////////
double Dms2Rad(double Dms)
{
double Degree, Miniute;
double Second;
int Sign;
double Rad;
if(Dms >= 0)
Sign = 1;
else
Sign = -1;
Dms = fabs(Dms);
Degree = floor(Dms);
Miniute = floor(fmod(Dms * 100.0, 100.0));
Second = fmod(Dms * 10000.0, 100.0);
Rad = Sign * (Degree + Miniute / 60.0 + Second / 3600.0) * PI / 180.0;
return Rad;
}
double Rad2Dms(double Rad)
{
double Degree, Miniute;
double Second;
int Sign;
double Dms;
if(Rad >= 0)
Sign = 1;
else
Sign = -1;
Rad = fabs(Rad * 180.0 / PI);
Degree = floor(Rad);
Miniute = floor(fmod(Rad * 60.0, 60.0));
Second = fmod(Rad * 3600.0, 60.0);
Dms = Sign * (Degree + Miniute / 100.0 + Second / 10000.0);
return Dms;
}
///////////////////////////////////////////////////
// Definition of PrjPoint
///////////////////////////////////////////////////
BOOL PrjPoint::BL2xy()
{
double X, N, t, t2, m, m2, ng2;
double sinB, cosB;
X = A1 * B * 180.0 / PI + A2 * sin(2 * B) + A3 * sin(4 * B) + A4 * sin(6 *
B);
sinB = sin(B);
cosB = cos(B);
t = tan(B);
t2 = t * t;
N = a / sqrt(1 - e2 * sinB * sinB);
m = cosB * (L - L0);
m2 = m * m;
ng2 = cosB * cosB * e2 / (1 - e2);
x = X + N * t * ((0.5 + ((5 - t2 + 9 * ng2 + 4 * ng2 * ng2) / 24.0 + (61 -
58 * t2 + t2 * t2) * m2 / 720.0) * m2) * m2);
y = N * m * ( 1 + m2 * ( (1 - t2 + ng2) / 6.0 + m2 * ( 5 - 18 * t2 + t2 * t
2 + 14 * ng2 - 58 * ng2 * t2 ) / 120.0));
y += 500000;
return TRUE;
}
BOOL PrjPoint::xy2BL()
{
double sinB, cosB, t, t2, N ,ng2, V, yN;
double preB0, B0;
double eta;
y -= 500000;
B0 = x / A1;
do
{
preB0 = B0;
B0 = B0 * PI / 180.0;
B0 = (x - (A2 * sin(2 * B0) + A3 * sin(4 * B0) + A4 * sin(6 * B0))) / A1;
eta = fabs(B0 - preB0);
}while(eta > 0.000000001);
B0 = B0 * PI / 180.0;
B = Rad2Dms(B0);
sinB = sin(B0);
cosB = cos(B0);
t = tan(B0);
t2 = t * t;
N = a / sqrt(1 - e2 * sinB * sinB);
ng2 = cosB * cosB * e2 / (1 - e2);
V = sqrt(1 + ng2);
yN = y / N;
B = B0 - (yN * yN - (5 + 3 * t2 + ng2 - 9 * ng2 * t2) * yN * yN * yN * yN /
12.0 + (61 + 90 * t2 + 45 * t2 * t2) * yN * yN * yN * yN * yN * yN / 360.0)
* V * V * t / 2;
L = L0 + (yN - (1 + 2 * t2 + ng2) * yN * yN * yN / 6.0 + (5 + 28 * t2 + 24
* t2 * t2 + 6 * ng2 + 8 * ng2 * t2) * yN * yN * yN * yN * yN / 120.0) / cosB
;
return TRUE;
}
BOOL PrjPoint::SetL0(double dL0)
{
L0 = Dms2Rad(dL0);
return TRUE;
}
BOOL PrjPoint::SetBL(double dB, double dL)
{
B = Dms2Rad(dB);
L = Dms2Rad(dL);
B = dB;
L = dL;
BL2xy();
return TRUE;
}
BOOL PrjPoint::GetBL(double *dB, double *dL)
{
*dB = Rad2Dms(B);
*dL = Rad2Dms(L);
return TRUE;
}
BOOL PrjPoint::Setxy(double dx, double dy)
{
x = dx;
y = dy;
xy2BL();
return TRUE;
}
BOOL PrjPoint::Getxy(double *dx, double *dy)
{
*dx = x;
*dy = y;
return TRUE;
}
///////////////////////////////////////////////////
// Definition of PrjPoint_IUGG1975
///////////////////////////////////////////////////
PrjPoint_IUGG1975::PrjPoint_IUGG1975()
{
a = 6378140;
f = 298.257;
e2 = 1 - ((f - 1) / f) * ((f - 1) / f);
e12 = (f / (f - 1)) * (f / (f - 1)) - 1;
A1 = 111133.0047;
A2 = -16038.5282;
A3 = 16.8326;
A4 = -0.0220;
}
PrjPoint_IUGG1975::~PrjPoint_IUGG1975()
{
}
///////////////////////////////////////////////////
// Definition of PrjPoint_Krasovsky
///////////////////////////////////////////////////
PrjPoint_Krasovsky::PrjPoint_Krasovsky()
{
a = 6378245;
f = 298.3;
e2 = 1 - ((f - 1) / f) * ((f - 1) / f);
e12 = (f / (f - 1)) * (f / (f - 1)) - 1;
A1 = 111134.8611;
A2 = -16036.4803;
A3 = 16.8281;
A4 = -0.0220;
}
PrjPoint_Krasovsky::~PrjPoint_Krasovsky()
{
}
转载： 高斯投影变换_cpp
#include
#include
#include
#include "CoorTrans.h"
////////////////////////////////////////////
// Common functions
////////////////////////////////////////////
double Dms2Rad(double Dms)
{
double Degree, Miniute;
double Second;
int Sign;
double Rad;
if(Dms >= 0)
Sign = 1;
else
Sign = -1;
Dms = fabs(Dms);
Degree = floor(Dms);
Miniute = floor(fmod(Dms * 100.0, 100.0));
Second = fmod(Dms * 10000.0, 100.0);
Rad = Sign * (Degree + Miniute / 60.0 + Second / 3600.0) * PI / 180.0;
return Rad;
}
double Rad2Dms(double Rad)
{
double Degree, Miniute;
double Second;
int Sign;
double Dms;
if(Rad >= 0)
Sign = 1;
else
Sign = -1;
Rad = fabs(Rad * 180.0 / PI);
Degree = floor(Rad);
Miniute = floor(fmod(Rad * 60.0, 60.0));
Second = fmod(Rad * 3600.0, 60.0);
Dms = Sign * (Degree + Miniute / 100.0 + Second / 10000.0);
return Dms;
}
///////////////////////////////////////////////////
// Definition of PrjPoint
///////////////////////////////////////////////////
BOOL PrjPoint::BL2xy()
{
double X, N, t, t2, m, m2, ng2;
double sinB, cosB;
X = A1 * B * 180.0 / PI + A2 * sin(2 * B) + A3 * sin(4 * B) + A4 * sin(6 *
B);
sinB = sin(B);
cosB = cos(B);
t = tan(B);
t2 = t * t;
N = a / sqrt(1 - e2 * sinB * sinB);
m = cosB * (L - L0);
m2 = m * m;
ng2 = cosB * cosB * e2 / (1 - e2);
x = X + N * t * ((0.5 + ((5 - t2 + 9 * ng2 + 4 * ng2 * ng2) / 24.0 + (61 -
58 * t2 + t2 * t2) * m2 / 720.0) * m2) * m2);
y = N * m * ( 1 + m2 * ( (1 - t2 + ng2) / 6.0 + m2 * ( 5 - 18 * t2 + t2 * t
2 + 14 * ng2 - 58 * ng2 * t2 ) / 120.0));
y += 500000;
return TRUE;
}
BOOL PrjPoint::xy2BL()
{
double sinB, cosB, t, t2, N ,ng2, V, yN;
double preB0, B0;
double eta;
y -= 500000;
B0 = x / A1;
do
{
preB0 = B0;
B0 = B0 * PI / 180.0;
B0 = (x - (A2 * sin(2 * B0) + A3 * sin(4 * B0) + A4 * sin(6 * B0))) / A1;
eta = fabs(B0 - preB0);
}while(eta > 0.000000001);
B0 = B0 * PI / 180.0;
B = Rad2Dms(B0);
sinB = sin(B0);
cosB = cos(B0);
t = tan(B0);
t2 = t * t;
N = a / sqrt(1 - e2 * sinB * sinB);
ng2 = cosB * cosB * e2 / (1 - e2);
V = sqrt(1 + ng2);
yN = y / N;
B = B0 - (yN * yN - (5 + 3 * t2 + ng2 - 9 * ng2 * t2) * yN * yN * yN * yN /
12.0 + (61 + 90 * t2 + 45 * t2 * t2) * yN * yN * yN * yN * yN * yN / 360.0)
* V * V * t / 2;
L = L0 + (yN - (1 + 2 * t2 + ng2) * yN * yN * yN / 6.0 + (5 + 28 * t2 + 24
* t2 * t2 + 6 * ng2 + 8 * ng2 * t2) * yN * yN * yN * yN * yN / 120.0) / cosB
;
return TRUE;
}
BOOL PrjPoint::SetL0(double dL0)
{
L0 = Dms2Rad(dL0);
return TRUE;
}
BOOL PrjPoint::SetBL(double dB, double dL)
{
B = Dms2Rad(dB);
L = Dms2Rad(dL);
B = dB;
L = dL;
BL2xy();
return TRUE;
}
BOOL PrjPoint::GetBL(double *dB, double *dL)
{
*dB = Rad2Dms(B);
*dL = Rad2Dms(L);
return TRUE;
}
BOOL PrjPoint::Setxy(double dx, double dy)
{
x = dx;
y = dy;
xy2BL();
return TRUE;
}
BOOL PrjPoint::Getxy(double *dx, double *dy)
{
*dx = x;
*dy = y;
return TRUE;
}
///////////////////////////////////////////////////
// Definition of PrjPoint_IUGG1975
///////////////////////////////////////////////////
PrjPoint_IUGG1975::PrjPoint_IUGG1975()
{
a = 6378140;
f = 298.257;
e2 = 1 - ((f - 1) / f) * ((f - 1) / f);
e12 = (f / (f - 1)) * (f / (f - 1)) - 1;
A1 = 111133.0047;
A2 = -16038.5282;
A3 = 16.8326;
A4 = -0.0220;
}
PrjPoint_IUGG1975::~PrjPoint_IUGG1975()
{
}
///////////////////////////////////////////////////
// Definition of PrjPoint_Krasovsky
///////////////////////////////////////////////////
PrjPoint_Krasovsky::PrjPoint_Krasovsky()
{
a = 6378245;
f = 298.3;
e2 = 1 - ((f - 1) / f) * ((f - 1) / f);
e12 = (f / (f - 1)) * (f / (f - 1)) - 1;
A1 = 111134.8611;
A2 = -16036.4803;
A3 = 16.8281;
A4 = -0.0220;
}
PrjPoint_Krasovsky::~PrjPoint_Krasovsky()
{
}
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