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komasaru/blh2enu.cpp

Last active Jun 11, 2021
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C++ source code to convert a coordinate from WGS84(BLH) to ENU.
/***********************************************************
BLH -> ENU 変換
: WGS84 の緯度(Beta)/経度(Lambda)/楕円体高(Height)を
ENU (East/North/Up; 地平) 座標に変換する。
* 途中、 ECEF(Earth Centered Earth Fixed; 地球中心・地
球固定直交座標系)座標への変換を経由。
DATE AUTHOR VERSION
2021.05.06 mk-mode.com 1.00 新規作成
Copyright(C) 2021 mk-mode.com All Rights Reserved.
----------------------------------------------------------
引数 : B_0 L_0 H_0 B_1 L_1 H_1
* B_0, L_0, H_0: 基準の BLH(WGS84) 座標
* B_1, L_1, H_1: 対象の BLH(WGS84) 座標
----------------------------------------------------------
$ g++102 -std=c++17 -Wall -O2 --pedantic-errors -o blh2enu blh2enu.cpp
***********************************************************/
#include <cmath>
#include <cstdlib> // for EXIT_XXXX
#include <iomanip>
#include <iostream>
#include <vector>
namespace blh2enu {
// 定数
static constexpr double kPi = atan(1.0) * 4.0;
static constexpr double kPi180 = kPi / 180;
// [ WGS84 座標パラメータ ]
// a(地球楕円体長半径(赤道面平均半径))
static constexpr double kA = 6378137.0;
// 1 / f(地球楕円体扁平率=(a - b) / a)
static constexpr double k1F = 298.257223563;
// b(地球楕円体短半径)
static constexpr double kB = kA * (1.0 - 1.0 / k1F);
// e^2 = 2 * f - f * f
// = (a^2 - b^2) / a^2
static constexpr double kE2 = (1.0 / k1F) * (2.0 - (1.0 / k1F));
// e'^2= (a^2 - b^2) / b^2
static constexpr double kEd2 = kE2 * kA * kA / (kB * kB);
// 座標
struct CoordB {
double b; // B(Beta)
double l; // L(Lambda)
double h; // H(Height)
};
struct CoordX {
double x; // X
double y; // Y
double z; // Z
};
struct CoordE {
double e; // E(East)
double n; // N(North)
double u; // U(Up)
};
/*
* @brief x 軸を軸とした回転行列
*
* @param[in] 回転量(°) (double)
* @return 回転行列(3x3) (vector<vector<double>>)
*/
std::vector<std::vector<double>> mat_x(double ang) {
double a;
double c;
double s;
std::vector<std::vector<double>> mat(3, std::vector<double>(3, 0.0));
try {
a = ang * kPi180;
c = cos(a);
s = sin(a);
mat[0][0] = 1.0;
mat[1][1] = c;
mat[1][2] = s;
mat[2][1] = -s;
mat[2][2] = c;
} catch (...) {
throw;
}
return mat;
}
/*
* @brief y 軸を軸とした回転行列
*
* @param[in] 回転量(°) (double)
* @return 回転行列(3x3) (vector<vector<double>>)
*/
std::vector<std::vector<double>> mat_y(double ang) {
double a;
double c;
double s;
std::vector<std::vector<double>> mat(3, std::vector<double>(3, 0.0));
try {
a = ang * kPi180;
c = cos(a);
s = sin(a);
mat[0][0] = c;
mat[0][2] = -s;
mat[1][1] = 1.0;
mat[2][0] = s;
mat[2][2] = c;
} catch (...) {
throw;
}
return mat;
}
/*
* @brief z 軸を軸とした回転行列
*
* @param[in] 回転量(°) (double)
* @return 回転行列(3x3) (vector<vector<double>>)
*/
std::vector<std::vector<double>> mat_z(double ang) {
double a;
double c;
double s;
std::vector<std::vector<double>> mat(3, std::vector<double>(3, 0.0));
try {
a = ang * kPi180;
c = cos(a);
s = sin(a);
mat[0][0] = c;
mat[0][1] = s;
mat[1][0] = -s;
mat[1][1] = c;
mat[2][2] = 1.0;
} catch (...) {
throw;
}
return mat;
}
/*
* @brief 2行列(3x3)の積
*
* @param[in] 元の 3x3 行列 (vector<vector<double>>)
* @param[in] 元の 3x3 行列 (vector<vector<double>>)
* @return 計算後の 3x3 行列 (vector<vector<double>>)
*/
std::vector<std::vector<double>> mul_mat(
std::vector<std::vector<double>> mat_a,
std::vector<std::vector<double>> mat_b) {
unsigned int i;
unsigned int j;
unsigned int k;
std::vector<std::vector<double>> mat(3, std::vector<double>(3, 0.0));
try {
for (i = 0; i < 3; ++i) {
for (j = 0; j < 3; ++j) {
for (k = 0; k < 3; ++k) {
mat[i][j] += mat_a[i][k] * mat_b[k][j];
}
}
}
} catch (...) {
throw;
}
return mat;
}
/*
* @brief 座標の回転
*
* @param[in] 3x3 回転行列 (vector<vector<double>>)
* @param[in] 回転前座標 (CoordX)
* @return 回転後座標 (CoordE)
*/
CoordE rotate(std::vector<std::vector<double>> mat_r, CoordX pt_0) {
CoordE pt;
try {
pt.e = mat_r[0][0] * pt_0.x
+ mat_r[0][1] * pt_0.y
+ mat_r[0][2] * pt_0.z;
pt.n = mat_r[1][0] * pt_0.x
+ mat_r[1][1] * pt_0.y
+ mat_r[1][2] * pt_0.z;
pt.u = mat_r[2][0] * pt_0.x
+ mat_r[2][1] * pt_0.y
+ mat_r[2][2] * pt_0.z;
} catch (...) {
throw;
}
return pt;
}
/*
* @brief 関数 N
*
* @param[in] X (double)
* @return 計算結果 (double)
*/
double n(double x) {
double res;
try {
res = kA / sqrt(1.0 - kE2 * pow(sin(x * kPi180), 2));
} catch (...) {
throw;
}
return res;
}
/*
* @brief BLH -> ECEF
*
* @param[in] BLH 座標 (CoordB)
* @return ECEF 座標 (CoordX)
*/
CoordX blh2ecef(CoordB c_src) {
CoordX ecef;
try {
ecef.x = (n(c_src.b) + c_src.h)
* cos(c_src.b * kPi180)
* cos(c_src.l * kPi180);
ecef.y = (n(c_src.b) + c_src.h)
* cos(c_src.b * kPi180)
* sin(c_src.l * kPi180);
ecef.z = (n(c_src.b) * (1.0 - kE2) + c_src.h)
* sin(c_src.b * kPi180);
} catch (...) {
throw;
}
return ecef;
}
/*
* @brief BLH -> ENU
*
* @param[in] BLH 座標(基準) (CoordB)
* @param[in] BLH 座標(対象) (CoordB)
* @return ENU 座標 (CoordE)
*/
CoordE blh2enu(CoordB c_0, CoordB c_1) {
CoordX ecef_x_0;
CoordX ecef_x_1;
CoordX ecef_x;
std::vector<std::vector<double>> mat_0(3, std::vector<double>(3, 0.0));
std::vector<std::vector<double>> mat_1(3, std::vector<double>(3, 0.0));
std::vector<std::vector<double>> mat_2(3, std::vector<double>(3, 0.0));
std::vector<std::vector<double>> mat;
CoordE enu;
try {
// BLH -> ECEF
ecef_x_0 = blh2ecef(c_0);
ecef_x_1 = blh2ecef(c_1);
ecef_x = {ecef_x_1.x - ecef_x_0.x,
ecef_x_1.y - ecef_x_0.y,
ecef_x_1.z - ecef_x_0.z};
// 回転行列生成
mat_0 = mat_z(90.0);
mat_1 = mat_y(90.0 - c_0.b);
mat_2 = mat_z(c_0.l);
mat = mul_mat(mul_mat(mat_0, mat_1), mat_2);
enu = rotate(mat, ecef_x);
} catch (...) {
throw;
}
return enu;
}
} // namespace blh2enu
int main(int argc, char* argv[]) {
namespace ns = blh2enu;
ns::CoordB blh_0; // 変換前の座標(基準)
ns::CoordB blh_1; // 変換前の座標(対象)
ns::CoordE enu; // 変換後の座標
double az; // 方位角
double el; // 仰角
double dst; // 距離
try {
// コマンドライン引数の個数チェック
if (argc < 7) {
std::cout << "Usage: ./blh2enu B_0 L_0 H_0 B_1 L_1 H_1" << std::endl;
return EXIT_SUCCESS;
}
// 基準、対象の BLH(WGS84) 座標取得
blh_0.b = std::stod(argv[1]);
blh_0.l = std::stod(argv[2]);
blh_0.h = std::stod(argv[3]);
blh_1.b = std::stod(argv[4]);
blh_1.l = std::stod(argv[5]);
blh_1.h = std::stod(argv[6]);
// BLH -> ENU
enu = ns::blh2enu(blh_0, blh_1);
// 方位角、仰角、距離
az = atan2(enu.e, enu.n) / ns::kPi180;
if (az < 0.0) { az += 360.0; }
el = atan2(enu.u, sqrt(enu.e * enu.e + enu.n * enu.n)) / ns::kPi180;
dst = 0;
dst += enu.e * enu.e;
dst += enu.n * enu.n;
dst += enu.u * enu.u;
dst = sqrt(dst);
// 結果出力
std::cout << std::fixed << std::setprecision(8);
std::cout << "BLH_0: LATITUDE(BETA) = "
<< std::setw(12) << blh_0.b << " °" << std::endl;
std::cout << " LONGITUDE(LAMBDA) = "
<< std::setw(12) << blh_0.l << " °" << std::endl;
std::cout << std::fixed << std::setprecision(3);
std::cout << " HEIGHT = "
<< std::setw(7) << blh_0.h << " m" << std::endl;
std::cout << std::fixed << std::setprecision(8);
std::cout << "BLH: LATITUDE(BETA) = "
<< std::setw(12) << blh_1.b << " °" << std::endl;
std::cout << " LONGITUDE(LAMBDA) = "
<< std::setw(12) << blh_1.l << " °" << std::endl;
std::cout << std::fixed << std::setprecision(3);
std::cout << " HEIGHT = "
<< std::setw(7) << blh_1.h << " m" << std::endl;
std::cout << "-->" << std::endl;
std::cout << "ENU: E = "
<< std::setw(12) << enu.e << " m" << std::endl;
std::cout << " N = "
<< std::setw(12) << enu.n << " m" << std::endl;
std::cout << " U = "
<< std::setw(12) << enu.u << " m" << std::endl;
std::cout << "方位角 = "
<< std::setw(12) << az << " °" << std::endl;
std::cout << " 仰角 = "
<< std::setw(12) << el << " °" << std::endl;
std::cout << " 距離 = "
<< std::setw(12) << dst << " m" << std::endl;
} catch (...) {
std::cerr << "EXCEPTION!" << std::endl;
return EXIT_FAILURE;
}
return EXIT_SUCCESS;
}
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