#include <iostream>
#include <math.h>
#include <cstdlib>
#include<bits/stdc++.h>
using namespace std;
typedef struct ANGLE_DEG;
struct ANGLE_DEG
{
double Deg;
double Min;
double Sec;
};
double orthodromie(double Long1, double Lat1, double Long2, double Lat2);
double orthodromie_2(double Long1, double Lat1, double Long2, double Lat2);
double Calcul_Direct(double Long_centre, double Lat_centre , double Lat0, double R_Rech);
void Angle_Rad_Deg(double Ang_Rad, ANGLE_DEG *Angle_Deg);
double Long0_Lat0(double Lat0, double Long_centre, double Lat_centre, double R_Rech);
double Rterre = 6371; // Rayon de la terre en km
// pour 1 minute -> 1 mile marin = 1852.22 metres
double Rterre_Pol = 6356.988; // Rayon polaire de la terre en km
double Rterre_Equa = 6378.388; // Rayon equatorial de la terre en km
// double Rterre_Pol = 6371; // Rayon polaire de la terre en km
//double Rterre_Equa = 6371; // Rayon equatorial de la terre en km
double Pi = 4 * atan(1);
int main(int argc, char *argv[])
{
int Lat_Deg, Lat_Min, Lat_Sec;
int Long_Deg, Long_Min, Long_Sec;
double Lat_centre, Long_centre, Lat0, Lat0_max, Lat0_min;
double R_Rech;
double Phi, Pas_Lat0;
ANGLE_DEG Lat; ANGLE_DEG Long;
int i;
double Lat0_Long0(double Long0, double Long_centre, double Lat_centre, double R_Rech);
/*
// Entrée Latitude
cout << "Latitude du centre de recherche en Degres Minute Seconde \n Entrer Valeur degres ? " << endl;
cin >> Lat_Deg;
cout << "\n Entrer Valeur minutes ? " << endl;
cin >> Lat_Min;
cout << "\n Entrer Valeur secondes ? " << endl;
cin >> Lat_Sec;
cout << "Latitude du centre de recherche = " << Lat_Deg << " Degres " << Lat_Min << " Minutes " << Lat_Sec << "Secondes" << endl;
Lat_centre = Lat_Deg + Lat_Min / 60.0 + Lat_Sec / 3600.0 ;
Lat_centre = Lat_centre * Pi / 180.0; // Conversion en radians
cout << "Latitude du centre de recherche en radians = " << Lat_centre << endl;
// Entrée Longitude
cout << "\n Longitude du centre de recherche en Degres Minute Seconde \n Entrer Valeur degres ? " << endl;
cin >> Long_Deg;
cout << "\n Entrer Valeur minutes ? " << endl;
cin >> Long_Min;
cout << "\n Entrer Valeur secondes ? " << endl;
cin >> Long_Sec;
cout << "Longitude du centre de recherche = " << Long_Deg << " Degres " << Long_Min << " Minutes " << Long_Sec << "Secondes" << endl;
Long_centre = Long_Deg + Long_Min / 60.0 + Long_Sec / 3600.0 ;
Long_centre = Long_centre * Pi / 180.0; // Conversion en radians
cout << "Longitude du centre de recherche en radians = " << Long_centre << endl;
cout << " Entrer la Valeur du rayon de recherche en km \n " << endl;
cin >> R_Rech;
cout << " Rayon de recherche en km \n " << R_Rech << endl;
*/
Long_centre = Pi/20.0;
Lat_centre = Pi/4.0;
R_Rech = 450.0; // en km
// Calcul du rayon de la terre en fonction de Lat_centre
Rterre = sqrt(Rterre_Equa * Rterre_Equa * cos(Lat_centre) * cos(Lat_centre) + Rterre_Pol * Rterre_Pol * sin(Lat_centre)* sin(Lat_centre));
cout << " Rterre equatorial = " << Rterre_Equa << " km" << endl;
cout << " Rterre polaire = " << Rterre_Pol << " km" << endl;
cout << " Rterre calcul = " << Rterre << " km" << endl;
// Calcul Lat0_min et Lat0_max
Phi = R_Rech / Rterre;
cout << " Phi = " << Phi <<endl;
Lat0_max = Lat_centre + Phi;
Lat0_min = Lat_centre - Phi;
cout << setprecision (12) << " Lat_centre = " << Lat_centre <<endl;
cout << setprecision (12) <<" Long_centre = " << Long_centre <<endl;
cout << setprecision (12) << " Lat0_min = " << Lat0_min <<endl;
cout << setprecision (12) << " Lat0_max = " << Lat0_max <<endl;
cout << setprecision (8) << " Rayon de recherche en km = " << R_Rech << " Rayon de recherche en miles = " << R_Rech/1.862 << endl;
cout << " Pi/2 = " << Pi/2.0 <<endl;
if (Lat0_min >= Pi/2.0 || Lat0_max >= Pi/2.0)
{
cout << " CALCUL IMPOSSIBLE Lat0_max >= 90°" << endl;
system ("PAUSE");
}
// Verif
cout << " ORTHO LAT0 MAX = " << orthodromie(Long_centre, Lat_centre,Long_centre, Lat0_max) << endl;
cout << " ORTHO LAT0 MIN = " << orthodromie(Long_centre, Lat_centre,Long_centre, Lat0_min) << endl;
Pas_Lat0 = (Lat0_max - Lat0_min) / 180.0; // en radians 1 degres
cout << " Pas_Lat0 = " << Pas_Lat0 << endl;
Phi = Pas_Lat0 * Pi / 180.0;
cout << " Phi en degres = " << Phi <<endl;
double Lg0, Lg1;
FILE * Fichier;
Fichier = fopen ("Toto.txt", "w+a");
fprintf(Fichier, "%s %f %s \n", " Rterre equatorial = ", Rterre_Equa, " km" );
fprintf(Fichier, "%s %f %s \n", " Rterre polaire = ", Rterre_Pol, " km" );
fprintf(Fichier, "%s %f %s \n", " Rterre calcul = ", Rterre, " km" );
fprintf(Fichier, "%s %12.11f %s %12.11f \n", "Lat_centre = ", Lat_centre, " Long_centre = " , Long_centre);
fprintf(Fichier, "%s %12.11f %s %12.11f \n", "Lat0_min = ", Lat0_min, " Lat0_max = ", Lat0_max);
fprintf(Fichier, "%s %6.2f %s \n\n\n", "Rayon de recherche = ", R_Rech, " km");
for (i = 0; i <= 180; i++)
{
Lat0 = Lat0_min + Pas_Lat0 * i ;
// Methode Dichotomie
Lg0 = Lat0_Long0(Lat0, Long_centre, Lat_centre, R_Rech);
Lg1 = 2 * Long_centre - Lg0;
Angle_Rad_Deg(Lat0, &Lat);
Angle_Rad_Deg(Lg0, &Long);
// fprintf(Fichier, " Lat0 = %12.11f Lg0 = %f Lat0 = %2.0d deg %2.0d ' %2.0d '' Lg0 = %2.0d deg %3.1d ' %3.1d ''\n",
// Lat0, Lg0, int(Lat.Deg),int(Lat.Min), int(Lat.Sec), int(Long.Deg), int(Long.Min), int(Long.Sec));
fprintf(Fichier, "%12.11f %12.11f \n", Lat0, Lg0);
printf( " Methode Dichotomie Lat0 = %12.11f Lg0 = %12.11f Lat0 = %2.0d deg %2.0d ' %2.0d '' Lg0 = %2.0d deg %3.1d ' %3.1d ''\n",
Lat0, Lg0, int(Lat.Deg),int(Lat.Min), int(Lat.Sec), int(Long.Deg), int(Long.Min), int(Long.Sec));
Angle_Rad_Deg(Lat0, &Lat);
Angle_Rad_Deg(Lg1, &Long);
printf( " Methode Dichotomie Lat0 = %12.11f Lg1 = %12.11f Lat0 = %2.0d deg %2.0d ' %2.0d '' Lg1 = %2.0d deg %3.1d ' %3.1d ''\n",
Lat0, Lg1, int(Lat.Deg),int(Lat.Min), int(Lat.Sec), int(Long.Deg), int(Long.Min), int(Long.Sec));
// Methode Directe
Lg0 = Calcul_Direct(Long_centre, Lat_centre , Lat0, R_Rech);
Lg1 = 2 * Long_centre - Lg0;
Angle_Rad_Deg(Lat0, &Lat);
Angle_Rad_Deg(Lg0, &Long);
printf( " Methode directe Lat0 = %12.11f Lg0 = %12.11f Lat0 = %2.0d deg %2.0d ' %2.0d '' Lg0 = %2.0d deg %3.1d ' %3.1d ''\n",
Lat0, Lg0, int(Lat.Deg),int(Lat.Min), int(Lat.Sec), int(Long.Deg), int(Long.Min), int(Long.Sec));
Angle_Rad_Deg(Lat0, &Lat);
Angle_Rad_Deg(Lg1, &Long);
printf( " Methode directe Lat0 = %12.11f Lg0 = %12.11f Lat0 = %2.0d deg %2.0d ' %2.0d '' Lg1 = %2.0d deg %3.1d ' %3.1d ''\n\n",
Lat0, Lg0, int(Lat.Deg),int(Lat.Min), int(Lat.Sec), int(Long.Deg), int(Long.Min), int(Long.Sec));
}
fclose(Fichier);
return 0;
}
//******************************************************************************
// orthodromie
// Calcul la longueur de la route orthonomique entre les points de
// longitude (Long1, Long2) et de latitude (Lat1, Lat2) exprimes en Radians
// orthodromie en km
//******************************************************************************
double orthodromie(double Long1, double Lat1, double Long2, double Lat2)
{
double Corde;
Corde = pow((sin(Long1) * cos(Lat1) - sin(Long2) * cos(Lat2)), 2);
Corde = Corde + pow((cos(Long1) * cos(Lat1) - cos(Long2) * cos(Lat2)),2);
Corde = Corde + pow((sin(Lat1) - sin(Lat2)),2);
Corde = sqrt(Corde);
return( 2.0 * Rterre * (asin(Corde / 2.0)));
}
//******************************************************************************
// orthodromie_2
// Calcul la longueur de la route orthonomique entre les points de
// longitude (Long1, Long2) et de latitude (Lat1, Lat2) exprimes en Radians
// orthodromie en km
// Pour calculer cette distance, on utilise la formule des cosinus de la trigonométrie sphérique.
// Soient Lat1, Lat2 les latitudes de A et B et Long1, Long2 leurs longitudes.
// Pour cela on considère le triangle ABC tel que C soit le pôle nord.
// Les cotés du triangle sont a (complémentaire de Lat1 pour A), b (complémentaire de Long2 pour B),
// et l'angle γ du triangle en C vaut Long2 − Long2 (différence des longitudes).
// L'arc AB vaut :
// c = arccos[sin(la).sin(lb) + cos(la).cos(lb).cos(LB − LA)]
// Si on exprime c en radian, la distance entre A et B est dAB = R.c km (R est le rayon terrestre moyen).
double orthodromie_2(double Long1, double Lat1, double Long2, double Lat2)
{
double c ;
c = acos(sin(Lat1) * sin(Lat2) + (cos(Lat1) * cos(Lat2) * cos(Long2 - Long1)));
return( Rterre * c);
}
// Calcul Direct : Inversion de orthodromie_2
double Calcul_Direct(double Long_centre, double Lat_centre , double Lat0, double R_Rech)
{
double c, Lg0;
c = R_Rech / Rterre;
Lg0 = Long_centre + acos(( cos(c) - sin(Lat_centre) * sin(Lat0)) / (cos(Lat_centre) * cos(Lat0)));
return Lg0;
}
// Transformation des angles de radians en degres minute seconde
void Angle_Rad_Deg(double Angle_Rad, ANGLE_DEG *Angle_Deg)
{
Angle_Deg-> Deg = Angle_Rad * 180.0/Pi;
Angle_Deg-> Min = (Angle_Deg -> Deg - int(Angle_Deg -> Deg)) * 60.0 ;
Angle_Deg-> Sec = (Angle_Deg-> Min - int(Angle_Deg-> Min)) * 60.0;
}
double Lat0_Long0(double Lat0, double Long_centre, double Lat_centre, double R_Rech)
//**********************************************************************************************************
// Renvoie la longitude Long0 en fonction de la latitude Lat0 et des coordonées du centre de recherches :
// (Long_centre, Lat_centre en radians) et du Rayon de recherche en km Methode par dichotomie
//**********************************************************************************************************
{
int i;
double Ortho0 = 0.0;
double Epsilon = 0.000000001; // précision du calcul
double Pas = R_Rech /100.0; // Valeur initiale du pas
double Long0_1;
double Long_Depart = Long_centre ;
T10:
for ( i = 0; i < 50; i++)
{
Long0_1 = Long_Depart + Pas * i;
Ortho0 = orthodromie(Long0_1, Lat0, Long_centre, Lat_centre);
if(abs(Ortho0 - R_Rech )<= Epsilon)
{
return ( Long0_1);
}
if ((Ortho0 - R_Rech) >= 0)
{
Long_Depart = Long0_1 - Pas;
Pas = Pas /2.0;
// system ("PAUSE");
goto T10;
}
else
{
Long_Depart = Long0_1 + Pas;
Pas = Pas /2.0;
// system ("PAUSE");
goto T10;
}
}
}
Rterre equatorial = 6378.388000 km
Rterre polaire = 6356.988000 km
Rterre calcul = 6367.696990 km
Lat_centre = 0.78539816340 Long_centre = 0.15707963268
Lat0_min = 0.71472897158 Lat0_max = 0.85606735521
Rayon de recherche = 450.00 km
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