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#include <HYDROData_Lambert93.h>
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#include <math.h>
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// Standard values
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const double PI = 3.14159265;
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// Base values of the Lambert-93
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const double a = 6378137; // m -- le demi-grand axe
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const double f = 1.0 / 298.257222101; // l'aplatissement
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const double phi_1_deg = 44; // deg -- le premier parallèle d'échelle
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const double phi_2_deg = 49; // deg -- le deuxième parallèle d'échell
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const double lambda_0_deg = 3; // deg -- la longitude d'origine donnée par le méridien central de Greenwich
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const double phi_0_deg = 46.5; // deg -- la latitude d'origine
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const double X_0 = 700000; // m -- la coordonnée à l'origine
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const double Y_0 = 6600000; // m -- la coordonnée à l'origine
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// Derived values of the Lambert-93
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const double b = a * ( 1 - f ); // m -- le demi-petit axe
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const double e = sqrt( a*a - b*b ) / a; // l'excentricité
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const double phi_0 = HYDROData_Lambert93::toRad( phi_0_deg );
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const double phi_1 = HYDROData_Lambert93::toRad( phi_1_deg );
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const double phi_2 = HYDROData_Lambert93::toRad( phi_2_deg );
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const double lambda_0 = HYDROData_Lambert93::toRad( lambda_0_deg );
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double cot( double x )
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{
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return cos( x ) / sin( x );
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}
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double ln( double x )
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{
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return log( x );
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}
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const double s1 = sin( phi_1 );
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const double s2 = sin( phi_2 );
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const double c1 = cos( phi_1 );
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const double c2 = cos( phi_2 );
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const double n1 = ln( c2/c1 ) + 1.0/2.0 * ln( (1-e*e*s1*s1)/(1-e*e*s2*s2) );
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const double n2 = tan( phi_1 / 2 + PI/4 ) * pow( 1-e*s1, e/2 ) * pow( 1+e*s2, e/2 );
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const double n3 = tan( phi_2 / 2 + PI/4 ) * pow( 1+e*s1, e/2 ) * pow( 1-e*s2, e/2 );
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const double n = n1 / ( ln( n2/n3 ) );
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const double p1 = a * c1 / ( n * sqrt( 1-e*e*s1*s1 ) );
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const double p2 = tan( phi_1 / 2 + PI / 4 );
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const double p3 = pow( (1-e*s1)/(1+e*s1), e/2 );
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const double p_0 = p1 * pow( p2*p3, n );
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double HYDROData_Lambert93::toRad( double theDeg )
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{
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return theDeg * PI / 180.0;
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}
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double HYDROData_Lambert93::toDeg( double theRad )
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{
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return theRad / PI * 180.0;
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}
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double HYDROData_Lambert93::calc_rho( double phi )
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{
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double c1 = cot( phi/2 + PI/4 );
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double c2 = ( 1 + e * sin( phi ) ) / ( 1 - e * sin( phi ) );
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double rho = p_0 * pow( c1 * pow( c2, e/2 ), n );
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return rho;
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}
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void HYDROData_Lambert93::toXY( double theLatitudeDeg, double theLongitudeDeg,
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double& theX, double& theY )
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{
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double phi = toRad( theLatitudeDeg );
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double lambda = toRad( theLongitudeDeg );
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double rho = calc_rho( phi );
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double rho_0 = calc_rho( phi_0 );
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double theta = n * ( lambda - lambda_0 );
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theX = X_0 + rho * sin( theta );
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theY = Y_0 + rho_0 - rho * cos( theta );
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}
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double arctan( double x )
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{
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return atan( x );
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}
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typedef double (*FUNC)( double );
double solve( FUNC f, double c, double x1, double x2, double eps )
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{
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double f1 = f( x1 ) - c;
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double f2 = f( x2 ) - c;
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while( fabs( x1 - x2 ) > eps )
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{
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double x = ( x1 + x2 ) / 2;
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double fx = f( x ) - c;
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bool b1 = f1>=0;
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bool b2 = f2>=0;
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bool b = fx>=0;
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if( b==b1 )
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{
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x1 = x;
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f1 = fx;
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}
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else
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{
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x2 = x;
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f2 = fx;
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}
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}
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return ( x1 + x2 ) / 2;
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}
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double F( double phi )
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{
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double f1 = tan( phi/2 + PI/4 );
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double f2 = ( 1 - e*sin(phi) ) / ( 1 + e*sin(phi) );
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return f1 * pow( f2, e/2 );
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}
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double Finv( double x, double eps )
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{
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return solve( F, x, 0, PI/2-eps, eps );
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}
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double HYDROData_Lambert93::calc_phi_inv( double rho, double eps )
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{
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double x = pow( p_0 / rho, 1/n );
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double phi = Finv( x, eps );
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return phi;
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}
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double HYDROData_Lambert93::calc_phi_ign( double rho, double eps )
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{
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double x = p_0 / rho;
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double y = pow( x, 1/n );
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double phi_i_1, phi_i = 2*arctan( y ) - PI/2;
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while( true )
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{
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phi_i_1 = phi_i;
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double z = y * pow( ( 1 + e*sin(phi_i_1) ) / ( 1 - e*sin(phi_i_1) ), e/2 );
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phi_i = 2*arctan( pow( x, 1/n ) * z ) - PI/2;
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if( fabs( phi_i - phi_i_1 ) < eps )
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return phi_i;
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}
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return -1;
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}
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void HYDROData_Lambert93::toGeo( double theX, double theY,
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- double& theLatitudeDeg, double& theLongitudeDeg,
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- double theEps )
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+ double& theLatitudeDeg, double& theLongitudeDeg,
+ double theEps )
{
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double rho_0 = calc_rho( phi_0 );
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double rho = sqrt( pow( theX - X_0, 2 ) + pow( Y_0 - theY + rho_0, 2 ) );
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double theta = 2 * arctan( ( theX - X_0 ) / ( Y_0 - theY + rho_0 + rho ) );
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double lambda = theta / n + lambda_0;
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double phi = calc_phi_inv( rho, theEps );
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theLatitudeDeg = toDeg( phi );
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theLongitudeDeg = toDeg( lambda );
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}
void HYDROData_Lambert93::DMSToDeg( int theDeg,
