From 7e60cb9b6e6e46019c188a935a97ef0d61d12abd Mon Sep 17 00:00:00 2001 From: asl Date: Fri, 6 Sep 2013 06:52:36 +0000 Subject: [PATCH] implementation of the Lambert coordinates transformation --- src/HYDROData/CMakeLists.txt | 2 + src/HYDROData/HYDROData_Lambert93.cxx | 167 ++++++++++++++++++++++++++ src/HYDROData/HYDROData_Lambert93.h | 22 ++++ 3 files changed, 191 insertions(+) create mode 100755 src/HYDROData/HYDROData_Lambert93.cxx create mode 100755 src/HYDROData/HYDROData_Lambert93.h diff --git a/src/HYDROData/CMakeLists.txt b/src/HYDROData/CMakeLists.txt index 3b9f345a..ba4f85aa 100644 --- a/src/HYDROData/CMakeLists.txt +++ b/src/HYDROData/CMakeLists.txt @@ -5,6 +5,7 @@ set(PROJECT_HEADERS HYDROData_Application.h HYDROData_Bathymetry.h HYDROData_Document.h + HYDROData_Lambert93.h HYDROData_Image.h HYDROData_Iterator.h HYDROData_Object.h @@ -19,6 +20,7 @@ set(PROJECT_SOURCES HYDROData_Document.cxx HYDROData_Image.cxx HYDROData_Iterator.cxx + HYDROData_Lambert93.cxx HYDROData_Object.cxx HYDROData_Polyline.cxx HYDROData_VisualState.cxx diff --git a/src/HYDROData/HYDROData_Lambert93.cxx b/src/HYDROData/HYDROData_Lambert93.cxx new file mode 100755 index 00000000..786eb7e6 --- /dev/null +++ b/src/HYDROData/HYDROData_Lambert93.cxx @@ -0,0 +1,167 @@ + +#include +#include + +// Standard values +const double PI = 3.14159265; + +// Base values of the Lambert-93 +const double a = 6378137; // m -- le demi-grand axe +const double f = 1.0 / 298.257222101; // l'aplatissement + +const double phi_1_deg = 44; // deg -- le premier parallèle d'échelle +const double phi_2_deg = 49; // deg -- le deuxième parallèle d'échell + +const double lambda_0_deg = 3; // deg -- la longitude d'origine donnée par le méridien central de Greenwich +const double phi_0_deg = 46.5; // deg -- la latitude d'origine + +const double X_0 = 700000; // m -- la coordonnée à l'origine +const double Y_0 = 6600000; // m -- la coordonnée à l'origine + +// Derived values of the Lambert-93 +const double b = a * ( 1 - f ); // m -- le demi-petit axe +const double e = sqrt( a*a - b*b ) / a; // l'excentricité + +const double phi_0 = HYDROData_Lambert93::toRad( phi_0_deg ); +const double phi_1 = HYDROData_Lambert93::toRad( phi_1_deg ); +const double phi_2 = HYDROData_Lambert93::toRad( phi_2_deg ); +const double lambda_0 = HYDROData_Lambert93::toRad( lambda_0_deg ); + + +double cot( double x ) +{ + return cos( x ) / sin( x ); +} + +double ln( double x ) +{ + return log( x ); +} + +const double s1 = sin( phi_1 ); +const double s2 = sin( phi_2 ); +const double c1 = cos( phi_1 ); +const double c2 = cos( phi_2 ); + +const double n1 = ln( c2/c1 ) + 1.0/2.0 * ln( (1-e*e*s1*s1)/(1-e*e*s2*s2) ); +const double n2 = tan( phi_1 / 2 + PI/4 ) * pow( 1-e*s1, e/2 ) * pow( 1+e*s2, e/2 ); +const double n3 = tan( phi_2 / 2 + PI/4 ) * pow( 1+e*s1, e/2 ) * pow( 1-e*s2, e/2 ); +const double n = n1 / ( ln( n2/n3 ) ); + +const double p1 = a * c1 / ( n * sqrt( 1-e*e*s1*s1 ) ); +const double p2 = tan( phi_1 / 2 + PI / 4 ); +const double p3 = pow( (1-e*s1)/(1+e*s1), e/2 ); +const double p_0 = p1 * pow( p2*p3, n ); + +double HYDROData_Lambert93::toRad( double theDeg ) +{ + return theDeg * PI / 180.0; +} + +double HYDROData_Lambert93::toDeg( double theRad ) +{ + return theRad / PI * 180.0; +} + +double HYDROData_Lambert93::calc_rho( double phi ) +{ + double c1 = cot( phi/2 + PI/4 ); + double c2 = ( 1 + e * sin( phi ) ) / ( 1 - e * sin( phi ) ); + double rho = p_0 * pow( c1 * pow( c2, e/2 ), n ); + return rho; +} + +void HYDROData_Lambert93::toXY( double theLatitudeDeg, double theLongitudeDeg, + double& theX, double& theY ) +{ + double phi = toRad( theLatitudeDeg ); + double lambda = toRad( theLongitudeDeg ); + + double rho = calc_rho( phi ); + double rho_0 = calc_rho( phi_0 ); + double theta = n * ( lambda - lambda_0 ); + + theX = X_0 + rho * sin( theta ); + theY = Y_0 + rho_0 - rho * cos( theta ); +} + +double arctan( double x ) +{ + return atan( x ); +} + +typedef double (*FUNC)( double ); +double solve( FUNC f, double c, double x1, double x2, double eps ) +{ + double f1 = f( x1 ) - c; + double f2 = f( x2 ) - c; + while( fabs( x1 - x2 ) > eps ) + { + double x = ( x1 + x2 ) / 2; + double fx = f( x ) - c; + bool b1 = f1>=0; + bool b2 = f2>=0; + bool b = fx>=0; + if( b==b1 ) + { + x1 = x; + f1 = fx; + } + else + { + x2 = x; + f2 = fx; + } + } + return ( x1 + x2 ) / 2; +} + +double F( double phi ) +{ + double f1 = tan( phi/2 + PI/4 ); + double f2 = ( 1 - e*sin(phi) ) / ( 1 + e*sin(phi) ); + return f1 * pow( f2, e/2 ); +} + +double Finv( double x, double eps ) +{ + return solve( F, x, 0, PI/2-eps, eps ); +} + +double HYDROData_Lambert93::calc_phi_inv( double rho, double eps ) +{ + double x = pow( p_0 / rho, 1/n ); + double phi = Finv( x, eps ); + return phi; +} + +double HYDROData_Lambert93::calc_phi_ign( double rho, double eps ) +{ + double x = p_0 / rho; + double y = pow( x, 1/n ); + double phi_i_1, phi_i = 2*arctan( y ) - PI/2; + while( true ) + { + phi_i_1 = phi_i; + double z = y * pow( ( 1 + e*sin(phi_i_1) ) / ( 1 - e*sin(phi_i_1) ), e/2 ); + phi_i = 2*arctan( pow( x, 1/n ) * z ) - PI/2; + if( fabs( phi_i - phi_i_1 ) < eps ) + return phi_i; + } + return -1; +} + +void HYDROData_Lambert93::toGeo( double theX, double theY, + double& theLatitudeDeg, double& theLongitudeDeg, + double theEps ) +{ + double rho_0 = calc_rho( phi_0 ); + double rho = sqrt( pow( theX - X_0, 2 ) + pow( Y_0 - theY + rho_0, 2 ) ); + double theta = 2 * arctan( ( theX - X_0 ) / ( Y_0 - theY + rho_0 + rho ) ); + + double lambda = theta / n + lambda_0; + double phi = calc_phi_inv( rho, theEps ); + + theLatitudeDeg = toDeg( phi ); + theLongitudeDeg = toDeg( lambda ); +} diff --git a/src/HYDROData/HYDROData_Lambert93.h b/src/HYDROData/HYDROData_Lambert93.h new file mode 100755 index 00000000..47f08754 --- /dev/null +++ b/src/HYDROData/HYDROData_Lambert93.h @@ -0,0 +1,22 @@ + +#ifndef HYDROData_Lambert93_HeaderFile +#define HYDROData_Lambert93_HeaderFile + +class HYDROData_Lambert93 +{ +public: + static double toRad( double theDeg ); + static double toDeg( double theRad ); + + static void toXY( double theLatitudeDeg, double theLongitudeDeg, + double& theX, double& theY ); + static void toGeo( double theX, double theY, + double& theLatitudeDeg, double& theLongitudeDeg, + double theEps ); +private: + static double calc_rho( double phi ); + static double calc_phi_inv( double rho, double eps ); + static double calc_phi_ign( double rho, double eps ); +}; + +#endif -- 2.39.2