491 lines
15 KiB
C++
491 lines
15 KiB
C++
// sg_geodesy.cxx -- routines to convert between geodetic and geocentric
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// coordinate systems.
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//
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// Copied and adapted directly from LaRCsim/ls_geodesy.c
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//
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// See below for the complete original LaRCsim comments.
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//
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// $Id$
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#include <simgear/compiler.h>
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#ifdef SG_HAVE_STD_INCLUDES
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# include <cmath>
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# include <cerrno>
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# include <cstdio>
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#else
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# include <math.h>
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# include <errno.h>
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# include <stdio.h>
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#endif
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#include <simgear/constants.h>
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#include <simgear/debug/logstream.hxx>
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#include "point3d.hxx"
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#include "sg_geodesy.hxx"
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#include "localconsts.hxx"
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SG_USING_STD(cout);
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// #define DOMAIN_ERR_DEBUG 1
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// sgGeocToGeod(lat_geoc, radius, *lat_geod, *alt, *sea_level_r)
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// INPUTS:
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// lat_geoc Geocentric latitude, radians, + = North
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// radius C.G. radius to earth center (meters)
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//
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// OUTPUTS:
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// lat_geod Geodetic latitude, radians, + = North
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// alt C.G. altitude above mean sea level (meters)
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// sea_level_r radius from earth center to sea level at
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// local vertical (surface normal) of C.G. (meters)
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void sgGeocToGeod( const double& lat_geoc, const double& radius,
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double *lat_geod, double *alt, double *sea_level_r )
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{
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#ifdef DOMAIN_ERR_DEBUG
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errno = 0; // start with error zero'd
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#endif
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double t_lat, x_alpha, mu_alpha, delt_mu, r_alpha, l_point, rho_alpha;
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double sin_mu_a, denom,delt_lambda, lambda_sl, sin_lambda_sl;
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if( ( (SGD_PI_2 - lat_geoc) < SG_ONE_SECOND ) // near North pole
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|| ( (SGD_PI_2 + lat_geoc) < SG_ONE_SECOND ) ) // near South pole
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{
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*lat_geod = lat_geoc;
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*sea_level_r = SG_EQUATORIAL_RADIUS_M*E;
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*alt = radius - *sea_level_r;
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} else {
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// cout << " lat_geoc = " << lat_geoc << endl;
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t_lat = tan(lat_geoc);
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// cout << " tan(t_lat) = " << t_lat << endl;
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x_alpha = E*SG_EQUATORIAL_RADIUS_M/sqrt(t_lat*t_lat + E*E);
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#ifdef DOMAIN_ERR_DEBUG
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if ( errno ) {
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perror("fgGeocToGeod()");
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SG_LOG( SG_GENERAL, SG_ALERT, "sqrt(" << t_lat*t_lat + E*E << ")" );
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}
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#endif
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// cout << " x_alpha = " << x_alpha << endl;
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double tmp = sqrt(SG_EQ_RAD_SQUARE_M - x_alpha * x_alpha);
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if ( tmp < 0.0 ) { tmp = 0.0; }
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#ifdef DOMAIN_ERR_DEBUG
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if ( errno ) {
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perror("fgGeocToGeod()");
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SG_LOG( SG_GENERAL, SG_ALERT, "sqrt(" << SG_EQ_RAD_SQUARE_M - x_alpha * x_alpha
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<< ")" );
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}
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#endif
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mu_alpha = atan2(tmp,E*x_alpha);
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if (lat_geoc < 0) mu_alpha = - mu_alpha;
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sin_mu_a = sin(mu_alpha);
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delt_lambda = mu_alpha - lat_geoc;
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r_alpha = x_alpha/cos(lat_geoc);
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l_point = radius - r_alpha;
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*alt = l_point*cos(delt_lambda);
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denom = sqrt(1-EPS*EPS*sin_mu_a*sin_mu_a);
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#ifdef DOMAIN_ERR_DEBUG
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if ( errno ) {
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perror("fgGeocToGeod()");
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SG_LOG( SG_GENERAL, SG_ALERT, "sqrt(" <<
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1-EPS*EPS*sin_mu_a*sin_mu_a << ")" );
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}
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#endif
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rho_alpha = SG_EQUATORIAL_RADIUS_M*(1-EPS)/
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(denom*denom*denom);
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delt_mu = atan2(l_point*sin(delt_lambda),rho_alpha + *alt);
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*lat_geod = mu_alpha - delt_mu;
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lambda_sl = atan( E*E * tan(*lat_geod) ); // SL geoc. latitude
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sin_lambda_sl = sin( lambda_sl );
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*sea_level_r =
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sqrt(SG_EQ_RAD_SQUARE_M / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl));
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#ifdef DOMAIN_ERR_DEBUG
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if ( errno ) {
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perror("fgGeocToGeod()");
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SG_LOG( SG_GENERAL, SG_ALERT, "sqrt(" <<
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SG_EQ_RAD_SQUARE_M / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl)
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<< ")" );
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}
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#endif
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}
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}
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// sgGeodToGeoc( lat_geod, alt, *sl_radius, *lat_geoc )
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// INPUTS:
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// lat_geod Geodetic latitude, radians, + = North
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// alt C.G. altitude above mean sea level (meters)
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//
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// OUTPUTS:
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// sl_radius SEA LEVEL radius to earth center (meters)
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// (add Altitude to get true distance from earth center.
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// lat_geoc Geocentric latitude, radians, + = North
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//
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void sgGeodToGeoc( const double& lat_geod, const double& alt, double *sl_radius,
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double *lat_geoc )
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{
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double lambda_sl, sin_lambda_sl, cos_lambda_sl, sin_mu, cos_mu, px, py;
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#ifdef DOMAIN_ERR_DEBUG
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errno = 0;
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#endif
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lambda_sl = atan( E*E * tan(lat_geod) ); // sea level geocentric latitude
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sin_lambda_sl = sin( lambda_sl );
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cos_lambda_sl = cos( lambda_sl );
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sin_mu = sin(lat_geod); // Geodetic (map makers') latitude
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cos_mu = cos(lat_geod);
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*sl_radius =
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sqrt(SG_EQ_RAD_SQUARE_M / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl));
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#ifdef DOMAIN_ERR_DEBUG
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if ( errno ) {
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perror("fgGeodToGeoc()");
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SG_LOG( SG_GENERAL, SG_ALERT, "sqrt(" <<
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SG_EQ_RAD_SQUARE_M / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl)
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<< ")" );
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}
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#endif
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py = *sl_radius*sin_lambda_sl + alt*sin_mu;
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px = *sl_radius*cos_lambda_sl + alt*cos_mu;
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*lat_geoc = atan2( py, px );
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}
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// Direct and inverse distance functions
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//
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// Proceedings of the 7th International Symposium on Geodetic
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// Computations, 1985
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//
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// "The Nested Coefficient Method for Accurate Solutions of Direct and
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// Inverse Geodetic Problems With Any Length"
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//
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// Zhang Xue-Lian
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// pp 747-763
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//
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// modified for FlightGear to use WGS84 only -- Norman Vine
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#define GEOD_INV_PI SGD_PI
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// s == distance
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// az = azimuth
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// for WGS_84 a = 6378137.000, rf = 298.257223563;
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static inline double M0( double e2 ) {
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//double e4 = e2*e2;
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return GEOD_INV_PI*(1.0 - e2*( 1.0/4.0 + e2*( 3.0/64.0 +
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e2*(5.0/256.0) )))/2.0;
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}
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// given, alt, lat1, lon1, az1 and distance (s), calculate lat2, lon2
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// and az2. Lat, lon, and azimuth are in degrees. distance in meters
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int geo_direct_wgs_84 ( const double& alt, const double& lat1,
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const double& lon1, const double& az1,
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const double& s, double *lat2, double *lon2,
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double *az2 )
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{
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double a = 6378137.000, rf = 298.257223563;
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double RADDEG = (GEOD_INV_PI)/180.0, testv = 1.0E-10;
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double f = ( rf > 0.0 ? 1.0/rf : 0.0 );
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double b = a*(1.0-f);
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double e2 = f*(2.0-f);
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double phi1 = lat1*RADDEG, lam1 = lon1*RADDEG;
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double sinphi1 = sin(phi1), cosphi1 = cos(phi1);
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double azm1 = az1*RADDEG;
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double sinaz1 = sin(azm1), cosaz1 = cos(azm1);
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if( fabs(s) < 0.01 ) { // distance < centimeter => congruency
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*lat2 = lat1;
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*lon2 = lon1;
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*az2 = 180.0 + az1;
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if( *az2 > 360.0 ) *az2 -= 360.0;
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return 0;
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} else if( cosphi1 ) { // non-polar origin
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// u1 is reduced latitude
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double tanu1 = sqrt(1.0-e2)*sinphi1/cosphi1;
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double sig1 = atan2(tanu1,cosaz1);
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double cosu1 = 1.0/sqrt( 1.0 + tanu1*tanu1 ), sinu1 = tanu1*cosu1;
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double sinaz = cosu1*sinaz1, cos2saz = 1.0-sinaz*sinaz;
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double us = cos2saz*e2/(1.0-e2);
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// Terms
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double ta = 1.0+us*(4096.0+us*(-768.0+us*(320.0-175.0*us)))/16384.0,
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tb = us*(256.0+us*(-128.0+us*(74.0-47.0*us)))/1024.0,
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tc = 0;
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// FIRST ESTIMATE OF SIGMA (SIG)
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double first = s/(b*ta); // !!
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double sig = first;
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double c2sigm, sinsig,cossig, temp,denom,rnumer, dlams, dlam;
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do {
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c2sigm = cos(2.0*sig1+sig);
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sinsig = sin(sig); cossig = cos(sig);
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temp = sig;
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sig = first +
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tb*sinsig*(c2sigm+tb*(cossig*(-1.0+2.0*c2sigm*c2sigm) -
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tb*c2sigm*(-3.0+4.0*sinsig*sinsig)
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*(-3.0+4.0*c2sigm*c2sigm)/6.0)
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/4.0);
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} while( fabs(sig-temp) > testv);
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// LATITUDE OF POINT 2
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// DENOMINATOR IN 2 PARTS (TEMP ALSO USED LATER)
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temp = sinu1*sinsig-cosu1*cossig*cosaz1;
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denom = (1.0-f)*sqrt(sinaz*sinaz+temp*temp);
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// NUMERATOR
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rnumer = sinu1*cossig+cosu1*sinsig*cosaz1;
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*lat2 = atan2(rnumer,denom)/RADDEG;
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// DIFFERENCE IN LONGITUDE ON AUXILARY SPHERE (DLAMS )
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rnumer = sinsig*sinaz1;
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denom = cosu1*cossig-sinu1*sinsig*cosaz1;
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dlams = atan2(rnumer,denom);
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// TERM C
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tc = f*cos2saz*(4.0+f*(4.0-3.0*cos2saz))/16.0;
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// DIFFERENCE IN LONGITUDE
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dlam = dlams-(1.0-tc)*f*sinaz*(sig+tc*sinsig*
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(c2sigm+
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tc*cossig*(-1.0+2.0*
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c2sigm*c2sigm)));
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*lon2 = (lam1+dlam)/RADDEG;
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if (*lon2 > 180.0 ) *lon2 -= 360.0;
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if (*lon2 < -180.0 ) *lon2 += 360.0;
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// AZIMUTH - FROM NORTH
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*az2 = atan2(-sinaz,temp)/RADDEG;
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if ( fabs(*az2) < testv ) *az2 = 0.0;
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if( *az2 < 0.0) *az2 += 360.0;
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return 0;
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} else { // phi1 == 90 degrees, polar origin
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double dM = a*M0(e2) - s;
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double paz = ( phi1 < 0.0 ? 180.0 : 0.0 );
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double zero = 0.0f;
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return geo_direct_wgs_84( alt, zero, lon1, paz, dM, lat2, lon2, az2 );
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}
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}
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// given alt, lat1, lon1, lat2, lon2, calculate starting and ending
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// az1, az2 and distance (s). Lat, lon, and azimuth are in degrees.
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// distance in meters
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int geo_inverse_wgs_84( const double& alt, const double& lat1,
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const double& lon1, const double& lat2,
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const double& lon2, double *az1, double *az2,
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double *s )
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{
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double a = 6378137.000, rf = 298.257223563;
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int iter=0;
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double RADDEG = (GEOD_INV_PI)/180.0, testv = 1.0E-10;
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double f = ( rf > 0.0 ? 1.0/rf : 0.0 );
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double b = a*(1.0-f);
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// double e2 = f*(2.0-f); // unused in this routine
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double phi1 = lat1*RADDEG, lam1 = lon1*RADDEG;
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double sinphi1 = sin(phi1), cosphi1 = cos(phi1);
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double phi2 = lat2*RADDEG, lam2 = lon2*RADDEG;
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double sinphi2 = sin(phi2), cosphi2 = cos(phi2);
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if( (fabs(lat1-lat2) < testv &&
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( fabs(lon1-lon2) < testv) || fabs(lat1-90.0) < testv ) )
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{
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// TWO STATIONS ARE IDENTICAL : SET DISTANCE & AZIMUTHS TO ZERO */
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*az1 = 0.0; *az2 = 0.0; *s = 0.0;
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return 0;
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} else if( fabs(cosphi1) < testv ) {
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// initial point is polar
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int k = geo_inverse_wgs_84( alt, lat2,lon2,lat1,lon1, az1,az2,s );
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k = k; // avoid compiler error since return result is unused
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b = *az1; *az1 = *az2; *az2 = b;
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return 0;
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} else if( fabs(cosphi2) < testv ) {
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// terminal point is polar
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double _lon1 = lon1 + 180.0f;
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int k = geo_inverse_wgs_84( alt, lat1, lon1, lat1, _lon1,
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az1, az2, s );
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k = k; // avoid compiler error since return result is unused
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*s /= 2.0;
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*az2 = *az1 + 180.0;
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if( *az2 > 360.0 ) *az2 -= 360.0;
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return 0;
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} else if( (fabs( fabs(lon1-lon2) - 180 ) < testv) &&
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(fabs(lat1+lat2) < testv) )
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{
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// Geodesic passes through the pole (antipodal)
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double s1,s2;
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geo_inverse_wgs_84( alt, lat1,lon1, lat1,lon2, az1,az2, &s1 );
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geo_inverse_wgs_84( alt, lat2,lon2, lat1,lon2, az1,az2, &s2 );
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*az2 = *az1;
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*s = s1 + s2;
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return 0;
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} else {
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// antipodal and polar points don't get here
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double dlam = lam2 - lam1, dlams = dlam;
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double sdlams,cdlams, sig,sinsig,cossig, sinaz,
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cos2saz, c2sigm;
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double tc,temp, us,rnumer,denom, ta,tb;
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double cosu1,sinu1, sinu2,cosu2;
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// Reduced latitudes
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temp = (1.0-f)*sinphi1/cosphi1;
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cosu1 = 1.0/sqrt(1.0+temp*temp);
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sinu1 = temp*cosu1;
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temp = (1.0-f)*sinphi2/cosphi2;
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cosu2 = 1.0/sqrt(1.0+temp*temp);
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sinu2 = temp*cosu2;
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do {
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sdlams = sin(dlams), cdlams = cos(dlams);
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sinsig = sqrt(cosu2*cosu2*sdlams*sdlams+
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(cosu1*sinu2-sinu1*cosu2*cdlams)*
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(cosu1*sinu2-sinu1*cosu2*cdlams));
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cossig = sinu1*sinu2+cosu1*cosu2*cdlams;
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sig = atan2(sinsig,cossig);
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sinaz = cosu1*cosu2*sdlams/sinsig;
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cos2saz = 1.0-sinaz*sinaz;
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c2sigm = (sinu1 == 0.0 || sinu2 == 0.0 ? cossig :
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cossig-2.0*sinu1*sinu2/cos2saz);
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tc = f*cos2saz*(4.0+f*(4.0-3.0*cos2saz))/16.0;
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temp = dlams;
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dlams = dlam+(1.0-tc)*f*sinaz*
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(sig+tc*sinsig*
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(c2sigm+tc*cossig*(-1.0+2.0*c2sigm*c2sigm)));
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if (fabs(dlams) > GEOD_INV_PI && iter++ > 50) {
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return iter;
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}
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} while ( fabs(temp-dlams) > testv);
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us = cos2saz*(a*a-b*b)/(b*b); // !!
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// BACK AZIMUTH FROM NORTH
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rnumer = -(cosu1*sdlams);
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denom = sinu1*cosu2-cosu1*sinu2*cdlams;
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*az2 = atan2(rnumer,denom)/RADDEG;
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if( fabs(*az2) < testv ) *az2 = 0.0;
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if(*az2 < 0.0) *az2 += 360.0;
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// FORWARD AZIMUTH FROM NORTH
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rnumer = cosu2*sdlams;
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denom = cosu1*sinu2-sinu1*cosu2*cdlams;
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*az1 = atan2(rnumer,denom)/RADDEG;
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if( fabs(*az1) < testv ) *az1 = 0.0;
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if(*az1 < 0.0) *az1 += 360.0;
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// Terms a & b
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ta = 1.0+us*(4096.0+us*(-768.0+us*(320.0-175.0*us)))/
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16384.0;
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tb = us*(256.0+us*(-128.0+us*(74.0-47.0*us)))/1024.0;
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// GEODETIC DISTANCE
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*s = b*ta*(sig-tb*sinsig*
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(c2sigm+tb*(cossig*(-1.0+2.0*c2sigm*c2sigm)-tb*
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c2sigm*(-3.0+4.0*sinsig*sinsig)*
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(-3.0+4.0*c2sigm*c2sigm)/6.0)/
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4.0));
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return 0;
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}
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}
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/***************************************************************************
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TITLE: ls_geodesy
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----------------------------------------------------------------------------
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FUNCTION: Converts geocentric coordinates to geodetic positions
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----------------------------------------------------------------------------
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MODULE STATUS: developmental
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----------------------------------------------------------------------------
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GENEALOGY: Written as part of LaRCSim project by E. B. Jackson
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----------------------------------------------------------------------------
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DESIGNED BY: E. B. Jackson
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CODED BY: E. B. Jackson
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MAINTAINED BY: E. B. Jackson
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----------------------------------------------------------------------------
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MODIFICATION HISTORY:
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DATE PURPOSE BY
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930208 Modified to avoid singularity near polar region. EBJ
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930602 Moved backwards calcs here from ls_step. EBJ
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931214 Changed erroneous Latitude and Altitude variables to
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*lat_geod and *alt in routine ls_geoc_to_geod. EBJ
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940111 Changed header files from old ls_eom.h style to ls_types,
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and ls_constants. Also replaced old DATA type with new
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SCALAR type. EBJ
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CURRENT RCS HEADER:
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$Header$
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* Revision 1.5 1994/01/11 18:47:05 bjax
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* Changed include files to use types and constants, not ls_eom.h
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* Also changed DATA type to SCALAR type.
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*
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* Revision 1.4 1993/12/14 21:06:47 bjax
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* Removed global variable references Altitude and Latitude. EBJ
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*
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* Revision 1.3 1993/06/02 15:03:40 bjax
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* Made new subroutine for calculating geodetic to geocentric; changed name
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* of forward conversion routine from ls_geodesy to ls_geoc_to_geod.
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*
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----------------------------------------------------------------------------
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REFERENCES:
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[ 1] Stevens, Brian L.; and Lewis, Frank L.: "Aircraft
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Control and Simulation", Wiley and Sons, 1992.
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ISBN 0-471-61397-5
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----------------------------------------------------------------------------
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CALLED BY: ls_aux
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----------------------------------------------------------------------------
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CALLS TO:
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----------------------------------------------------------------------------
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INPUTS:
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lat_geoc Geocentric latitude, radians, + = North
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radius C.G. radius to earth center, ft
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----------------------------------------------------------------------------
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OUTPUTS:
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lat_geod Geodetic latitude, radians, + = North
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alt C.G. altitude above mean sea level, ft
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sea_level_r radius from earth center to sea level at
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local vertical (surface normal) of C.G.
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--------------------------------------------------------------------------*/
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