// fg_geodesy.cxx -- routines to convert between geodetic and geocentric
// coordinate systems.
//
// Copied and adapted directly from LaRCsim/ls_geodesy.c
//
// See below for the complete original LaRCsim comments.
//
// $Id$
#include "Include/compiler.h"
#ifdef FG_HAVE_STD_INCLUDES
# include <cmath>
# include <cerrno>
#else
# include <math.h>
# include <errno.h>
#endif
#include <Include/fg_constants.h>
#include <Math/fg_geodesy.hxx>
#include <Math/point3d.hxx>
#ifndef FG_HAVE_NATIVE_SGI_COMPILERS
FG_USING_STD(cout);
#endif
// ONE_SECOND is pi/180/60/60, or about 100 feet at earths' equator
#define ONE_SECOND 4.848136811E-6
// fgGeocToGeod(lat_geoc, radius, *lat_geod, *alt, *sea_level_r)
// INPUTS:
// lat_geoc Geocentric latitude, radians, + = North
// radius C.G. radius to earth center (meters)
//
// OUTPUTS:
// lat_geod Geodetic latitude, radians, + = North
// alt C.G. altitude above mean sea level (meters)
// sea_level_r radius from earth center to sea level at
// local vertical (surface normal) of C.G. (meters)
void fgGeocToGeod( double lat_geoc, double radius, double
*lat_geod, double *alt, double *sea_level_r )
{
double t_lat, x_alpha, mu_alpha, delt_mu, r_alpha, l_point, rho_alpha;
double sin_mu_a, denom,delt_lambda, lambda_sl, sin_lambda_sl;
if( ( (FG_PI_2 - lat_geoc) < ONE_SECOND ) // near North pole
|| ( (FG_PI_2 + lat_geoc) < ONE_SECOND ) ) // near South pole
{
*lat_geod = lat_geoc;
*sea_level_r = EQUATORIAL_RADIUS_M*E;
*alt = radius - *sea_level_r;
} else {
t_lat = tan(lat_geoc);
x_alpha = E*EQUATORIAL_RADIUS_M/sqrt(t_lat*t_lat + E*E);
double tmp = RESQ_M - x_alpha * x_alpha;
if ( tmp < 0.0 ) { tmp = 0.0; }
mu_alpha = atan2(sqrt(tmp),E*x_alpha);
if (lat_geoc < 0) mu_alpha = - mu_alpha;
sin_mu_a = sin(mu_alpha);
delt_lambda = mu_alpha - lat_geoc;
r_alpha = x_alpha/cos(lat_geoc);
l_point = radius - r_alpha;
*alt = l_point*cos(delt_lambda);
// check for domain error
if ( errno == EDOM ) {
cout << "Domain ERROR in fgGeocToGeod!!!!\n";
*alt = 0.0;
}
denom = sqrt(1-EPS*EPS*sin_mu_a*sin_mu_a);
rho_alpha = EQUATORIAL_RADIUS_M*(1-EPS)/
(denom*denom*denom);
delt_mu = atan2(l_point*sin(delt_lambda),rho_alpha + *alt);
*lat_geod = mu_alpha - delt_mu;
lambda_sl = atan( E*E * tan(*lat_geod) ); // SL geoc. latitude
sin_lambda_sl = sin( lambda_sl );
*sea_level_r =
sqrt(RESQ_M / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl));
// check for domain error
if ( errno == EDOM ) {
cout << "Domain ERROR in fgGeocToGeod!!!!\n";
*sea_level_r = 0.0;
}
}
}
// fgGeodToGeoc( lat_geod, alt, *sl_radius, *lat_geoc )
// INPUTS:
// lat_geod Geodetic latitude, radians, + = North
// alt C.G. altitude above mean sea level (meters)
//
// OUTPUTS:
// sl_radius SEA LEVEL radius to earth center (meters)
// (add Altitude to get true distance from earth center.
// lat_geoc Geocentric latitude, radians, + = North
//
void fgGeodToGeoc( double lat_geod, double alt, double *sl_radius,
double *lat_geoc )
{
double lambda_sl, sin_lambda_sl, cos_lambda_sl, sin_mu, cos_mu, px, py;
lambda_sl = atan( E*E * tan(lat_geod) ); // sea level geocentric latitude
sin_lambda_sl = sin( lambda_sl );
cos_lambda_sl = cos( lambda_sl );
sin_mu = sin(lat_geod); // Geodetic (map makers') latitude
cos_mu = cos(lat_geod);
*sl_radius =
sqrt(RESQ_M / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl));
py = *sl_radius*sin_lambda_sl + alt*sin_mu;
px = *sl_radius*cos_lambda_sl + alt*cos_mu;
*lat_geoc = atan2( py, px );
}
/***************************************************************************
TITLE: ls_geodesy
----------------------------------------------------------------------------
FUNCTION: Converts geocentric coordinates to geodetic positions
----------------------------------------------------------------------------
MODULE STATUS: developmental
----------------------------------------------------------------------------
GENEALOGY: Written as part of LaRCSim project by E. B. Jackson
----------------------------------------------------------------------------
DESIGNED BY: E. B. Jackson
CODED BY: E. B. Jackson
MAINTAINED BY: E. B. Jackson
----------------------------------------------------------------------------
MODIFICATION HISTORY:
DATE PURPOSE BY
930208 Modified to avoid singularity near polar region. EBJ
930602 Moved backwards calcs here from ls_step. EBJ
931214 Changed erroneous Latitude and Altitude variables to
*lat_geod and *alt in routine ls_geoc_to_geod. EBJ
940111 Changed header files from old ls_eom.h style to ls_types,
and ls_constants. Also replaced old DATA type with new
SCALAR type. EBJ
CURRENT RCS HEADER:
$Header$
* Revision 1.5 1994/01/11 18:47:05 bjax
* Changed include files to use types and constants, not ls_eom.h
* Also changed DATA type to SCALAR type.
*
* Revision 1.4 1993/12/14 21:06:47 bjax
* Removed global variable references Altitude and Latitude. EBJ
*
* Revision 1.3 1993/06/02 15:03:40 bjax
* Made new subroutine for calculating geodetic to geocentric; changed name
* of forward conversion routine from ls_geodesy to ls_geoc_to_geod.
*
----------------------------------------------------------------------------
REFERENCES:
[ 1] Stevens, Brian L.; and Lewis, Frank L.: "Aircraft
Control and Simulation", Wiley and Sons, 1992.
ISBN 0-471-61397-5
----------------------------------------------------------------------------
CALLED BY: ls_aux
----------------------------------------------------------------------------
CALLS TO:
----------------------------------------------------------------------------
INPUTS:
lat_geoc Geocentric latitude, radians, + = North
radius C.G. radius to earth center, ft
----------------------------------------------------------------------------
OUTPUTS:
lat_geod Geodetic latitude, radians, + = North
alt C.G. altitude above mean sea level, ft
sea_level_r radius from earth center to sea level at
local vertical (surface normal) of C.G.
--------------------------------------------------------------------------*/