flightgear/Lib/Math/fg_geodesy.cxx

// 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.

--------------------------------------------------------------------------*/