1 // sg_geodesy.cxx -- routines to convert between geodetic and geocentric
4 // Copied and adapted directly from LaRCsim/ls_geodesy.c
6 // See below for the complete original LaRCsim comments.
10 #include <simgear/compiler.h>
12 #ifdef SG_HAVE_STD_INCLUDES
22 #include <simgear/constants.h>
23 #include <simgear/debug/logstream.hxx>
25 #include "point3d.hxx"
26 #include "sg_geodesy.hxx"
27 #include "localconsts.hxx"
30 #ifndef SG_HAVE_NATIVE_SGI_COMPILERS
34 // ONE_SECOND is pi/180/60/60, or about 100 feet at earths' equator
35 #define ONE_SECOND 4.848136811E-6
38 #define DOMAIN_ERR_DEBUG 1
41 // sgGeocToGeod(lat_geoc, radius, *lat_geod, *alt, *sea_level_r)
43 // lat_geoc Geocentric latitude, radians, + = North
44 // radius C.G. radius to earth center (meters)
47 // lat_geod Geodetic latitude, radians, + = North
48 // alt C.G. altitude above mean sea level (meters)
49 // sea_level_r radius from earth center to sea level at
50 // local vertical (surface normal) of C.G. (meters)
53 void sgGeocToGeod( double lat_geoc, double radius, double
54 *lat_geod, double *alt, double *sea_level_r )
56 #ifdef DOMAIN_ERR_DEBUG
57 errno = 0; // start with error zero'd
60 double t_lat, x_alpha, mu_alpha, delt_mu, r_alpha, l_point, rho_alpha;
61 double sin_mu_a, denom,delt_lambda, lambda_sl, sin_lambda_sl;
63 if( ( (SG_PI_2 - lat_geoc) < ONE_SECOND ) // near North pole
64 || ( (SG_PI_2 + lat_geoc) < ONE_SECOND ) ) // near South pole
67 *sea_level_r = EQUATORIAL_RADIUS_M*E;
68 *alt = radius - *sea_level_r;
70 // cout << " lat_geoc = " << lat_geoc << endl;
71 t_lat = tan(lat_geoc);
72 // cout << " tan(t_lat) = " << t_lat << endl;
73 x_alpha = E*EQUATORIAL_RADIUS_M/sqrt(t_lat*t_lat + E*E);
74 #ifdef DOMAIN_ERR_DEBUG
76 perror("fgGeocToGeod()");
77 FG_LOG( FG_GENERAL, FG_ALERT, "sqrt(" << t_lat*t_lat + E*E << ")" );
80 // cout << " x_alpha = " << x_alpha << endl;
81 double tmp = sqrt(RESQ_M - x_alpha * x_alpha);
82 if ( tmp < 0.0 ) { tmp = 0.0; }
83 #ifdef DOMAIN_ERR_DEBUG
85 perror("fgGeocToGeod()");
86 FG_LOG( FG_GENERAL, FG_ALERT, "sqrt(" << RESQ_M - x_alpha * x_alpha
90 mu_alpha = atan2(tmp,E*x_alpha);
91 if (lat_geoc < 0) mu_alpha = - mu_alpha;
92 sin_mu_a = sin(mu_alpha);
93 delt_lambda = mu_alpha - lat_geoc;
94 r_alpha = x_alpha/cos(lat_geoc);
95 l_point = radius - r_alpha;
96 *alt = l_point*cos(delt_lambda);
98 denom = sqrt(1-EPS*EPS*sin_mu_a*sin_mu_a);
99 #ifdef DOMAIN_ERR_DEBUG
101 perror("fgGeocToGeod()");
102 FG_LOG( FG_GENERAL, FG_ALERT, "sqrt(" <<
103 1-EPS*EPS*sin_mu_a*sin_mu_a << ")" );
106 rho_alpha = EQUATORIAL_RADIUS_M*(1-EPS)/
108 delt_mu = atan2(l_point*sin(delt_lambda),rho_alpha + *alt);
109 *lat_geod = mu_alpha - delt_mu;
110 lambda_sl = atan( E*E * tan(*lat_geod) ); // SL geoc. latitude
111 sin_lambda_sl = sin( lambda_sl );
113 sqrt(RESQ_M / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl));
114 #ifdef DOMAIN_ERR_DEBUG
116 perror("fgGeocToGeod()");
117 FG_LOG( FG_GENERAL, FG_ALERT, "sqrt(" <<
118 RESQ_M / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl)
128 // sgGeodToGeoc( lat_geod, alt, *sl_radius, *lat_geoc )
130 // lat_geod Geodetic latitude, radians, + = North
131 // alt C.G. altitude above mean sea level (meters)
134 // sl_radius SEA LEVEL radius to earth center (meters)
135 // (add Altitude to get true distance from earth center.
136 // lat_geoc Geocentric latitude, radians, + = North
140 void sgGeodToGeoc( double lat_geod, double alt, double *sl_radius,
143 double lambda_sl, sin_lambda_sl, cos_lambda_sl, sin_mu, cos_mu, px, py;
145 #ifdef DOMAIN_ERR_DEBUG
149 lambda_sl = atan( E*E * tan(lat_geod) ); // sea level geocentric latitude
150 sin_lambda_sl = sin( lambda_sl );
151 cos_lambda_sl = cos( lambda_sl );
152 sin_mu = sin(lat_geod); // Geodetic (map makers') latitude
153 cos_mu = cos(lat_geod);
155 sqrt(RESQ_M / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl));
156 #ifdef DOMAIN_ERR_DEBUG
158 perror("fgGeodToGeoc()");
159 FG_LOG( FG_GENERAL, FG_ALERT, "sqrt(" <<
160 RESQ_M / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl)
164 py = *sl_radius*sin_lambda_sl + alt*sin_mu;
165 px = *sl_radius*cos_lambda_sl + alt*cos_mu;
166 *lat_geoc = atan2( py, px );
170 // Direct and inverse distance functions
172 // Proceedings of the 7th International Symposium on Geodetic
173 // Computations, 1985
175 // "The Nested Coefficient Method for Accurate Solutions of Direct and
176 // Inverse Geodetic Problems With Any Length"
181 // modified for FlightGear to use WGS84 only -- Norman Vine
183 #define GEOD_INV_PI SG_PI
188 // for WGS_84 a = 6378137.000, rf = 298.257223563;
190 static double M0( double e2 ) {
192 return GEOD_INV_PI*(1.0 - e2*( 1.0/4.0 + e2*( 3.0/64.0 +
193 e2*(5.0/256.0) )))/2.0;
197 // given, alt, lat1, lon1, az1 and distance (s), calculate lat2, lon2
198 // and az2. Lat, lon, and azimuth are in degrees. distance in meters
199 int geo_direct_wgs_84 ( double alt, double lat1, double lon1, double az1,
200 double s, double *lat2, double *lon2, double *az2 )
202 double a = 6378137.000, rf = 298.257223563;
203 double RADDEG = (GEOD_INV_PI)/180.0, testv = 1.0E-10;
204 double f = ( rf > 0.0 ? 1.0/rf : 0.0 );
205 double b = a*(1.0-f);
206 double e2 = f*(2.0-f);
207 double phi1 = lat1*RADDEG, lam1 = lon1*RADDEG;
208 double sinphi1 = sin(phi1), cosphi1 = cos(phi1);
209 double azm1 = az1*RADDEG;
210 double sinaz1 = sin(azm1), cosaz1 = cos(azm1);
213 if( fabs(s) < 0.01 ) { // distance < centimeter => congruency
217 if( *az2 > 360.0 ) *az2 -= 360.0;
219 } else if( cosphi1 ) { // non-polar origin
220 // u1 is reduced latitude
221 double tanu1 = sqrt(1.0-e2)*sinphi1/cosphi1;
222 double sig1 = atan2(tanu1,cosaz1);
223 double cosu1 = 1.0/sqrt( 1.0 + tanu1*tanu1 ), sinu1 = tanu1*cosu1;
224 double sinaz = cosu1*sinaz1, cos2saz = 1.0-sinaz*sinaz;
225 double us = cos2saz*e2/(1.0-e2);
228 double ta = 1.0+us*(4096.0+us*(-768.0+us*(320.0-175.0*us)))/16384.0,
229 tb = us*(256.0+us*(-128.0+us*(74.0-47.0*us)))/1024.0,
232 // FIRST ESTIMATE OF SIGMA (SIG)
233 double first = s/(b*ta); // !!
235 double c2sigm, sinsig,cossig, temp,denom,rnumer, dlams, dlam;
237 c2sigm = cos(2.0*sig1+sig);
238 sinsig = sin(sig); cossig = cos(sig);
241 tb*sinsig*(c2sigm+tb*(cossig*(-1.0+2.0*c2sigm*c2sigm) -
242 tb*c2sigm*(-3.0+4.0*sinsig*sinsig)
243 *(-3.0+4.0*c2sigm*c2sigm)/6.0)
245 } while( fabs(sig-temp) > testv);
247 // LATITUDE OF POINT 2
248 // DENOMINATOR IN 2 PARTS (TEMP ALSO USED LATER)
249 temp = sinu1*sinsig-cosu1*cossig*cosaz1;
250 denom = (1.0-f)*sqrt(sinaz*sinaz+temp*temp);
253 rnumer = sinu1*cossig+cosu1*sinsig*cosaz1;
254 *lat2 = atan2(rnumer,denom)/RADDEG;
256 // DIFFERENCE IN LONGITUDE ON AUXILARY SPHERE (DLAMS )
257 rnumer = sinsig*sinaz1;
258 denom = cosu1*cossig-sinu1*sinsig*cosaz1;
259 dlams = atan2(rnumer,denom);
262 tc = f*cos2saz*(4.0+f*(4.0-3.0*cos2saz))/16.0;
264 // DIFFERENCE IN LONGITUDE
265 dlam = dlams-(1.0-tc)*f*sinaz*(sig+tc*sinsig*
269 *lon2 = (lam1+dlam)/RADDEG;
270 if (*lon2 > 180.0 ) *lon2 -= 360.0;
271 if (*lon2 < -180.0 ) *lon2 += 360.0;
273 // AZIMUTH - FROM NORTH
274 *az2 = atan2(-sinaz,temp)/RADDEG;
275 if ( fabs(*az2) < testv ) *az2 = 0.0;
276 if( *az2 < 0.0) *az2 += 360.0;
278 } else { // phi1 == 90 degrees, polar origin
279 double dM = a*M0(e2) - s;
280 double paz = ( phi1 < 0.0 ? 180.0 : 0.0 );
281 return geo_direct_wgs_84( alt, 0.0, lon1, paz, dM,lat2,lon2,az2 );
286 // given alt, lat1, lon1, lat2, lon2, calculate starting and ending
287 // az1, az2 and distance (s). Lat, lon, and azimuth are in degrees.
288 // distance in meters
289 int geo_inverse_wgs_84( double alt, double lat1, double lon1, double lat2,
290 double lon2, double *az1, double *az2, double *s )
292 double a = 6378137.000, rf = 298.257223563;
294 double RADDEG = (GEOD_INV_PI)/180.0, testv = 1.0E-10;
295 double f = ( rf > 0.0 ? 1.0/rf : 0.0 );
296 double b = a*(1.0-f);
297 // double e2 = f*(2.0-f); // unused in this routine
298 double phi1 = lat1*RADDEG, lam1 = lon1*RADDEG;
299 double sinphi1 = sin(phi1), cosphi1 = cos(phi1);
300 double phi2 = lat2*RADDEG, lam2 = lon2*RADDEG;
301 double sinphi2 = sin(phi2), cosphi2 = cos(phi2);
303 if( (fabs(lat1-lat2) < testv &&
304 ( fabs(lon1-lon2) < testv) || fabs(lat1-90.0) < testv ) )
306 // TWO STATIONS ARE IDENTICAL : SET DISTANCE & AZIMUTHS TO ZERO */
307 *az1 = 0.0; *az2 = 0.0; *s = 0.0;
309 } else if( fabs(cosphi1) < testv ) {
310 // initial point is polar
311 int k = geo_inverse_wgs_84( alt, lat2,lon2,lat1,lon1, az1,az2,s );
312 k = k; // avoid compiler error since return result is unused
313 b = *az1; *az1 = *az2; *az2 = b;
315 } else if( fabs(cosphi2) < testv ) {
316 // terminal point is polar
317 int k = geo_inverse_wgs_84( alt, lat1,lon1,lat1,lon1+180.0,
319 k = k; // avoid compiler error since return result is unused
322 if( *az2 > 360.0 ) *az2 -= 360.0;
324 } else if( (fabs( fabs(lon1-lon2) - 180 ) < testv) &&
325 (fabs(lat1+lat2) < testv) )
327 // Geodesic passes through the pole (antipodal)
329 geo_inverse_wgs_84( alt, lat1,lon1, lat1,lon2, az1,az2, &s1 );
330 geo_inverse_wgs_84( alt, lat2,lon2, lat1,lon2, az1,az2, &s2 );
335 // antipodal and polar points don't get here
336 double dlam = lam2 - lam1, dlams = dlam;
337 double sdlams,cdlams, sig,sinsig,cossig, sinaz,
339 double tc,temp, us,rnumer,denom, ta,tb;
340 double cosu1,sinu1, sinu2,cosu2;
343 temp = (1.0-f)*sinphi1/cosphi1;
344 cosu1 = 1.0/sqrt(1.0+temp*temp);
346 temp = (1.0-f)*sinphi2/cosphi2;
347 cosu2 = 1.0/sqrt(1.0+temp*temp);
351 sdlams = sin(dlams), cdlams = cos(dlams);
352 sinsig = sqrt(cosu2*cosu2*sdlams*sdlams+
353 (cosu1*sinu2-sinu1*cosu2*cdlams)*
354 (cosu1*sinu2-sinu1*cosu2*cdlams));
355 cossig = sinu1*sinu2+cosu1*cosu2*cdlams;
357 sig = atan2(sinsig,cossig);
358 sinaz = cosu1*cosu2*sdlams/sinsig;
359 cos2saz = 1.0-sinaz*sinaz;
360 c2sigm = (sinu1 == 0.0 || sinu2 == 0.0 ? cossig :
361 cossig-2.0*sinu1*sinu2/cos2saz);
362 tc = f*cos2saz*(4.0+f*(4.0-3.0*cos2saz))/16.0;
364 dlams = dlam+(1.0-tc)*f*sinaz*
366 (c2sigm+tc*cossig*(-1.0+2.0*c2sigm*c2sigm)));
367 if (fabs(dlams) > GEOD_INV_PI && iter++ > 50) {
370 } while ( fabs(temp-dlams) > testv);
372 us = cos2saz*(a*a-b*b)/(b*b); // !!
373 // BACK AZIMUTH FROM NORTH
374 rnumer = -(cosu1*sdlams);
375 denom = sinu1*cosu2-cosu1*sinu2*cdlams;
376 *az2 = atan2(rnumer,denom)/RADDEG;
377 if( fabs(*az2) < testv ) *az2 = 0.0;
378 if(*az2 < 0.0) *az2 += 360.0;
380 // FORWARD AZIMUTH FROM NORTH
381 rnumer = cosu2*sdlams;
382 denom = cosu1*sinu2-sinu1*cosu2*cdlams;
383 *az1 = atan2(rnumer,denom)/RADDEG;
384 if( fabs(*az1) < testv ) *az1 = 0.0;
385 if(*az1 < 0.0) *az1 += 360.0;
388 ta = 1.0+us*(4096.0+us*(-768.0+us*(320.0-175.0*us)))/
390 tb = us*(256.0+us*(-128.0+us*(74.0-47.0*us)))/1024.0;
393 *s = b*ta*(sig-tb*sinsig*
394 (c2sigm+tb*(cossig*(-1.0+2.0*c2sigm*c2sigm)-tb*
395 c2sigm*(-3.0+4.0*sinsig*sinsig)*
396 (-3.0+4.0*c2sigm*c2sigm)/6.0)/
403 /***************************************************************************
407 ----------------------------------------------------------------------------
409 FUNCTION: Converts geocentric coordinates to geodetic positions
411 ----------------------------------------------------------------------------
413 MODULE STATUS: developmental
415 ----------------------------------------------------------------------------
417 GENEALOGY: Written as part of LaRCSim project by E. B. Jackson
419 ----------------------------------------------------------------------------
421 DESIGNED BY: E. B. Jackson
423 CODED BY: E. B. Jackson
425 MAINTAINED BY: E. B. Jackson
427 ----------------------------------------------------------------------------
429 MODIFICATION HISTORY:
433 930208 Modified to avoid singularity near polar region. EBJ
434 930602 Moved backwards calcs here from ls_step. EBJ
435 931214 Changed erroneous Latitude and Altitude variables to
436 *lat_geod and *alt in routine ls_geoc_to_geod. EBJ
437 940111 Changed header files from old ls_eom.h style to ls_types,
438 and ls_constants. Also replaced old DATA type with new
444 * Revision 1.5 1994/01/11 18:47:05 bjax
445 * Changed include files to use types and constants, not ls_eom.h
446 * Also changed DATA type to SCALAR type.
448 * Revision 1.4 1993/12/14 21:06:47 bjax
449 * Removed global variable references Altitude and Latitude. EBJ
451 * Revision 1.3 1993/06/02 15:03:40 bjax
452 * Made new subroutine for calculating geodetic to geocentric; changed name
453 * of forward conversion routine from ls_geodesy to ls_geoc_to_geod.
456 ----------------------------------------------------------------------------
460 [ 1] Stevens, Brian L.; and Lewis, Frank L.: "Aircraft
461 Control and Simulation", Wiley and Sons, 1992.
465 ----------------------------------------------------------------------------
469 ----------------------------------------------------------------------------
473 ----------------------------------------------------------------------------
476 lat_geoc Geocentric latitude, radians, + = North
477 radius C.G. radius to earth center, ft
479 ----------------------------------------------------------------------------
482 lat_geod Geodetic latitude, radians, + = North
483 alt C.G. altitude above mean sea level, ft
484 sea_level_r radius from earth center to sea level at
485 local vertical (surface normal) of C.G.
487 --------------------------------------------------------------------------*/