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 FG_HAVE_STD_INCLUDES
20 #include <simgear/constants.h>
21 #include <simgear/debug/logstream.hxx>
23 #include "point3d.hxx"
24 #include "sg_geodesy.hxx"
25 #include "localconsts.hxx"
28 #ifndef FG_HAVE_NATIVE_SGI_COMPILERS
32 // ONE_SECOND is pi/180/60/60, or about 100 feet at earths' equator
33 #define ONE_SECOND 4.848136811E-6
36 // sgGeocToGeod(lat_geoc, radius, *lat_geod, *alt, *sea_level_r)
38 // lat_geoc Geocentric latitude, radians, + = North
39 // radius C.G. radius to earth center (meters)
42 // lat_geod Geodetic latitude, radians, + = North
43 // alt C.G. altitude above mean sea level (meters)
44 // sea_level_r radius from earth center to sea level at
45 // local vertical (surface normal) of C.G. (meters)
48 void sgGeocToGeod( double lat_geoc, double radius, double
49 *lat_geod, double *alt, double *sea_level_r )
51 double t_lat, x_alpha, mu_alpha, delt_mu, r_alpha, l_point, rho_alpha;
52 double sin_mu_a, denom,delt_lambda, lambda_sl, sin_lambda_sl;
54 if( ( (FG_PI_2 - lat_geoc) < ONE_SECOND ) // near North pole
55 || ( (FG_PI_2 + lat_geoc) < ONE_SECOND ) ) // near South pole
58 *sea_level_r = EQUATORIAL_RADIUS_M*E;
59 *alt = radius - *sea_level_r;
61 // cout << " lat_geoc = " << lat_geoc << endl;
62 t_lat = tan(lat_geoc);
63 // cout << " tan(t_lat) = " << t_lat << endl;
64 x_alpha = E*EQUATORIAL_RADIUS_M/sqrt(t_lat*t_lat + E*E);
65 // cout << " x_alpha = " << x_alpha << endl;
66 double tmp = RESQ_M - x_alpha * x_alpha;
67 if ( tmp < 0.0 ) { tmp = 0.0; }
68 mu_alpha = atan2(sqrt(tmp),E*x_alpha);
69 if (lat_geoc < 0) mu_alpha = - mu_alpha;
70 sin_mu_a = sin(mu_alpha);
71 delt_lambda = mu_alpha - lat_geoc;
72 r_alpha = x_alpha/cos(lat_geoc);
73 l_point = radius - r_alpha;
74 *alt = l_point*cos(delt_lambda);
76 // check for domain error
77 if ( errno == EDOM ) {
78 FG_LOG( FG_GENERAL, FG_ALERT, "Domain ERROR in fgGeocToGeod!!!!" );
82 denom = sqrt(1-EPS*EPS*sin_mu_a*sin_mu_a);
83 rho_alpha = EQUATORIAL_RADIUS_M*(1-EPS)/
85 delt_mu = atan2(l_point*sin(delt_lambda),rho_alpha + *alt);
86 *lat_geod = mu_alpha - delt_mu;
87 lambda_sl = atan( E*E * tan(*lat_geod) ); // SL geoc. latitude
88 sin_lambda_sl = sin( lambda_sl );
90 sqrt(RESQ_M / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl));
92 // check for domain error
93 if ( errno == EDOM ) {
94 FG_LOG( FG_GENERAL, FG_ALERT, "Domain ERROR in sgGeocToGeod!!!!" );
102 // sgGeodToGeoc( lat_geod, alt, *sl_radius, *lat_geoc )
104 // lat_geod Geodetic latitude, radians, + = North
105 // alt C.G. altitude above mean sea level (meters)
108 // sl_radius SEA LEVEL radius to earth center (meters)
109 // (add Altitude to get true distance from earth center.
110 // lat_geoc Geocentric latitude, radians, + = North
114 void sgGeodToGeoc( double lat_geod, double alt, double *sl_radius,
117 double lambda_sl, sin_lambda_sl, cos_lambda_sl, sin_mu, cos_mu, px, py;
119 lambda_sl = atan( E*E * tan(lat_geod) ); // sea level geocentric latitude
120 sin_lambda_sl = sin( lambda_sl );
121 cos_lambda_sl = cos( lambda_sl );
122 sin_mu = sin(lat_geod); // Geodetic (map makers') latitude
123 cos_mu = cos(lat_geod);
125 sqrt(RESQ_M / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl));
126 py = *sl_radius*sin_lambda_sl + alt*sin_mu;
127 px = *sl_radius*cos_lambda_sl + alt*cos_mu;
128 *lat_geoc = atan2( py, px );
132 // Direct and inverse distance functions
134 // Proceedings of the 7th International Symposium on Geodetic
135 // Computations, 1985
137 // "The Nested Coefficient Method for Accurate Solutions of Direct and
138 // Inverse Geodetic Problems With Any Length"
143 // modified for FlightGear to use WGS84 only -- Norman Vine
145 #define GEOD_INV_PI FG_PI
150 // for WGS_84 a = 6378137.000, rf = 298.257223563;
152 static double M0( double e2 ) {
154 return GEOD_INV_PI*(1.0 - e2*( 1.0/4.0 + e2*( 3.0/64.0 +
155 e2*(5.0/256.0) )))/2.0;
159 // given, alt, lat1, lon1, az1 and distance (s), calculate lat2, lon2
160 // and az2. Lat, lon, and azimuth are in degrees. distance in meters
161 int geo_direct_wgs_84 ( double alt, double lat1, double lon1, double az1,
162 double s, double *lat2, double *lon2, double *az2 )
164 double a = 6378137.000, rf = 298.257223563;
165 double RADDEG = (GEOD_INV_PI)/180.0, testv = 1.0E-10;
166 double f = ( rf > 0.0 ? 1.0/rf : 0.0 );
167 double b = a*(1.0-f);
168 double e2 = f*(2.0-f);
169 double phi1 = lat1*RADDEG, lam1 = lon1*RADDEG;
170 double sinphi1 = sin(phi1), cosphi1 = cos(phi1);
171 double azm1 = az1*RADDEG;
172 double sinaz1 = sin(azm1), cosaz1 = cos(azm1);
175 if( fabs(s) < 0.01 ) { // distance < centimeter => congruency
179 if( *az2 > 360.0 ) *az2 -= 360.0;
181 } else if( cosphi1 ) { // non-polar origin
182 // u1 is reduced latitude
183 double tanu1 = sqrt(1.0-e2)*sinphi1/cosphi1;
184 double sig1 = atan2(tanu1,cosaz1);
185 double cosu1 = 1.0/sqrt( 1.0 + tanu1*tanu1 ), sinu1 = tanu1*cosu1;
186 double sinaz = cosu1*sinaz1, cos2saz = 1.0-sinaz*sinaz;
187 double us = cos2saz*e2/(1.0-e2);
190 double ta = 1.0+us*(4096.0+us*(-768.0+us*(320.0-175.0*us)))/16384.0,
191 tb = us*(256.0+us*(-128.0+us*(74.0-47.0*us)))/1024.0,
194 // FIRST ESTIMATE OF SIGMA (SIG)
195 double first = s/(b*ta); // !!
197 double c2sigm, sinsig,cossig, temp,denom,rnumer, dlams, dlam;
199 c2sigm = cos(2.0*sig1+sig);
200 sinsig = sin(sig); cossig = cos(sig);
203 tb*sinsig*(c2sigm+tb*(cossig*(-1.0+2.0*c2sigm*c2sigm) -
204 tb*c2sigm*(-3.0+4.0*sinsig*sinsig)
205 *(-3.0+4.0*c2sigm*c2sigm)/6.0)
207 } while( fabs(sig-temp) > testv);
209 // LATITUDE OF POINT 2
210 // DENOMINATOR IN 2 PARTS (TEMP ALSO USED LATER)
211 temp = sinu1*sinsig-cosu1*cossig*cosaz1;
212 denom = (1.0-f)*sqrt(sinaz*sinaz+temp*temp);
215 rnumer = sinu1*cossig+cosu1*sinsig*cosaz1;
216 *lat2 = atan2(rnumer,denom)/RADDEG;
218 // DIFFERENCE IN LONGITUDE ON AUXILARY SPHERE (DLAMS )
219 rnumer = sinsig*sinaz1;
220 denom = cosu1*cossig-sinu1*sinsig*cosaz1;
221 dlams = atan2(rnumer,denom);
224 tc = f*cos2saz*(4.0+f*(4.0-3.0*cos2saz))/16.0;
226 // DIFFERENCE IN LONGITUDE
227 dlam = dlams-(1.0-tc)*f*sinaz*(sig+tc*sinsig*
231 *lon2 = (lam1+dlam)/RADDEG;
232 if (*lon2 > 180.0 ) *lon2 -= 360.0;
233 if (*lon2 < -180.0 ) *lon2 += 360.0;
235 // AZIMUTH - FROM NORTH
236 *az2 = atan2(-sinaz,temp)/RADDEG;
237 if ( fabs(*az2) < testv ) *az2 = 0.0;
238 if( *az2 < 0.0) *az2 += 360.0;
240 } else { // phi1 == 90 degrees, polar origin
241 double dM = a*M0(e2) - s;
242 double paz = ( phi1 < 0.0 ? 180.0 : 0.0 );
243 return geo_direct_wgs_84( alt, 0.0, lon1, paz, dM,lat2,lon2,az2 );
248 // given alt, lat1, lon1, lat2, lon2, calculate starting and ending
249 // az1, az2 and distance (s). Lat, lon, and azimuth are in degrees.
250 // distance in meters
251 int geo_inverse_wgs_84( double alt, double lat1, double lon1, double lat2,
252 double lon2, double *az1, double *az2, double *s )
254 double a = 6378137.000, rf = 298.257223563;
256 double RADDEG = (GEOD_INV_PI)/180.0, testv = 1.0E-10;
257 double f = ( rf > 0.0 ? 1.0/rf : 0.0 );
258 double b = a*(1.0-f);
259 // double e2 = f*(2.0-f); // unused in this routine
260 double phi1 = lat1*RADDEG, lam1 = lon1*RADDEG;
261 double sinphi1 = sin(phi1), cosphi1 = cos(phi1);
262 double phi2 = lat2*RADDEG, lam2 = lon2*RADDEG;
263 double sinphi2 = sin(phi2), cosphi2 = cos(phi2);
265 if( (fabs(lat1-lat2) < testv &&
266 ( fabs(lon1-lon2) < testv) || fabs(lat1-90.0) < testv ) )
268 // TWO STATIONS ARE IDENTICAL : SET DISTANCE & AZIMUTHS TO ZERO */
269 *az1 = 0.0; *az2 = 0.0; *s = 0.0;
271 } else if( fabs(cosphi1) < testv ) {
272 // initial point is polar
273 int k = geo_inverse_wgs_84( alt, lat2,lon2,lat1,lon1, az1,az2,s );
274 k = k; // avoid compiler error since return result is unused
275 b = *az1; *az1 = *az2; *az2 = b;
277 } else if( fabs(cosphi2) < testv ) {
278 // terminal point is polar
279 int k = geo_inverse_wgs_84( alt, lat1,lon1,lat1,lon1+180.0,
281 k = k; // avoid compiler error since return result is unused
284 if( *az2 > 360.0 ) *az2 -= 360.0;
286 } else if( (fabs( fabs(lon1-lon2) - 180 ) < testv) &&
287 (fabs(lat1+lat2) < testv) )
289 // Geodesic passes through the pole (antipodal)
291 geo_inverse_wgs_84( alt, lat1,lon1, lat1,lon2, az1,az2, &s1 );
292 geo_inverse_wgs_84( alt, lat2,lon2, lat1,lon2, az1,az2, &s2 );
297 // antipodal and polar points don't get here
298 double dlam = lam2 - lam1, dlams = dlam;
299 double sdlams,cdlams, sig,sinsig,cossig, sinaz,
301 double tc,temp, us,rnumer,denom, ta,tb;
302 double cosu1,sinu1, sinu2,cosu2;
305 temp = (1.0-f)*sinphi1/cosphi1;
306 cosu1 = 1.0/sqrt(1.0+temp*temp);
308 temp = (1.0-f)*sinphi2/cosphi2;
309 cosu2 = 1.0/sqrt(1.0+temp*temp);
313 sdlams = sin(dlams), cdlams = cos(dlams);
314 sinsig = sqrt(cosu2*cosu2*sdlams*sdlams+
315 (cosu1*sinu2-sinu1*cosu2*cdlams)*
316 (cosu1*sinu2-sinu1*cosu2*cdlams));
317 cossig = sinu1*sinu2+cosu1*cosu2*cdlams;
319 sig = atan2(sinsig,cossig);
320 sinaz = cosu1*cosu2*sdlams/sinsig;
321 cos2saz = 1.0-sinaz*sinaz;
322 c2sigm = (sinu1 == 0.0 || sinu2 == 0.0 ? cossig :
323 cossig-2.0*sinu1*sinu2/cos2saz);
324 tc = f*cos2saz*(4.0+f*(4.0-3.0*cos2saz))/16.0;
326 dlams = dlam+(1.0-tc)*f*sinaz*
328 (c2sigm+tc*cossig*(-1.0+2.0*c2sigm*c2sigm)));
329 if (fabs(dlams) > GEOD_INV_PI && iter++ > 50) {
332 } while ( fabs(temp-dlams) > testv);
334 us = cos2saz*(a*a-b*b)/(b*b); // !!
335 // BACK AZIMUTH FROM NORTH
336 rnumer = -(cosu1*sdlams);
337 denom = sinu1*cosu2-cosu1*sinu2*cdlams;
338 *az2 = atan2(rnumer,denom)/RADDEG;
339 if( fabs(*az2) < testv ) *az2 = 0.0;
340 if(*az2 < 0.0) *az2 += 360.0;
342 // FORWARD AZIMUTH FROM NORTH
343 rnumer = cosu2*sdlams;
344 denom = cosu1*sinu2-sinu1*cosu2*cdlams;
345 *az1 = atan2(rnumer,denom)/RADDEG;
346 if( fabs(*az1) < testv ) *az1 = 0.0;
347 if(*az1 < 0.0) *az1 += 360.0;
350 ta = 1.0+us*(4096.0+us*(-768.0+us*(320.0-175.0*us)))/
352 tb = us*(256.0+us*(-128.0+us*(74.0-47.0*us)))/1024.0;
355 *s = b*ta*(sig-tb*sinsig*
356 (c2sigm+tb*(cossig*(-1.0+2.0*c2sigm*c2sigm)-tb*
357 c2sigm*(-3.0+4.0*sinsig*sinsig)*
358 (-3.0+4.0*c2sigm*c2sigm)/6.0)/
365 /***************************************************************************
369 ----------------------------------------------------------------------------
371 FUNCTION: Converts geocentric coordinates to geodetic positions
373 ----------------------------------------------------------------------------
375 MODULE STATUS: developmental
377 ----------------------------------------------------------------------------
379 GENEALOGY: Written as part of LaRCSim project by E. B. Jackson
381 ----------------------------------------------------------------------------
383 DESIGNED BY: E. B. Jackson
385 CODED BY: E. B. Jackson
387 MAINTAINED BY: E. B. Jackson
389 ----------------------------------------------------------------------------
391 MODIFICATION HISTORY:
395 930208 Modified to avoid singularity near polar region. EBJ
396 930602 Moved backwards calcs here from ls_step. EBJ
397 931214 Changed erroneous Latitude and Altitude variables to
398 *lat_geod and *alt in routine ls_geoc_to_geod. EBJ
399 940111 Changed header files from old ls_eom.h style to ls_types,
400 and ls_constants. Also replaced old DATA type with new
406 * Revision 1.5 1994/01/11 18:47:05 bjax
407 * Changed include files to use types and constants, not ls_eom.h
408 * Also changed DATA type to SCALAR type.
410 * Revision 1.4 1993/12/14 21:06:47 bjax
411 * Removed global variable references Altitude and Latitude. EBJ
413 * Revision 1.3 1993/06/02 15:03:40 bjax
414 * Made new subroutine for calculating geodetic to geocentric; changed name
415 * of forward conversion routine from ls_geodesy to ls_geoc_to_geod.
418 ----------------------------------------------------------------------------
422 [ 1] Stevens, Brian L.; and Lewis, Frank L.: "Aircraft
423 Control and Simulation", Wiley and Sons, 1992.
427 ----------------------------------------------------------------------------
431 ----------------------------------------------------------------------------
435 ----------------------------------------------------------------------------
438 lat_geoc Geocentric latitude, radians, + = North
439 radius C.G. radius to earth center, ft
441 ----------------------------------------------------------------------------
444 lat_geod Geodetic latitude, radians, + = North
445 alt C.G. altitude above mean sea level, ft
446 sea_level_r radius from earth center to sea level at
447 local vertical (surface normal) of C.G.
449 --------------------------------------------------------------------------*/