X-Git-Url: https://git.mxchange.org/?a=blobdiff_plain;f=simgear%2Fmath%2FSGGeodesy.cxx;h=b9974f14c66601be2063896c99d59fc8bfa5adc3;hb=3cd4c5566f8c418bc9bbb6026072eb0192027993;hp=079c368b547411d2c39f5d79dad6d495e49c5b61;hpb=4e7fe460a5c5c1b64dd1d540bc197dbb89614b7f;p=simgear.git

diff --git a/simgear/math/SGGeodesy.cxx b/simgear/math/SGGeodesy.cxx
index 079c368b..b9974f14 100644
--- a/simgear/math/SGGeodesy.cxx
+++ b/simgear/math/SGGeodesy.cxx
@@ -10,10 +10,9 @@
 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 // Library General Public License for more details.
 //
-// You should have received a copy of the GNU Library General Public
-// License along with this library; if not, write to the
-// Free Software Foundation, Inc., 59 Temple Place - Suite 330,
-// Boston, MA  02111-1307, USA.
+// You should have received a copy of the GNU General Public License
+// along with this program; if not, write to the Free Software
+// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 //
 
 #ifdef HAVE_CONFIG_H
@@ -22,14 +21,16 @@
 
 #include <cmath>
 
+#include <simgear/structure/exception.hxx>
 #include "SGMath.hxx"
 
 // These are hard numbers from the WGS84 standard.  DON'T MODIFY
 // unless you want to change the datum.
 #define _EQURAD 6378137.0
-// You should have received a copy of the GNU General Public License
-// along with this program; if not, write to the Free Software
-// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+#define _FLATTENING 298.257223563
+
+// These are derived quantities more useful to the code:
+#if 0
 #define _SQUASH (1 - 1/_FLATTENING)
 #define _STRETCH (1/_SQUASH)
 #define _POLRAD (EQURAD * _SQUASH)
@@ -56,7 +57,7 @@ const double SGGeodesy::POLRAD = _POLRAD;
 #define E2 fabs(1 - _SQUASH*_SQUASH)
 static double a = _EQURAD;
 static double ra2 = 1/(_EQURAD*_EQURAD);
-static double e = sqrt(E2);
+//static double e = sqrt(E2);
 static double e2 = E2;
 static double e4 = E2*E2;
 
@@ -78,11 +79,30 @@ SGGeodesy::SGCartToGeod(const SGVec3<double>& cart, SGGeod& geod)
   double Y = cart(1);
   double Z = cart(2);
   double XXpYY = X*X+Y*Y;
+  if( XXpYY + Z*Z < 25 ) {
+    // This function fails near the geocenter region, so catch that special case here.
+    // Define the innermost sphere of small radius as earth center and return the 
+    // coordinates 0/0/-EQURAD. It may be any other place on geoide's surface,
+    // the Northpole, Hawaii or Wentorf. This one was easy to code ;-)
+    geod.setLongitudeRad( 0.0 );
+    geod.setLongitudeRad( 0.0 );
+    geod.setElevationM( -EQURAD );
+    return;
+  }
+    
   double sqrtXXpYY = sqrt(XXpYY);
   double p = XXpYY*ra2;
   double q = Z*Z*(1-e2)*ra2;
   double r = 1/6.0*(p+q-e4);
   double s = e4*p*q/(4*r*r*r);
+/* 
+  s*(2+s) is negative for s = [-2..0]
+  slightly negative values for s due to floating point rounding errors
+  cause nan for sqrt(s*(2+s))
+  We can probably clamp the resulting parable to positive numbers
+*/
+  if( s >= -2.0 && s <= 0.0 )
+    s = 0.0;
   double t = pow(1+s+sqrt(s*(2+s)), 1/3.0);
   double u = r*(1+t+1/t);
   double v = sqrt(u*u+e4*q);
@@ -155,3 +175,387 @@ SGGeodesy::SGGeocToCart(const SGGeoc& geoc, SGVec3<double>& cart)
   double clon = cos(lon);
   cart = geoc.getRadiusM()*SGVec3<double>(clat*clon, clat*slon, slat);
 }
+
+// Notes:
+//
+// The XYZ/cartesian coordinate system in use puts the X axis through
+// zero lat/lon (off west Africa), the Z axis through the north pole,
+// and the Y axis through 90 degrees longitude (in the Indian Ocean).
+//
+// All latitude and longitude values are in radians.  Altitude is in
+// meters, with zero on the WGS84 ellipsoid.
+//
+// The code below makes use of the notion of "squashed" space.  This
+// is a 2D cylindrical coordinate system where the radius from the Z
+// axis is multiplied by SQUASH; the earth in this space is a perfect
+// circle with a radius of POLRAD.
+
+////////////////////////////////////////////////////////////////////////
+//
+// Direct and inverse distance functions 
+//
+// Proceedings of the 7th International Symposium on Geodetic
+// Computations, 1985
+//
+// "The Nested Coefficient Method for Accurate Solutions of Direct and
+// Inverse Geodetic Problems With Any Length"
+//
+// Zhang Xue-Lian
+// pp 747-763
+//
+// modified for FlightGear to use WGS84 only -- Norman Vine
+
+static inline double M0( double e2 ) {
+    //double e4 = e2*e2;
+  return SGMiscd::pi()*0.5*(1.0 - e2*( 1.0/4.0 + e2*( 3.0/64.0 + 
+						  e2*(5.0/256.0) )));
+}
+
+
+// given, lat1, lon1, az1 and distance (s), calculate lat2, lon2
+// and az2.  Lat, lon, and azimuth are in degrees.  distance in meters
+static int _geo_direct_wgs_84 ( double lat1, double lon1, double az1,
+                        double s, double *lat2, double *lon2,
+                        double *az2 )
+{
+    double a = SGGeodesy::EQURAD, rf = SGGeodesy::iFLATTENING;
+    double testv = 1.0E-10;
+    double f = ( rf > 0.0 ? 1.0/rf : 0.0 );
+    double b = a*(1.0-f);
+    double e2 = f*(2.0-f);
+    double phi1 = SGMiscd::deg2rad(lat1), lam1 = SGMiscd::deg2rad(lon1);
+    double sinphi1 = sin(phi1), cosphi1 = cos(phi1);
+    double azm1 = SGMiscd::deg2rad(az1);
+    double sinaz1 = sin(azm1), cosaz1 = cos(azm1);
+	
+	
+    if( fabs(s) < 0.01 ) {	// distance < centimeter => congruency
+	*lat2 = lat1;
+	*lon2 = lon1;
+	*az2 = 180.0 + az1;
+	if( *az2 > 360.0 ) *az2 -= 360.0;
+	return 0;
+    } else if( SGLimitsd::min() < fabs(cosphi1) ) {	// non-polar origin
+	// u1 is reduced latitude
+	double tanu1 = sqrt(1.0-e2)*sinphi1/cosphi1;
+	double sig1 = atan2(tanu1,cosaz1);
+	double cosu1 = 1.0/sqrt( 1.0 + tanu1*tanu1 ), sinu1 = tanu1*cosu1;
+	double sinaz =  cosu1*sinaz1, cos2saz = 1.0-sinaz*sinaz;
+	double us = cos2saz*e2/(1.0-e2);
+
+	// Terms
+	double	ta = 1.0+us*(4096.0+us*(-768.0+us*(320.0-175.0*us)))/16384.0,
+	    tb = us*(256.0+us*(-128.0+us*(74.0-47.0*us)))/1024.0,
+	    tc = 0;
+
+	// FIRST ESTIMATE OF SIGMA (SIG)
+	double first = s/(b*ta);  // !!
+	double sig = first;
+	double c2sigm, sinsig,cossig, temp,denom,rnumer, dlams, dlam;
+	do {
+	    c2sigm = cos(2.0*sig1+sig);
+	    sinsig = sin(sig); cossig = cos(sig);
+	    temp = sig;
+	    sig = first + 
+		tb*sinsig*(c2sigm+tb*(cossig*(-1.0+2.0*c2sigm*c2sigm) - 
+				      tb*c2sigm*(-3.0+4.0*sinsig*sinsig)
+				      *(-3.0+4.0*c2sigm*c2sigm)/6.0)
+			   /4.0);
+	} while( fabs(sig-temp) > testv);
+
+	// LATITUDE OF POINT 2
+	// DENOMINATOR IN 2 PARTS (TEMP ALSO USED LATER)
+	temp = sinu1*sinsig-cosu1*cossig*cosaz1;
+	denom = (1.0-f)*sqrt(sinaz*sinaz+temp*temp);
+
+	// NUMERATOR
+	rnumer = sinu1*cossig+cosu1*sinsig*cosaz1;
+	*lat2 = SGMiscd::rad2deg(atan2(rnumer,denom));
+
+	// DIFFERENCE IN LONGITUDE ON AUXILARY SPHERE (DLAMS )
+	rnumer = sinsig*sinaz1;
+	denom = cosu1*cossig-sinu1*sinsig*cosaz1;
+	dlams = atan2(rnumer,denom);
+
+	// TERM C
+	tc = f*cos2saz*(4.0+f*(4.0-3.0*cos2saz))/16.0;
+
+	// DIFFERENCE IN LONGITUDE
+	dlam = dlams-(1.0-tc)*f*sinaz*(sig+tc*sinsig*
+				       (c2sigm+
+					tc*cossig*(-1.0+2.0*
+						   c2sigm*c2sigm)));
+	*lon2 = SGMiscd::rad2deg(lam1+dlam);
+	if (*lon2 > 180.0  ) *lon2 -= 360.0;
+	if (*lon2 < -180.0 ) *lon2 += 360.0;
+
+	// AZIMUTH - FROM NORTH
+	*az2 = SGMiscd::rad2deg(atan2(-sinaz,temp));
+	if ( fabs(*az2) < testv ) *az2 = 0.0;
+	if( *az2 < 0.0) *az2 += 360.0;
+	return 0;
+    } else {			// phi1 == 90 degrees, polar origin
+	double dM = a*M0(e2) - s;
+	double paz = ( phi1 < 0.0 ? 180.0 : 0.0 );
+        double zero = 0.0f;
+	return _geo_direct_wgs_84( zero, lon1, paz, dM, lat2, lon2, az2 );
+    } 
+}
+
+bool
+SGGeodesy::direct(const SGGeod& p1, double course1,
+                  double distance, SGGeod& p2, double& course2)
+{
+  double lat2, lon2;
+  int ret = _geo_direct_wgs_84(p1.getLatitudeDeg(), p1.getLongitudeDeg(),
+                               course1, distance, &lat2, &lon2, &course2);
+  p2.setLatitudeDeg(lat2);
+  p2.setLongitudeDeg(lon2);
+  p2.setElevationM(0);
+  return ret == 0;
+}
+
+// given lat1, lon1, lat2, lon2, calculate starting and ending
+// az1, az2 and distance (s).  Lat, lon, and azimuth are in degrees.
+// distance in meters
+static int _geo_inverse_wgs_84( double lat1, double lon1, double lat2,
+			double lon2, double *az1, double *az2,
+                        double *s )
+{
+    double a = SGGeodesy::EQURAD, rf = SGGeodesy::iFLATTENING;
+    int iter=0;
+    double testv = 1.0E-10;
+    double f = ( rf > 0.0 ? 1.0/rf : 0.0 );
+    double b = a*(1.0-f);
+    // double e2 = f*(2.0-f); // unused in this routine
+    double phi1 = SGMiscd::deg2rad(lat1), lam1 = SGMiscd::deg2rad(lon1);
+    double sinphi1 = sin(phi1), cosphi1 = cos(phi1);
+    double phi2 = SGMiscd::deg2rad(lat2), lam2 = SGMiscd::deg2rad(lon2);
+    double sinphi2 = sin(phi2), cosphi2 = cos(phi2);
+	
+    if( (fabs(lat1-lat2) < testv && 
+	 ( fabs(lon1-lon2) < testv)) || (fabs(lat1-90.0) < testv ) )
+    {	
+	// TWO STATIONS ARE IDENTICAL : SET DISTANCE & AZIMUTHS TO ZERO */
+	*az1 = 0.0; *az2 = 0.0; *s = 0.0;
+	return 0;
+    } else if(  fabs(cosphi1) < testv ) {
+	// initial point is polar
+	int k = _geo_inverse_wgs_84( lat2,lon2,lat1,lon1, az1,az2,s );
+	k = k; // avoid compiler error since return result is unused
+	b = *az1; *az1 = *az2; *az2 = b;
+	return 0;
+    } else if( fabs(cosphi2) < testv ) {
+	// terminal point is polar
+        double _lon1 = lon1 + 180.0f;
+	int k = _geo_inverse_wgs_84( lat1, lon1, lat1, _lon1, 
+				    az1, az2, s );
+	k = k; // avoid compiler error since return result is unused
+	*s /= 2.0;
+	*az2 = *az1 + 180.0;
+	if( *az2 > 360.0 ) *az2 -= 360.0; 
+	return 0;
+    } else if( (fabs( fabs(lon1-lon2) - 180 ) < testv) && 
+	       (fabs(lat1+lat2) < testv) ) 
+    {
+	// Geodesic passes through the pole (antipodal)
+	double s1,s2;
+	_geo_inverse_wgs_84( lat1,lon1, lat1,lon2, az1,az2, &s1 );
+	_geo_inverse_wgs_84( lat2,lon2, lat1,lon2, az1,az2, &s2 );
+	*az2 = *az1;
+	*s = s1 + s2;
+	return 0;
+    } else {
+	// antipodal and polar points don't get here
+	double dlam = lam2 - lam1, dlams = dlam;
+	double sdlams,cdlams, sig,sinsig,cossig, sinaz,
+	    cos2saz, c2sigm;
+	double tc,temp, us,rnumer,denom, ta,tb;
+	double cosu1,sinu1, sinu2,cosu2;
+
+	// Reduced latitudes
+	temp = (1.0-f)*sinphi1/cosphi1;
+	cosu1 = 1.0/sqrt(1.0+temp*temp);
+	sinu1 = temp*cosu1;
+	temp = (1.0-f)*sinphi2/cosphi2;
+	cosu2 = 1.0/sqrt(1.0+temp*temp);
+	sinu2 = temp*cosu2;
+    
+	do {
+	    sdlams = sin(dlams), cdlams = cos(dlams);
+	    sinsig = sqrt(cosu2*cosu2*sdlams*sdlams+
+			  (cosu1*sinu2-sinu1*cosu2*cdlams)*
+			  (cosu1*sinu2-sinu1*cosu2*cdlams));
+	    cossig = sinu1*sinu2+cosu1*cosu2*cdlams;
+	    
+	    sig = atan2(sinsig,cossig);
+	    sinaz = cosu1*cosu2*sdlams/sinsig;
+	    cos2saz = 1.0-sinaz*sinaz;
+	    c2sigm = (sinu1 == 0.0 || sinu2 == 0.0 ? cossig : 
+		      cossig-2.0*sinu1*sinu2/cos2saz);
+	    tc = f*cos2saz*(4.0+f*(4.0-3.0*cos2saz))/16.0;
+	    temp = dlams;
+	    dlams = dlam+(1.0-tc)*f*sinaz*
+		(sig+tc*sinsig*
+		 (c2sigm+tc*cossig*(-1.0+2.0*c2sigm*c2sigm)));
+	    if (fabs(dlams) > SGMiscd::pi() && iter++ > 50) {
+		return iter;
+	    }
+	} while ( fabs(temp-dlams) > testv);
+
+	us = cos2saz*(a*a-b*b)/(b*b); // !!
+	// BACK AZIMUTH FROM NORTH
+	rnumer = -(cosu1*sdlams);
+	denom = sinu1*cosu2-cosu1*sinu2*cdlams;
+	*az2 = SGMiscd::rad2deg(atan2(rnumer,denom));
+	if( fabs(*az2) < testv ) *az2 = 0.0;
+	if(*az2 < 0.0) *az2 += 360.0;
+
+	// FORWARD AZIMUTH FROM NORTH
+	rnumer = cosu2*sdlams;
+	denom = cosu1*sinu2-sinu1*cosu2*cdlams;
+	*az1 = SGMiscd::rad2deg(atan2(rnumer,denom));
+	if( fabs(*az1) < testv ) *az1 = 0.0;
+	if(*az1 < 0.0) *az1 += 360.0;
+
+	// Terms a & b
+	ta = 1.0+us*(4096.0+us*(-768.0+us*(320.0-175.0*us)))/
+	    16384.0;
+	tb = us*(256.0+us*(-128.0+us*(74.0-47.0*us)))/1024.0;
+
+	// GEODETIC DISTANCE
+	*s = b*ta*(sig-tb*sinsig*
+		   (c2sigm+tb*(cossig*(-1.0+2.0*c2sigm*c2sigm)-tb*
+			       c2sigm*(-3.0+4.0*sinsig*sinsig)*
+			       (-3.0+4.0*c2sigm*c2sigm)/6.0)/
+		    4.0));
+	return 0;
+    }
+}
+
+bool
+SGGeodesy::inverse(const SGGeod& p1, const SGGeod& p2, double& course1,
+                   double& course2, double& distance)
+{
+  int ret = _geo_inverse_wgs_84(p1.getLatitudeDeg(), p1.getLongitudeDeg(),
+                                p2.getLatitudeDeg(), p2.getLongitudeDeg(),
+                                &course1, &course2, &distance);
+  return ret == 0;
+}
+
+double
+SGGeodesy::courseDeg(const SGGeod& p1, const SGGeod& p2)
+{
+  double course1, course2, distance;
+  int r = _geo_inverse_wgs_84(p1.getLatitudeDeg(), p1.getLongitudeDeg(),
+                                p2.getLatitudeDeg(), p2.getLongitudeDeg(),
+                                &course1, &course2, &distance);
+  if (r != 0) {
+    throw sg_exception("SGGeodesy::courseDeg, unable to compute course");
+  }
+  
+  return course1;
+}
+
+double
+SGGeodesy::distanceM(const SGGeod& p1, const SGGeod& p2)
+{
+  double course1, course2, distance;
+  int r = _geo_inverse_wgs_84(p1.getLatitudeDeg(), p1.getLongitudeDeg(),
+                                p2.getLatitudeDeg(), p2.getLongitudeDeg(),
+                                &course1, &course2, &distance);
+  if (r != 0) {
+    throw sg_exception("SGGeodesy::distanceM, unable to compute distance");
+  }
+  
+  return distance;
+}
+
+double
+SGGeodesy::distanceNm(const SGGeod& from, const SGGeod& to)
+{
+  return distanceM(from, to) * SG_METER_TO_NM;
+}
+
+/// Geocentric routines
+
+void
+SGGeodesy::advanceRadM(const SGGeoc& geoc, double course, double distance,
+                       SGGeoc& result)
+{
+  result.setRadiusM(geoc.getRadiusM());
+
+  // lat=asin(sin(lat1)*cos(d)+cos(lat1)*sin(d)*cos(tc))
+  // IF (cos(lat)=0)
+  //   lon=lon1      // endpoint a pole
+  // ELSE
+  //   lon=mod(lon1-asin(sin(tc)*sin(d)/cos(lat))+pi,2*pi)-pi
+  // ENDIF
+  
+  distance *= SG_METER_TO_NM * SG_NM_TO_RAD;
+  
+  double sinDistance = sin(distance);
+  double cosDistance = cos(distance);
+
+  double sinLat = sin(geoc.getLatitudeRad()) * cosDistance +
+    cos(geoc.getLatitudeRad()) * sinDistance * cos(course);
+  sinLat = SGMiscd::clip(sinLat, -1, 1);
+  result.setLatitudeRad(asin(sinLat));
+  double cosLat = cos(result.getLatitudeRad());
+  
+  
+  if (cosLat <= SGLimitsd::min()) {
+    // endpoint a pole
+    result.setLongitudeRad(geoc.getLongitudeRad());
+  } else {
+    double tmp = SGMiscd::clip(sin(course) * sinDistance / cosLat, -1, 1);
+    double lon = SGMiscd::normalizeAngle(geoc.getLongitudeRad() - asin( tmp ));
+    result.setLongitudeRad(lon);
+  }
+}
+
+double
+SGGeodesy::courseRad(const SGGeoc& from, const SGGeoc& to)
+{
+  double diffLon = to.getLongitudeRad() - from.getLongitudeRad();
+
+  double sinLatFrom = sin(from.getLatitudeRad());
+  double cosLatFrom = cos(from.getLatitudeRad());
+
+  double sinLatTo = sin(to.getLatitudeRad());
+  double cosLatTo = cos(to.getLatitudeRad());
+
+  double x = cosLatTo*sin(diffLon);
+  double y = cosLatFrom*sinLatTo - sinLatFrom*cosLatTo*cos(diffLon);
+
+  // guard atan2 returning NaN's
+  if (fabs(x) <= SGLimitsd::min() && fabs(y) <= SGLimitsd::min())
+    return 0;
+
+  double c = atan2(x, y);
+  if (c >= 0)
+    return SGMiscd::twopi() - c;
+  else
+    return -c;
+}
+
+double
+SGGeodesy::distanceRad(const SGGeoc& from, const SGGeoc& to)
+{
+  // d = 2*asin(sqrt((sin((lat1-lat2)/2))^2 +
+  //            cos(lat1)*cos(lat2)*(sin((lon1-lon2)/2))^2))
+  double cosLatFrom = cos(from.getLatitudeRad());
+  double cosLatTo = cos(to.getLatitudeRad());
+  double tmp1 = sin(0.5*(from.getLatitudeRad() - to.getLatitudeRad()));
+  double tmp2 = sin(0.5*(from.getLongitudeRad() - to.getLongitudeRad()));
+  double square = tmp1*tmp1 + cosLatFrom*cosLatTo*tmp2*tmp2;
+  double s = SGMiscd::min(sqrt(SGMiscd::max(square, 0)), 1);
+  return 2 * asin(s);
+}
+
+
+double
+SGGeodesy::distanceM(const SGGeoc& from, const SGGeoc& to)
+{
+  return distanceRad(from, to) * SG_RAD_TO_NM * SG_NM_TO_METER;
+}