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;
+}
+
+/// 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::distanceM(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) * SG_RAD_TO_NM * SG_NM_TO_METER;
+}
projects / simgear.git / blobdiff