//
// Copyright (C) 1997 Curtis L. Olson - curt@infoplane.com
//
-// This program is free software; you can redistribute it and/or
-// modify it under the terms of the GNU General Public License as
-// published by the Free Software Foundation; either version 2 of the
-// License, or (at your option) any later version.
+// This library is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Library General Public
+// License as published by the Free Software Foundation; either
+// version 2 of the License, or (at your option) any later version.
//
-// This program is distributed in the hope that it will be useful, but
-// WITHOUT ANY WARRANTY; without even the implied warranty of
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
-// General Public License for more details.
+// Library General Public License for more details.
//
-// 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., 675 Mass Ave, Cambridge, MA 02139, USA.
+// 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.
//
// $Id$
#endif
+#include <math.h>
+
#include <simgear/constants.h>
-#include <simgear/point3d.hxx>
+#include <simgear/math/point3d.hxx>
// Find the Altitude above the Ellipsoid (WGS84) given the Earth
// Centered Cartesian coordinate vector Distances are specified in
// meters.
-double fgGeodAltFromCart(const Point3D& cp);
+double sgGeodAltFromCart(const Point3D& cp);
// Convert a polar coordinate to a cartesian coordinate. Lon and Lat
-// must be specified in radians. The FG convention is for distances
+// must be specified in radians. The SG convention is for distances
// to be specified in meters
-inline Point3D fgPolarToCart3d(const Point3D& p) {
+inline Point3D sgPolarToCart3d(const Point3D& p) {
double tmp = cos( p.lat() ) * p.radius();
return Point3D( cos( p.lon() ) * tmp,
// Convert a cartesian coordinate to polar coordinates (lon/lat
// specified in radians. Distances are specified in meters.
-inline Point3D fgCartToPolar3d(const Point3D& cp) {
+inline Point3D sgCartToPolar3d(const Point3D& cp) {
return Point3D( atan2( cp.y(), cp.x() ),
- FG_PI_2 -
+ SGD_PI_2 -
atan2( sqrt(cp.x()*cp.x() + cp.y()*cp.y()), cp.z() ),
sqrt(cp.x()*cp.x() + cp.y()*cp.y() + cp.z()*cp.z()) );
}
// distance. NOTE: starting point is specifed in radians, distance is
// specified in meters (and converted internally to radians)
// ... assumes a spherical world
-inline Point3D calc_lon_lat( const Point3D& orig, double course, double dist ) {
+inline Point3D calc_gc_lon_lat( const Point3D& orig, double course,
+ double dist ) {
Point3D result;
// lat=asin(sin(lat1)*cos(d)+cos(lat1)*sin(d)*cos(tc))
// printf("calc_lon_lat() offset.theta = %.2f offset.dist = %.2f\n",
// offset.theta, offset.dist);
- dist *= METER_TO_NM * NM_TO_RAD;
+ dist *= SG_METER_TO_NM * SG_NM_TO_RAD;
result.sety( asin( sin(orig.y()) * cos(dist) +
cos(orig.y()) * sin(dist) * cos(course) ) );
- if ( cos(result.y()) < FG_EPSILON ) {
+ if ( cos(result.y()) < SG_EPSILON ) {
result.setx( orig.x() ); // endpoint a pole
} else {
result.setx(
fmod(orig.x() - asin( sin(course) * sin(dist) /
- cos(result.y()) ) + FG_PI, FG_2PI) - FG_PI );
+ cos(result.y()) )
+ + SGD_PI, SGD_2PI) - SGD_PI );
}
return result;
}
-#endif // _POLAR_HXX
+// calc course/dist
+inline void calc_gc_course_dist( const Point3D& start, const Point3D& dest,
+ double *course, double *dist ) {
+ // d = 2*asin(sqrt((sin((lat1-lat2)/2))^2 +
+ // cos(lat1)*cos(lat2)*(sin((lon1-lon2)/2))^2))
+ double tmp1 = sin( (start.y() - dest.y()) / 2 );
+ double tmp2 = sin( (start.x() - dest.x()) / 2 );
+ double d = 2.0 * asin( sqrt( tmp1 * tmp1 +
+ cos(start.y()) * cos(dest.y()) * tmp2 * tmp2));
+
+ // We obtain the initial course, tc1, (at point 1) from point 1 to
+ // point 2 by the following. The formula fails if the initial
+ // point is a pole. We can special case this with:
+ //
+ // IF (cos(lat1) < EPS) // EPS a small number ~ machine precision
+ // IF (lat1 > 0)
+ // tc1= pi // starting from N pole
+ // ELSE
+ // tc1= 0 // starting from S pole
+ // ENDIF
+ // ENDIF
+ //
+ // For starting points other than the poles:
+ //
+ // IF sin(lon2-lon1)<0
+ // tc1=acos((sin(lat2)-sin(lat1)*cos(d))/(sin(d)*cos(lat1)))
+ // ELSE
+ // tc1=2*pi-acos((sin(lat2)-sin(lat1)*cos(d))/(sin(d)*cos(lat1)))
+ // ENDIF
+
+ double tc1;
+
+ if ( cos(start.y()) < SG_EPSILON ) {
+ // EPS a small number ~ machine precision
+ if ( start.y() > 0 ) {
+ tc1 = SGD_PI; // starting from N pole
+ } else {
+ tc1 = 0; // starting from S pole
+ }
+ }
+
+ // For starting points other than the poles:
+ double tmp3 = sin(d)*cos(start.y());
+ double tmp4 = sin(dest.y())-sin(start.y())*cos(d);
+ double tmp5 = acos(tmp4/tmp3);
+ if ( sin( dest.x() - start.x() ) < 0 ) {
+ tc1 = tmp5;
+ } else {
+ tc1 = 2 * SGD_PI - tmp5;
+ }
+ *course = tc1;
+ *dist = d * SG_RAD_TO_NM * SG_NM_TO_METER;
+}
+
+#endif // _POLAR_HXX