-// polar.hxx -- routines to deal with polar math and transformations
-//
+/**
+ * \file polar3d.hxx
+ * Routines to deal with polar math and transformations.
+ */
+
// Written by Curtis Olson, started June 1997.
//
// Copyright (C) 1997 Curtis L. Olson - curt@infoplane.com
// $Id$
-#ifndef _POLAR_HXX
-#define _POLAR_HXX
+#ifndef _POLAR3D_HXX
+#define _POLAR3D_HXX
#ifndef __cplusplus
#include <simgear/math/point3d.hxx>
-// Find the Altitude above the Ellipsoid (WGS84) given the Earth
-// Centered Cartesian coordinate vector Distances are specified in
-// meters.
+/**
+ * Find the Altitude above the Ellipsoid (WGS84) given the Earth
+ * Centered Cartesian coordinate vector Distances are specified in
+ * meters.
+ * @param cp point specified in cartesian coordinates
+ * @return altitude above the (wgs84) earth in meters
+ */
double sgGeodAltFromCart(const Point3D& cp);
-// Convert a polar coordinate to a cartesian coordinate. Lon and Lat
-// must be specified in radians. The SG convention is for distances
-// to be specified in meters
+/**
+ * Convert a polar coordinate to a cartesian coordinate. Lon and Lat
+ * must be specified in radians. The SG convention is for distances
+ * to be specified in meters
+ * @param p point specified in polar coordinates
+ * @return the same point in cartesian coordinates
+ */
inline Point3D sgPolarToCart3d(const Point3D& p) {
double tmp = cos( p.lat() ) * p.radius();
}
-// Convert a cartesian coordinate to polar coordinates (lon/lat
-// specified in radians. Distances are specified in meters.
+/**
+ * Convert a cartesian coordinate to polar coordinates (lon/lat
+ * specified in radians. Distances are specified in meters.
+ * @param cp point specified in cartesian coordinates
+ * @return the same point in polar coordinates
+ */
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()) );
}
-// calc new lon/lat given starting lon/lat, and offset radial, and
-// distance. NOTE: starting point is specifed in radians, distance is
-// specified in meters (and converted internally to radians)
-// ... assumes a spherical world
+/**
+ * Calculate new lon/lat given starting lon/lat, and offset radial, and
+ * distance. NOTE: starting point is specifed in radians, distance is
+ * specified in meters (and converted internally to radians)
+ * ... assumes a spherical world.
+ * @param orig specified in polar coordinates
+ * @param course offset radial
+ * @param dist offset distance
+ * @return destination point in polar coordinates
+ */
inline Point3D calc_gc_lon_lat( const Point3D& orig, double course,
double dist ) {
Point3D result;
// 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;
}
-// calc course/dist
+/**
+ * Calculate course/dist given two spherical points.
+ * @param start starting point
+ * @param dest ending point
+ * @param course resulting course
+ * @param dist resulting distance
+ */
+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 cos_start_y = cos( start.y() );
+ volatile double tmp1 = sin( (start.y() - dest.y()) * 0.5 );
+ volatile double tmp2 = sin( (start.x() - dest.x()) * 0.5 );
+ double d = 2.0 * asin( sqrt( tmp1 * tmp1 +
+ cos_start_y * cos(dest.y()) * tmp2 * tmp2));
+
+ *dist = d * SG_RAD_TO_NM * SG_NM_TO_METER;
+
+ // 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
+
+ // if ( cos(start.y()) < SG_EPSILON ) {
+ // doing it this way saves a transcendental call
+ double sin_start_y = sin( start.y() );
+ if ( fabs(1.0-sin_start_y) < SG_EPSILON ) {
+ // EPS a small number ~ machine precision
+ if ( start.y() > 0 ) {
+ *course = SGD_PI; // starting from N pole
+ } else {
+ *course = 0; // starting from S pole
+ }
+ } else {
+ // 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);
+
+ // Doing this way gaurentees that the temps are
+ // not stored into memory
+ double tmp5 = acos( (sin(dest.y()) - sin_start_y * cos(d)) /
+ (sin(d) * cos_start_y) );
+
+ // if ( sin( dest.x() - start.x() ) < 0 ) {
+ // the sin of the negative angle is just the opposite sign
+ // of the sin of the angle so tmp2 will have the opposite
+ // sign of sin( dest.x() - start.x() )
+ if ( tmp2 >= 0 ) {
+ *course = tmp5;
+ } else {
+ *course = 2 * SGD_PI - tmp5;
+ }
+ }
+}
+
+#if 0
+/**
+ * Calculate course/dist given two spherical points.
+ * @param start starting point
+ * @param dest ending point
+ * @param course resulting course
+ * @param dist resulting distance
+ */
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 +
double tc1;
- if ( cos(start.y()) < FG_EPSILON ) {
+ if ( cos(start.y()) < SG_EPSILON ) {
// EPS a small number ~ machine precision
if ( start.y() > 0 ) {
- tc1 = FG_PI; // starting from N pole
+ tc1 = SGD_PI; // starting from N pole
} else {
tc1 = 0; // starting from S pole
}
if ( sin( dest.x() - start.x() ) < 0 ) {
tc1 = tmp5;
} else {
- tc1 = 2 * FG_PI - tmp5;
+ tc1 = 2 * SGD_PI - tmp5;
}
*course = tc1;
- *dist = d * RAD_TO_NM * NM_TO_METER;
+ *dist = d * SG_RAD_TO_NM * SG_NM_TO_METER;
}
+#endif // 0
-#endif // _POLAR_HXX
+#endif // _POLAR3D_HXX
projects / simgear.git / blobdiff