GPXSee/src/map/lambertazimuthal.cpp

/*
 * Based on libgeotrans with the following Source Code Disclaimer:

1. The GEOTRANS source code ("the software") is provided free of charge by
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2. Warranty Disclaimer: The software was developed to meet only the internal
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developed using GEOTRANS, a product of the National Imagery and Mapping
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*/

#include "lambertazimuthal.h"


#ifndef M_PI_2
	#define M_PI_2 1.57079632679489661923
#endif // M_PI_2

LambertAzimuthal::LambertAzimuthal(const Ellipsoid &ellipsoid,
  double latitudeOrigin, double longitudeOrigin, double falseEasting,
  double falseNorthing)
{
	double es2, es4, es6;

	_e = ellipsoid;
	es2 = 2 * _e.flattening() - _e.flattening() * _e.flattening();

	es4 = es2 * es2;
	es6 = es4 * es2;
	_ra = _e.radius() * (1.0 - es2 / 6.0 - 17.0 * es4 / 360.0 - 67.0 * es6
	  / 3024.0);
	_latOrigin = deg2rad(latitudeOrigin);
	_sinLatOrigin = sin(_latOrigin);
	_cosLatOrigin = cos(_latOrigin);
	_absLatOrigin = fabs(_latOrigin);
	_lonOrigin = deg2rad(longitudeOrigin);
	if (_lonOrigin > M_PI)
		_lonOrigin -= 2.0 * M_PI;

	_falseNorthing = falseNorthing;
	_falseEasting = falseEasting;
}

QPointF LambertAzimuthal::ll2xy(const Coordinates &c) const
{
	double dlam;
	double k_prime;
	double cd;
	double rlat = deg2rad(c.lat());
	double slat = sin(rlat);
	double clat = cos(rlat);
	double cos_c;
	double sin_dlam, cos_dlam;
	double Ra_kprime;
	double Ra_PI_OVER_2_Lat;
	QPointF p;


	dlam = deg2rad(c.lon()) - _lonOrigin;
	if (dlam > M_PI)
		dlam -= 2.0 * M_PI;
	if (dlam < -M_PI)
		dlam += 2.0 * M_PI;

	sin_dlam = sin(dlam);
	cos_dlam = cos(dlam);
	if (fabs(_absLatOrigin - M_PI_2) < 1.0e-10) {
		if (_latOrigin >= 0.0) {
			Ra_PI_OVER_2_Lat = _ra * (M_PI_2 - rlat);
			p.rx() = Ra_PI_OVER_2_Lat * sin_dlam + _falseEasting;
			p.ry() = -1.0 * (Ra_PI_OVER_2_Lat * cos_dlam) + _falseNorthing;
		} else {
			Ra_PI_OVER_2_Lat = _ra * (M_PI_2 + rlat);
			p.rx() = Ra_PI_OVER_2_Lat * sin_dlam + _falseEasting;
			p.ry() = Ra_PI_OVER_2_Lat * cos_dlam + _falseNorthing;
		}
	} else if (_absLatOrigin <= 1.0e-10) {
		cos_c = clat * cos_dlam;
		if (fabs(fabs(cos_c) - 1.0) < 1.0e-14) {
			if (cos_c >= 0.0) {
				p.rx() = _falseEasting;
				p.ry() = _falseNorthing;
			} else
				return QPointF(NAN, NAN);
		} else {
			cd = acos(cos_c);
			k_prime = cd / sin(cd);
			Ra_kprime = _ra * k_prime;
			p.rx() = Ra_kprime * clat * sin_dlam + _falseEasting;
			p.ry() = Ra_kprime * slat + _falseNorthing;
		}
	} else {
		cos_c = (_sinLatOrigin * slat) + (_cosLatOrigin * clat * cos_dlam);
		if (fabs(fabs(cos_c) - 1.0) < 1.0e-14) {
			if (cos_c >= 0.0) {
				p.rx() = _falseEasting;
				p.ry() = _falseNorthing;
			} else
				return QPointF(NAN, NAN);
		} else {
			cd = acos(cos_c);
			k_prime = cd / sin(cd);
			Ra_kprime = _ra * k_prime;
			p.rx() = Ra_kprime * clat * sin_dlam + _falseEasting;
			p.ry() = Ra_kprime * (_cosLatOrigin * slat - _sinLatOrigin * clat
			  * cos_dlam) + _falseNorthing;
		}
	}

	return p;
}

Coordinates LambertAzimuthal::xy2ll(const QPointF &p) const
{
	double dx, dy;
	double rho;
	double cd;
	double sin_c, cos_c, dy_sinc;
	double lat, lon;


	dy = p.y() - _falseNorthing;
	dx = p.x() - _falseEasting;
	rho = sqrt(dx * dx + dy * dy);
	if (fabs(rho) <= 1.0e-10) {
		lat = _latOrigin;
		lon = _lonOrigin;
	} else {
		cd = rho / _ra;
		sin_c = sin(cd);
		cos_c = cos(cd);
		dy_sinc = dy * sin_c;
		lat = asin((cos_c * _sinLatOrigin) + ((dy_sinc * _cosLatOrigin) / rho));
		if (fabs(_absLatOrigin - M_PI_2) < 1.0e-10) {
			if (_latOrigin >= 0.0)
				lon = _lonOrigin + atan2(dx, -dy);
			else
				lon = _lonOrigin + atan2(dx, dy);
			}
		else
			lon = _lonOrigin + atan2((dx * sin_c), ((rho * _cosLatOrigin
			  * cos_c) - (dy_sinc * _sinLatOrigin)));
	}

	if (lat > M_PI_2)
		lat = M_PI_2;
	else if (lat < -M_PI_2)
		lat = -M_PI_2;

	if (lon > M_PI)
		lon -= 2.0 * M_PI;
	if (lon < -M_PI)
		lon += 2.0 * M_PI;

	if (lon > M_PI)
		lon = M_PI;
	else if (lon < -M_PI)
		lon = -M_PI;

	return Coordinates(rad2deg(lon), rad2deg(lat));
}