GPXSee/src/map/polarstereographic.cpp

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

1. The GEOTRANS source code ("the software") is provided free of charge by
the National Imagery and Mapping Agency (NIMA) of the United States
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U.S.C., NIMA claims copyrights in the source code under other legal regimes.
NIMA hereby grants to each user of the software a license to use and
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2. Warranty Disclaimer: The software was developed to meet only the internal
requirements of the U.S. National Imagery and Mapping Agency. The software
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limited to the implied warranties of merchantability and fitness for
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source of the software with the following statement, "The product was
developed using GEOTRANS, a product of the National Imagery and Mapping
Agency and U.S. Army Engineering Research and Development Center."

6. For any products developed using the software, NIMA requires a disclaimer
that use of the software does not indicate endorsement or approval of the
product by the Secretary of Defense or the National Imagery and Mapping
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*/

#include "ellipsoid.h"
#include "polarstereographic.h"


#define POLAR_POW(EsSin) pow((1.0 - EsSin) / (1.0 + EsSin), _es_OVER_2)

PolarStereographic::PolarStereographic(const Ellipsoid *ellipsoid,
  double latitudeOrigin, double longitudeOrigin,
  double falseEasting, double falseNorthing)
{
	_two_a = 2.0 * ellipsoid->radius();

	if (longitudeOrigin > M_PI)
		longitudeOrigin -= 2*M_PI;

	if (latitudeOrigin < 0) {
		_southernHemisphere = 1;
		_originLatitude = -deg2rad(latitudeOrigin);
		_originLongitude = -deg2rad(longitudeOrigin);
	} else {
		_southernHemisphere = 0;
		_originLatitude = deg2rad(latitudeOrigin);
		_originLongitude = deg2rad(longitudeOrigin);
	}
	_falseEasting = falseEasting;
	_falseNorthing = falseNorthing;

	double es2 = ellipsoid->es();
	_es = sqrt(es2);
	_es_OVER_2 = _es / 2.0;

	if (fabs(fabs(_originLatitude) - M_PI_2) > 1.0e-10) {
		double slat = sin(_originLatitude);
		double essin = _es * slat;
		double pow_es = POLAR_POW(essin);
		double clat = cos(_originLatitude);
		_mc = clat / sqrt(1.0 - essin * essin);
		_a_mc = ellipsoid->radius() * _mc;
		_tc = tan(M_PI_4 - _originLatitude / 2.0) / pow_es;
	} else {
		double one_PLUS_es = 1.0 + _es;
		double one_MINUS_es = 1.0 - _es;
		_e4 = sqrt(pow(one_PLUS_es, one_PLUS_es) * pow(one_MINUS_es,
		  one_MINUS_es));
	}
}

PointD PolarStereographic::ll2xy(const Coordinates &c) const
{
	double Easting, Northing;
	double Longitude = deg2rad(c.lon());
	double Latitude = deg2rad(c.lat());


	if (fabs(fabs(Latitude) - M_PI_2) < 1.0e-10) {
		Easting = 0.0;
		Northing = 0.0;
	} else {
		if (_southernHemisphere != 0) {
			Longitude *= -1.0;
			Latitude *= -1.0;
		}

		double dlam = Longitude - _originLongitude;
		if (dlam > M_PI)
			dlam -= 2*M_PI;
		if (dlam < -M_PI)
			dlam += 2*M_PI;

		double slat = sin(Latitude);
		double essin = _es * slat;
		double pow_es = POLAR_POW(essin);
		double t = tan(M_PI_4 - Latitude / 2.0) / pow_es;

		double rho;
		if (fabs(fabs(_originLatitude) - M_PI_2) > 1.0e-10)
			rho = _a_mc * t / _tc;
		else
			rho = _two_a * t / _e4;

		Easting = rho * sin(dlam) + _falseEasting;

		if (_southernHemisphere != 0) {
			Easting *= -1.0;
			Northing = rho * cos(dlam) + _falseNorthing;
		} else
			Northing = -rho * cos(dlam) + _falseNorthing;
	}

	return PointD(Easting, Northing);
}

Coordinates PolarStereographic::xy2ll(const PointD &p) const
{
	double Latitude, Longitude;
	double dy = p.y() - _falseNorthing;
	double dx = p.x() - _falseEasting;

	if ((dy == 0.0) && (dx == 0.0)) {
		Latitude = M_PI_2;
		Longitude = _originLongitude;
	} else {
		if (_southernHemisphere != 0) {
			dy *= -1.0;
			dx *= -1.0;
		}

		double rho = sqrt(dx * dx + dy * dy);
		double t;
		if (fabs(fabs(_originLatitude) - M_PI_2) > 1.0e-10)
			t = rho * _tc / (_a_mc);
		else
			t = rho * _e4 / (_two_a);
		double PHI = M_PI_2 - 2.0 * atan(t);

		double tempPHI = 0.0;
		while (fabs(PHI - tempPHI) > 1.0e-10) {
			tempPHI = PHI;
			double sin_PHI = sin(PHI);
			double essin =  _es * sin_PHI;
			double pow_es = POLAR_POW(essin);
			PHI = M_PI_2 - 2.0 * atan(t * pow_es);
		}
		Latitude = PHI;
		Longitude = _originLongitude + atan2(dx, -dy);

		if (Longitude > M_PI)
			Longitude -= 2*M_PI;
		else if (Longitude < -M_PI)
			Longitude += 2*M_PI;

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

		if (Longitude > M_PI)
			Longitude = M_PI;
		else if (Longitude < -M_PI)
			Longitude = -M_PI;
	}

	if (_southernHemisphere != 0) {
		Latitude *= -1.0;
		Longitude *= -1.0;
	}

	return Coordinates(rad2deg(Longitude), rad2deg(Latitude));
}

bool PolarStereographic::operator==(const CT &ct) const
{
	const PolarStereographic *other
	  = dynamic_cast<const PolarStereographic*>(&ct);
	return (other != 0 && _originLatitude == other->_originLatitude
	  && _originLongitude == other->_originLongitude
	  && _falseEasting == other->_falseEasting
	  && _falseNorthing == other->_falseNorthing && _two_a == other->_two_a
	  && _es == other->_es);
}