GPXSee/src/map/lambertconic.cpp

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

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*/

#include <cmath>
#include "ellipsoid.h"
#include "lambertconic.h"


#define LAMBERT_m(clat, essin) (clat / sqrt(1.0 - essin * essin))
#define LAMBERT2_t(lat, essin, es_over_2) \
	(tan(M_PI_4 - lat / 2) * pow((1.0 + essin) / (1.0 - essin), es_over_2))
#define LAMBERT1_t(lat, essin, es_over_2) \
	(tan(M_PI_4 - lat / 2) / pow((1.0 - essin) / (1.0 + essin), es_over_2))


LambertConic1::LambertConic1(const Ellipsoid *ellipsoid, double latitudeOrigin,
  double longitudeOrigin, double scale, double falseEasting,
  double falseNorthing)
{
	double e_sin;
	double m0;
	double lat_orig;


	lat_orig = deg2rad(latitudeOrigin);
	_longitudeOrigin = deg2rad(longitudeOrigin);
	if (_longitudeOrigin > M_PI)
		_longitudeOrigin -= M_2_PI;

	_falseEasting = falseEasting;
	_falseNorthing = falseNorthing;

	_e = sqrt(ellipsoid->es());
	_e_over_2 = _e / 2.0;

	_n = sin(lat_orig);

	e_sin = _e * sin(lat_orig);
	m0 = LAMBERT_m(cos(lat_orig), e_sin);
	_t0 = LAMBERT1_t(lat_orig, e_sin, _e_over_2);

	_rho0 = ellipsoid->radius() * scale * m0 / _n;

	_rho_olat = _rho0;
}

PointD LambertConic1::ll2xy(const Coordinates &c) const
{
	double t;
	double rho;
	double dlam;
	double theta;
	double lat = deg2rad(c.lat());


	if (fabs(fabs(lat) - M_PI_2) > 1.0e-10) {
		t = LAMBERT1_t(lat, _e * sin(lat), _e_over_2);
		rho = _rho0 * pow(t / _t0, _n);
	} else
		rho = 0.0;

	dlam = deg2rad(c.lon()) - _longitudeOrigin;

	if (dlam > M_PI)
		dlam -= M_2_PI;
	if (dlam < -M_PI)
		dlam += M_2_PI;

	theta = _n * dlam;

	return PointD(rho * sin(theta) + _falseEasting, _rho_olat - rho
	  * cos(theta) + _falseNorthing);
}

Coordinates LambertConic1::xy2ll(const PointD &p) const
{
	double dx;
	double dy;
	double rho;
	double rho_olat_minus_dy;
	double t;
	double PHI;
	double es_sin;
	double tempPHI = 0.0;
	double theta = 0.0;
	double tolerance = 4.85e-10;
	int count = 30;
	double lat, lon;


	dy = p.y() - _falseNorthing;
	dx = p.x() - _falseEasting;
	rho_olat_minus_dy = _rho_olat - dy;
	rho = sqrt(dx * dx + (rho_olat_minus_dy) * (rho_olat_minus_dy));

	if (_n < 0.0) {
		rho *= -1.0;
		dx *= -1.0;
		rho_olat_minus_dy *= -1.0;
	}

	if (rho != 0.0) {
		theta = atan2(dx, rho_olat_minus_dy) / _n;
		t = _t0 * pow(rho / _rho0, 1 / _n);
		PHI = M_PI_2 - 2.0 * atan(t);
		while (fabs(PHI - tempPHI) > tolerance && count) {
			tempPHI = PHI;
			es_sin = _e * sin(PHI);
			PHI = M_PI_2 - 2.0 * atan(t * pow((1.0 - es_sin) / (1.0 + es_sin),
			  _e_over_2));
			count--;
		}

		if (!count)
			return Coordinates();

		lat = PHI;
		lon = theta + _longitudeOrigin;

		if (fabs(lat) < 2.0e-7)
			lat = 0.0;
		if (lat > M_PI_2)
			lat = M_PI_2;
		else if (lat < -M_PI_2)
			lat = -M_PI_2;

		if (lon > M_PI) {
			if (lon - M_PI < 3.5e-6)
				lon = M_PI;
			else
				lon -= M_2_PI;
		}
		if (lon < -M_PI) {
			if (fabs(lon + M_PI) < 3.5e-6)
				lon = -M_PI;
			else
				lon += M_2_PI;
		}

		if (fabs(lon) < 2.0e-7)
			lon = 0.0;
		if (lon > M_PI)
			lon = M_PI;
		else if (lon < -M_PI)
			lon = -M_PI;
	} else {
		if (_n > 0.0)
			lat = M_PI_2;
		else
			lat = -M_PI_2;
		lon = _longitudeOrigin;
	}

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

LambertConic2::LambertConic2(const Ellipsoid *ellipsoid,
  double standardParallel1, double standardParallel2, double latitudeOrigin,
  double longitudeOrigin, double falseEasting, double falseNorthing)
{
	double e, e_over_2, e_sin;
	double lat0;
	double k0;
	double t0;
	double t1, t2;
	double t_olat;
	double m0;
	double m1;
	double m2;
	double n;
	double const_value;
	double sp1, sp2;
	double lat_orig;


	lat_orig = deg2rad(latitudeOrigin);
	sp1 = deg2rad(standardParallel1);
	sp2 = deg2rad(standardParallel2);

	if (fabs(sp1 - sp2) > 1.0e-10) {
		e = sqrt(ellipsoid->es());
		e_over_2 = e / 2.0;

		e_sin = e * sin(lat_orig);
		t_olat = LAMBERT2_t(lat_orig, e_sin, e_over_2);

		e_sin = e * sin(sp1);
		m1 = LAMBERT_m(cos(sp1), e_sin);
		t1 = LAMBERT2_t(sp1, e_sin, e_over_2);

		e_sin = e * sin(sp2);
		m2 = LAMBERT_m(cos(sp2), e_sin);
		t2 = LAMBERT2_t(sp2, e_sin, e_over_2);

		n = log(m1 / m2) / log(t1 / t2);

		lat0 = asin(n);

		e_sin = e * sin(lat0);
		m0 = LAMBERT_m(cos(lat0), e_sin);
		t0 = LAMBERT2_t(lat0, e_sin, e_over_2);

		k0 = (m1 / m0) * (pow(t0 / t1, n));

		const_value = ((ellipsoid->radius() * m2) / (n * pow(t2, n)));

		falseNorthing += (const_value * pow(t_olat, n)) - (const_value
		  * pow(t0, n));
	} else {
		lat0 = sp1;
		k0 = 1.0;
	}

	_lc1 = LambertConic1(ellipsoid, rad2deg(lat0), longitudeOrigin, k0,
	  falseEasting, falseNorthing);
}

PointD LambertConic2::ll2xy(const Coordinates &c) const
{
	return _lc1.ll2xy(c);
}

Coordinates LambertConic2::xy2ll(const PointD &p) const
{
	return _lc1.xy2ll(p);
}