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Using the correct projection for Lambert azimuthal equal area
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/*
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* Based on libgeotrans with the following Source Code Disclaimer:
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1. The GEOTRANS source code ("the software") is provided free of charge by
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the National Imagery and Mapping Agency (NIMA) of the United States
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Department of Defense. Although NIMA makes no copyright claim under Title 17
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U.S.C., NIMA claims copyrights in the source code under other legal regimes.
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NIMA hereby grants to each user of the software a license to use and
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distribute the software, and develop derivative works.
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2. Warranty Disclaimer: The software was developed to meet only the internal
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requirements of the U.S. National Imagery and Mapping Agency. The software
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is provided "as is," and no warranty, express or implied, including but not
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limited to the implied warranties of merchantability and fitness for
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particular purpose or arising by statute or otherwise in law or from a
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course of dealing or usage in trade, is made by NIMA as to the accuracy and
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functioning of the software.
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3. NIMA and its personnel are not required to provide technical support or
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general assistance with respect to the software.
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4. Neither NIMA nor its personnel will be liable for any claims, losses, or
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damages arising from or connected with the use of the software. The user
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agrees to hold harmless the United States National Imagery and Mapping
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Agency. The user's sole and exclusive remedy is to stop using the software.
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5. NIMA requests that products developed using the software credit the
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source of the software with the following statement, "The product was
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developed using GEOTRANS, a product of the National Imagery and Mapping
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Agency and U.S. Army Engineering Research and Development Center."
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6. For any products developed using the software, NIMA requires a disclaimer
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that use of the software does not indicate endorsement or approval of the
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product by the Secretary of Defense or the National Imagery and Mapping
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Agency. Pursuant to the United States Code, 10 U.S.C. Sec. 2797, the name of
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the National Imagery and Mapping Agency, the initials "NIMA", the seal of
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the National Imagery and Mapping Agency, or any colorable imitation thereof
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shall not be used to imply approval, endorsement, or authorization of a
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product without prior written permission from United States Secretary of
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Defense.
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*/
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#include "lambertazimuthal.h"
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#ifndef M_PI_2
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#define M_PI_2 1.57079632679489661923
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#endif // M_PI_2
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#define sin2(x) (sin(x) * sin(x))
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#define sqr(x) ((x) * (x))
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LambertAzimuthal::LambertAzimuthal(const Ellipsoid *ellipsoid,
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double latitudeOrigin, double longitudeOrigin, double falseEasting,
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double falseNorthing)
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{
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double es2, es4, es6;
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double lat0 = deg2rad(latitudeOrigin);
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es2 = 2 * ellipsoid->flattening() - ellipsoid->flattening()
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* ellipsoid->flattening();
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es4 = es2 * es2;
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es6 = es4 * es2;
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_ra = ellipsoid->radius() * (1.0 - es2 / 6.0 - 17.0 * es4 / 360.0 - 67.0
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* es6 / 3024.0);
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_latOrigin = deg2rad(latitudeOrigin);
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_sinLatOrigin = sin(_latOrigin);
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_cosLatOrigin = cos(_latOrigin);
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_absLatOrigin = fabs(_latOrigin);
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_lonOrigin = deg2rad(longitudeOrigin);
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if (_lonOrigin > M_PI)
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_lonOrigin -= 2.0 * M_PI;
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_falseNorthing = falseNorthing;
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_falseEasting = falseEasting;
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_falseNorthing = falseNorthing;
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_lon0 = deg2rad(longitudeOrigin);
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_a = ellipsoid->radius();
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_es2 = 2.0 * ellipsoid->flattening() - ellipsoid->flattening()
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* ellipsoid->flattening();
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_es = sqrt(_es2);
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double q0 = (1.0 - _es2) * ((sin(lat0) / (1.0 - _es2 * sin2(lat0)))
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- ((1.0/(2.0*_es)) * log((1.0 - _es * sin(lat0)) / (1.0 + _es
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* sin(lat0)))));
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_qP = (1.0 - _es2) * ((1.0 / (1.0 - _es2)) - ((1.0/(2.0*_es))
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* log((1.0 - _es) / (1.0 + _es))));
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_beta0 = asin(q0 / _qP);
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_Rq = _a * sqrt(_qP / 2.0);
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_D = _a * (cos(lat0) / sqrt(1.0 - _es2 * sin2(lat0))) / (_Rq * cos(_beta0));
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}
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QPointF LambertAzimuthal::ll2xy(const Coordinates &c) const
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{
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double dlam;
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double k_prime;
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double cd;
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double rlat = deg2rad(c.lat());
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double slat = sin(rlat);
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double clat = cos(rlat);
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double cos_c;
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double sin_dlam, cos_dlam;
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double Ra_kprime;
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double Ra_PI_OVER_2_Lat;
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QPointF p;
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double lon = deg2rad(c.lon());
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double lat = deg2rad(c.lat());
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double q = (1.0 - _es2) * ((sin(lat) / (1.0 - _es2 * sin2(lat)))
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- ((1.0/(2.0*_es)) * log((1.0 - _es * sin(lat)) / (1.0 + _es
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* sin(lat)))));
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double beta = asin(q / _qP);
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double B = _Rq * sqrt(2.0 / (1.0 + sin(_beta0) * sin(beta) + (cos(_beta0)
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* cos(beta) * cos(lon - _lon0))));
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dlam = deg2rad(c.lon()) - _lonOrigin;
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if (dlam > M_PI)
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dlam -= 2.0 * M_PI;
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if (dlam < -M_PI)
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dlam += 2.0 * M_PI;
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double x = _falseEasting + ((B * _D) * (cos(beta) * sin(lon - _lon0)));
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double y = _falseNorthing + (B / _D) * ((cos(_beta0) * sin(beta))
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- (sin(_beta0) * cos(beta) * cos(lon - _lon0)));
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sin_dlam = sin(dlam);
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cos_dlam = cos(dlam);
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if (fabs(_absLatOrigin - M_PI_2) < 1.0e-10) {
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if (_latOrigin >= 0.0) {
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Ra_PI_OVER_2_Lat = _ra * (M_PI_2 - rlat);
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p.rx() = Ra_PI_OVER_2_Lat * sin_dlam + _falseEasting;
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p.ry() = -1.0 * (Ra_PI_OVER_2_Lat * cos_dlam) + _falseNorthing;
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} else {
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Ra_PI_OVER_2_Lat = _ra * (M_PI_2 + rlat);
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p.rx() = Ra_PI_OVER_2_Lat * sin_dlam + _falseEasting;
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p.ry() = Ra_PI_OVER_2_Lat * cos_dlam + _falseNorthing;
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}
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} else if (_absLatOrigin <= 1.0e-10) {
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cos_c = clat * cos_dlam;
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if (fabs(fabs(cos_c) - 1.0) < 1.0e-14) {
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if (cos_c >= 0.0) {
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p.rx() = _falseEasting;
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p.ry() = _falseNorthing;
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} else
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return QPointF(NAN, NAN);
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} else {
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cd = acos(cos_c);
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k_prime = cd / sin(cd);
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Ra_kprime = _ra * k_prime;
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p.rx() = Ra_kprime * clat * sin_dlam + _falseEasting;
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p.ry() = Ra_kprime * slat + _falseNorthing;
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}
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} else {
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cos_c = (_sinLatOrigin * slat) + (_cosLatOrigin * clat * cos_dlam);
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if (fabs(fabs(cos_c) - 1.0) < 1.0e-14) {
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if (cos_c >= 0.0) {
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p.rx() = _falseEasting;
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p.ry() = _falseNorthing;
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} else
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return QPointF(NAN, NAN);
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} else {
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cd = acos(cos_c);
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k_prime = cd / sin(cd);
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Ra_kprime = _ra * k_prime;
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p.rx() = Ra_kprime * clat * sin_dlam + _falseEasting;
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p.ry() = Ra_kprime * (_cosLatOrigin * slat - _sinLatOrigin * clat
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* cos_dlam) + _falseNorthing;
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}
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}
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return p;
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return QPointF(x, y);
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}
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Coordinates LambertAzimuthal::xy2ll(const QPointF &p) const
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{
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double dx, dy;
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double rho;
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double cd;
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double sin_c, cos_c, dy_sinc;
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double lat, lon;
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double e4 = _es2 * _es2;
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double e6 = _es2 * e4;
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double rho = sqrt(sqr((p.x() - _falseEasting) / _D) + sqr(_D * (p.y()
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- _falseNorthing)));
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double C = 2.0 * asin(rho / (2.0*_Rq));
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double betaS = asin((cos(C) * sin(_beta0)) + ((_D * (p.y() -_falseNorthing)
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* sin(C) * cos(_beta0)) / rho));
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dy = p.y() - _falseNorthing;
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dx = p.x() - _falseEasting;
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rho = sqrt(dx * dx + dy * dy);
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if (fabs(rho) <= 1.0e-10) {
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lat = _latOrigin;
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lon = _lonOrigin;
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} else {
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cd = rho / _ra;
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sin_c = sin(cd);
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cos_c = cos(cd);
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dy_sinc = dy * sin_c;
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lat = asin((cos_c * _sinLatOrigin) + ((dy_sinc * _cosLatOrigin) / rho));
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if (fabs(_absLatOrigin - M_PI_2) < 1.0e-10) {
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if (_latOrigin >= 0.0)
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lon = _lonOrigin + atan2(dx, -dy);
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else
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lon = _lonOrigin + atan2(dx, dy);
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}
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else
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lon = _lonOrigin + atan2((dx * sin_c), ((rho * _cosLatOrigin
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* cos_c) - (dy_sinc * _sinLatOrigin)));
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}
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if (lat > M_PI_2)
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lat = M_PI_2;
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else if (lat < -M_PI_2)
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lat = -M_PI_2;
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if (lon > M_PI)
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lon -= 2.0 * M_PI;
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if (lon < -M_PI)
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lon += 2.0 * M_PI;
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if (lon > M_PI)
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lon = M_PI;
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else if (lon < -M_PI)
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lon = -M_PI;
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double lon = _lon0 + atan((p.x() - _falseEasting) * sin(C) / (_D * rho
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* cos(_beta0) * cos(C) - sqr(_D) * (p.y() - _falseNorthing) * sin(_beta0)
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* sin(C)));
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double lat = betaS + ((_es2/3.0 + 31.0*e4/180.0 + 517.0*e6/5040.0)
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* sin(2.0*betaS)) + ((23.0*e4/360.0 + 251.0*e6/3780.0) * sin(4.0*betaS))
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+ ((761.0*e6/45360.0)*sin(6.0*betaS));
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return Coordinates(rad2deg(lon), rad2deg(lat));
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}
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@ -16,15 +16,10 @@ public:
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virtual Coordinates xy2ll(const QPointF &p) const;
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private:
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double _ra;
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double _sinLatOrigin;
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double _cosLatOrigin;
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double _absLatOrigin;
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double _latOrigin;
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double _lonOrigin;
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double _lon0;
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double _falseNorthing;
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double _falseEasting;
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double _a, _es, _es2, _qP, _beta0, _Rq, _D;
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};
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#endif // LAMBERTAZIMUTHAL_H
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