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Datum shift optimization (precompute ellipsoid constants)
+ projections code unification
This commit is contained in:
parent
b3940283a8
commit
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@ -46,11 +46,11 @@ Defense.
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#define ONE_MINUS_SQR(x) (1.0 - (x) * (x))
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#define ALBERS_Q(slat, one_minus_sqr_es_sin, es_sin) \
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(_one_minus_es2 * ((slat) / (one_minus_sqr_es_sin) - \
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(1 / (_two_es)) * log((1 - (es_sin)) / (1 + (es_sin)))))
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#define ALBERS_M(clat, one_minus_sqr_es_sin) \
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((clat) / sqrt(one_minus_sqr_es_sin))
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#define ALBERS_Q(slat, one_minus_sqr_e_sin, es_sin) \
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(_one_minus_es * ((slat) / (one_minus_sqr_e_sin) - \
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(1 / (_two_e)) * log((1 - (es_sin)) / (1 + (es_sin)))))
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#define ALBERS_M(clat, one_minus_sqr_e_sin) \
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((clat) / sqrt(one_minus_sqr_e_sin))
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AlbersEqual::AlbersEqual(const Ellipsoid *ellipsoid, double standardParallel1,
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@ -60,8 +60,8 @@ AlbersEqual::AlbersEqual(const Ellipsoid *ellipsoid, double standardParallel1,
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double sin_lat, sin_lat1, sin_lat2, cos_lat1, cos_lat2;
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double m1, m2, sqr_m1, sqr_m2;
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double q0, q1, q2;
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double es_sin, es_sin1, es_sin2;
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double one_minus_sqr_es_sin1, one_minus_sqr_es_sin2;
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double e_sin, e_sin1, e_sin2;
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double one_minus_sqr_e_sin1, one_minus_sqr_e_sin2;
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double nq0;
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double sp1, sp2;
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@ -75,31 +75,30 @@ AlbersEqual::AlbersEqual(const Ellipsoid *ellipsoid, double standardParallel1,
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sp2 = deg2rad(standardParallel2);
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_a2 = ellipsoid->radius() * ellipsoid->radius();
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_es2 = 2 * ellipsoid->flattening() - ellipsoid->flattening()
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* ellipsoid->flattening();
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_es = sqrt(_es2);
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_one_minus_es2 = 1 - _es2;
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_two_es = 2 * _es;
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_es = ellipsoid->es();
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_e = sqrt(_es);
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_one_minus_es = 1 - _es;
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_two_e = 2 * _e;
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sin_lat = sin(_latitudeOrigin);
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es_sin = _es * sin_lat;
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q0 = ALBERS_Q(sin_lat, ONE_MINUS_SQR(es_sin), es_sin);
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e_sin = _e * sin_lat;
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q0 = ALBERS_Q(sin_lat, ONE_MINUS_SQR(e_sin), e_sin);
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sin_lat1 = sin(sp1);
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cos_lat1 = cos(sp1);
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es_sin1 = _es * sin_lat1;
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one_minus_sqr_es_sin1 = ONE_MINUS_SQR(es_sin1);
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m1 = ALBERS_M(cos_lat1, one_minus_sqr_es_sin1);
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q1 = ALBERS_Q(sin_lat1, one_minus_sqr_es_sin1, es_sin1);
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e_sin1 = _e * sin_lat1;
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one_minus_sqr_e_sin1 = ONE_MINUS_SQR(e_sin1);
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m1 = ALBERS_M(cos_lat1, one_minus_sqr_e_sin1);
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q1 = ALBERS_Q(sin_lat1, one_minus_sqr_e_sin1, e_sin1);
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sqr_m1 = m1 * m1;
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if (fabs(sp1 - sp2) > 1.0e-10) {
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sin_lat2 = sin(sp2);
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cos_lat2 = cos(sp2);
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es_sin2 = _es * sin_lat2;
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one_minus_sqr_es_sin2 = ONE_MINUS_SQR(es_sin2);
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m2 = ALBERS_M(cos_lat2, one_minus_sqr_es_sin2);
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q2 = ALBERS_Q(sin_lat2, one_minus_sqr_es_sin2, es_sin2);
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e_sin2 = _e * sin_lat2;
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one_minus_sqr_e_sin2 = ONE_MINUS_SQR(e_sin2);
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m2 = ALBERS_M(cos_lat2, one_minus_sqr_e_sin2);
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q2 = ALBERS_Q(sin_lat2, one_minus_sqr_e_sin2, e_sin2);
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sqr_m2 = m2 * m2;
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_n = (sqr_m1 - sqr_m2) / (q2 - q1);
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} else
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@ -115,7 +114,7 @@ PointD AlbersEqual::ll2xy(const Coordinates &c) const
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{
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double dlam;
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double sin_lat;
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double es_sin;
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double e_sin;
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double q;
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double rho;
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double theta;
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@ -129,8 +128,8 @@ PointD AlbersEqual::ll2xy(const Coordinates &c) const
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dlam += M_2_PI;
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sin_lat = sin(deg2rad(c.lat()));
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es_sin = _es * sin_lat;
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q = ALBERS_Q(sin_lat, ONE_MINUS_SQR(es_sin), es_sin);
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e_sin = _e * sin_lat;
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q = ALBERS_Q(sin_lat, ONE_MINUS_SQR(e_sin), e_sin);
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nq = _n * q;
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rho = (_C < nq) ? 0 : _a_over_n * sqrt(_C - nq);
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theta = _n * dlam;
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@ -147,7 +146,7 @@ Coordinates AlbersEqual::xy2ll(const PointD &p) const
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double rho, rho_n;
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double phi, delta_phi = 1.0;
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double sin_phi;
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double es_sin, one_minus_sqr_es_sin;
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double e_sin, one_minus_sqr_e_sin;
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double theta = 0.0;
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int count = 30;
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double tolerance = 4.85e-10;
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@ -170,7 +169,7 @@ Coordinates AlbersEqual::xy2ll(const PointD &p) const
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theta = atan2(dx, rho0_minus_dy);
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rho_n = rho * _n;
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q = (_C - (rho_n * rho_n) / _a2) / _n;
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qc = 1 - ((_one_minus_es2) / (_two_es)) * log((1.0 - _es) / (1.0 + _es));
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qc = 1 - ((_one_minus_es) / (_two_e)) * log((1.0 - _e) / (1.0 + _e));
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if (fabs(fabs(qc) - fabs(q)) > 1.0e-6) {
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q_over_2 = q / 2.0;
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if (q_over_2 > 1.0)
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@ -179,17 +178,17 @@ Coordinates AlbersEqual::xy2ll(const PointD &p) const
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lat = -M_PI_2;
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else {
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phi = asin(q_over_2);
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if (_es < 1.0e-10)
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if (_e < 1.0e-10)
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lat = phi;
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else {
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while ((fabs(delta_phi) > tolerance) && count) {
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sin_phi = sin(phi);
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es_sin = _es * sin_phi;
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one_minus_sqr_es_sin = ONE_MINUS_SQR(es_sin);
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delta_phi = (one_minus_sqr_es_sin * one_minus_sqr_es_sin)
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/ (2.0 * cos(phi)) * (q / (_one_minus_es2) - sin_phi
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/ one_minus_sqr_es_sin + (log((1.0 - es_sin)
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/ (1.0 + es_sin)) / (_two_es)));
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e_sin = _e * sin_phi;
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one_minus_sqr_e_sin = ONE_MINUS_SQR(e_sin);
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delta_phi = (one_minus_sqr_e_sin * one_minus_sqr_e_sin)
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/ (2.0 * cos(phi)) * (q / (_one_minus_es) - sin_phi
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/ one_minus_sqr_e_sin + (log((1.0 - e_sin)
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/ (1.0 + e_sin)) / (_two_e)));
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phi += delta_phi;
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count --;
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}
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@ -27,11 +27,11 @@ private:
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double _rho0;
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double _C;
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double _n;
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double _e;
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double _es;
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double _es2;
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double _a_over_n;
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double _one_minus_es2;
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double _two_es;
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double _one_minus_es;
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double _two_e;
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};
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#endif // ALBERSEQUAL_H
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@ -113,7 +113,7 @@ Coordinates Datum::toWGS84(const Coordinates &c) const
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switch (_transformation) {
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case Helmert:
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return Geocentric::toGeodetic(helmert(Geocentric::fromGeodetic(c,
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*this)), WGS84);
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ellipsoid())), WGS84.ellipsoid());
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case Molodensky:
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return molodensky(c, *this, WGS84);
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default:
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@ -126,7 +126,7 @@ Coordinates Datum::fromWGS84(const Coordinates &c) const
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switch (_transformation) {
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case Helmert:
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return Geocentric::toGeodetic(helmertr(Geocentric::fromGeodetic(c,
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WGS84)), *this);
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WGS84.ellipsoid())), ellipsoid());
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case Molodensky:
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return molodensky(c, WGS84, *this);
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default:
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@ -66,6 +66,13 @@ void Ellipsoid::loadList(const QString &path)
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}
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}
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Ellipsoid::Ellipsoid(double radius, double flattening)
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: _radius(radius), _flattening(flattening)
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{
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_es = 2.0 * flattening - flattening * flattening;
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_b = radius * (1.0 - flattening);
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}
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#ifndef QT_NO_DEBUG
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QDebug operator<<(QDebug dbg, const Ellipsoid &ellipsoid)
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{
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@ -9,12 +9,13 @@
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class Ellipsoid
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{
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public:
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Ellipsoid() : _radius(NAN), _flattening(NAN) {}
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Ellipsoid(double radius, double flattening)
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: _radius(radius), _flattening(flattening) {}
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Ellipsoid() : _radius(NAN), _flattening(NAN), _es(NAN), _b(NAN) {}
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Ellipsoid(double radius, double flattening);
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double radius() const {return _radius;}
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double flattening() const {return _flattening;}
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double es() const {return _es;}
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double b() const {return _b;}
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bool isNull() const
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{return (std::isnan(_radius) && std::isnan(_flattening));}
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@ -27,6 +28,7 @@ public:
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private:
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double _radius;
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double _flattening;
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double _es, _b;
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static QMap<int, Ellipsoid> WGS84();
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static QMap<int, Ellipsoid> _ellipsoids;
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@ -41,42 +41,34 @@ Defense.
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*/
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#include "datum.h"
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#include "ellipsoid.h"
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#include "geocentric.h"
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#define AD_C 1.0026000
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Point3D Geocentric::fromGeodetic(const Coordinates &c, const Datum &datum)
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Point3D Geocentric::fromGeodetic(const Coordinates &c, const Ellipsoid *e)
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{
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const Ellipsoid *e = datum.ellipsoid();
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double e2 = 2.0 * e->flattening() - e->flattening() * e->flattening();
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double lat = deg2rad(c.lat());
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double lon = deg2rad(c.lon());
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double slat = sin(lat);
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double slat2 = slat * slat;
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double clat = cos(lat);
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double Rn = e->radius() / (sqrt(1.0 - e2 * slat2));
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double Rn = e->radius() / (sqrt(1.0 - e->es() * slat2));
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if (lon > M_PI)
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lon -= M_2_PI;
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return Point3D(Rn * clat * cos(lon), Rn * clat * sin(lon),
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(Rn * (1 - e2)) * slat);
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(Rn * (1 - e->es())) * slat);
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}
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Coordinates Geocentric::toGeodetic(const Point3D &p, const Datum &datum)
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Coordinates Geocentric::toGeodetic(const Point3D &p, const Ellipsoid *e)
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{
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const Ellipsoid *e = datum.ellipsoid();
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double b = e->radius() * (1.0 - e->flattening());
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double e2 = 2.0 * e->flattening() - e->flattening() * e->flattening();
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double ep2 = (1.0 / (1.0 - e2)) - 1.0;
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double ep2 = (1.0 / (1.0 - e->es())) - 1.0;
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bool pole = false;
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double lat, lon;
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if (p.x() == 0.0) {
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if (p.y() > 0)
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lon = M_PI_2;
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@ -102,8 +94,8 @@ Coordinates Geocentric::toGeodetic(const Point3D &p, const Datum &datum)
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double Sin_B0 = T0 / S0;
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double Cos_B0 = W / S0;
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double Sin3_B0 = Sin_B0 * Sin_B0 * Sin_B0;
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double T1 = p.z() + b * ep2 * Sin3_B0;
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double Sum = W - e->radius() * e2 * Cos_B0 * Cos_B0 * Cos_B0;
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double T1 = p.z() + e->b() * ep2 * Sin3_B0;
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double Sum = W - e->radius() * e->es() * Cos_B0 * Cos_B0 * Cos_B0;
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double S1 = sqrt(T1*T1 + Sum * Sum);
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double Sin_p1 = T1 / S1;
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double Cos_p1 = Sum / S1;
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@ -4,7 +4,7 @@
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#include <cmath>
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#include "common/coordinates.h"
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class Datum;
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class Ellipsoid;
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class Point3D {
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public:
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@ -22,8 +22,8 @@ private:
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};
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namespace Geocentric {
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Point3D fromGeodetic(const Coordinates &c, const Datum &datum);
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Coordinates toGeodetic(const Point3D &p, const Datum &datum);
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Point3D fromGeodetic(const Coordinates &c, const Ellipsoid *e);
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Coordinates toGeodetic(const Point3D &p, const Ellipsoid *e);
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}
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#endif // GEOCENTRIC_H
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@ -16,19 +16,17 @@ LambertAzimuthal::LambertAzimuthal(const Ellipsoid *ellipsoid,
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_lon0 = deg2rad(longitudeOrigin);
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_a = ellipsoid->radius();
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_es = ellipsoid->es();
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_e = sqrt(_es);
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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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double q0 = (1.0 - _es) * ((sin(lat0) / (1.0 - _es * sin2(lat0)))
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- ((1.0/(2.0*_e)) * log((1.0 - _e * sin(lat0)) / (1.0 + _e
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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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_qP = (1.0 - _es) * ((1.0 / (1.0 - _es)) - ((1.0/(2.0*_e))
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* log((1.0 - _e) / (1.0 + _e))));
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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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_D = _a * (cos(lat0) / sqrt(1.0 - _es * sin2(lat0))) / (_Rq * cos(_beta0));
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}
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PointD LambertAzimuthal::ll2xy(const Coordinates &c) const
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@ -36,8 +34,8 @@ PointD LambertAzimuthal::ll2xy(const Coordinates &c) const
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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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double q = (1.0 - _es) * ((sin(lat) / (1.0 - _es * sin2(lat)))
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- ((1.0/(2.0*_e)) * log((1.0 - _e * sin(lat)) / (1.0 + _e
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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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@ -52,8 +50,8 @@ PointD LambertAzimuthal::ll2xy(const Coordinates &c) const
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Coordinates LambertAzimuthal::xy2ll(const PointD &p) const
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{
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double es4 = _es2 * _es2;
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double es6 = _es2 * es4;
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double es4 = _es * _es;
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double es6 = _es * es4;
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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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@ -64,7 +62,7 @@ Coordinates LambertAzimuthal::xy2ll(const PointD &p) const
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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*es4/180.0 + 517.0*es6/5040.0)
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double lat = betaS + ((_es/3.0 + 31.0*es4/180.0 + 517.0*es6/5040.0)
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* sin(2.0*betaS)) + ((23.0*es4/360.0 + 251.0*es6/3780.0) * sin(4.0*betaS))
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+ ((761.0*es6/45360.0)*sin(6.0*betaS));
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@ -20,7 +20,7 @@ private:
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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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double _a, _e, _es, _qP, _beta0, _Rq, _D;
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};
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#endif // LAMBERTAZIMUTHAL_H
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@ -57,8 +57,7 @@ LambertConic1::LambertConic1(const Ellipsoid *ellipsoid, double latitudeOrigin,
|
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double longitudeOrigin, double scale, double falseEasting,
|
||||
double falseNorthing)
|
||||
{
|
||||
double es2;
|
||||
double es_sin;
|
||||
double e_sin;
|
||||
double m0;
|
||||
double lat_orig;
|
||||
|
||||
@ -71,16 +70,14 @@ LambertConic1::LambertConic1(const Ellipsoid *ellipsoid, double latitudeOrigin,
|
||||
_falseEasting = falseEasting;
|
||||
_falseNorthing = falseNorthing;
|
||||
|
||||
es2 = 2.0 * ellipsoid->flattening() - ellipsoid->flattening()
|
||||
* ellipsoid->flattening();
|
||||
_es = sqrt(es2);
|
||||
_es_over_2 = _es / 2.0;
|
||||
_e = sqrt(ellipsoid->es());
|
||||
_e_over_2 = _e / 2.0;
|
||||
|
||||
_n = sin(lat_orig);
|
||||
|
||||
es_sin = _es * sin(lat_orig);
|
||||
m0 = LAMBERT_m(cos(lat_orig), es_sin);
|
||||
_t0 = LAMBERT1_t(lat_orig, es_sin, _es_over_2);
|
||||
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;
|
||||
|
||||
@ -97,7 +94,7 @@ PointD LambertConic1::ll2xy(const Coordinates &c) const
|
||||
|
||||
|
||||
if (fabs(fabs(lat) - M_PI_2) > 1.0e-10) {
|
||||
t = LAMBERT1_t(lat, _es * sin(lat), _es_over_2);
|
||||
t = LAMBERT1_t(lat, _e * sin(lat), _e_over_2);
|
||||
rho = _rho0 * pow(t / _t0, _n);
|
||||
} else
|
||||
rho = 0.0;
|
||||
@ -148,9 +145,9 @@ Coordinates LambertConic1::xy2ll(const PointD &p) const
|
||||
PHI = M_PI_2 - 2.0 * atan(t);
|
||||
while (fabs(PHI - tempPHI) > tolerance && count) {
|
||||
tempPHI = PHI;
|
||||
es_sin = _es * sin(PHI);
|
||||
es_sin = _e * sin(PHI);
|
||||
PHI = M_PI_2 - 2.0 * atan(t * pow((1.0 - es_sin) / (1.0 + es_sin),
|
||||
_es_over_2));
|
||||
_e_over_2));
|
||||
count--;
|
||||
}
|
||||
|
||||
|
||||
@ -23,8 +23,8 @@ private:
|
||||
double _falseEasting;
|
||||
double _falseNorthing;
|
||||
|
||||
double _es;
|
||||
double _es_over_2;
|
||||
double _e;
|
||||
double _e_over_2;
|
||||
double _n;
|
||||
double _t0;
|
||||
double _rho0;
|
||||
|
||||
@ -47,28 +47,29 @@ Defense.
|
||||
Mercator::Mercator(const Ellipsoid *ellipsoid, double latitudeOrigin,
|
||||
double longitudeOrigin, double falseEasting, double falseNorthing)
|
||||
{
|
||||
double es = ellipsoid->es();
|
||||
double es2;
|
||||
double es3;
|
||||
double es4;
|
||||
double sin_olat;
|
||||
|
||||
_a = ellipsoid->radius();
|
||||
_latitudeOrigin = deg2rad(latitudeOrigin);
|
||||
_longitudeOrigin = deg2rad(longitudeOrigin);
|
||||
if (_longitudeOrigin > M_PI)
|
||||
_longitudeOrigin -= M_2_PI;
|
||||
_falseNorthing = falseNorthing;
|
||||
_falseEasting = falseEasting;
|
||||
_es = 2 * ellipsoid->flattening() - ellipsoid->flattening()
|
||||
* ellipsoid->flattening();
|
||||
_e = sqrt(_es);
|
||||
|
||||
_a = ellipsoid->radius();
|
||||
_e = sqrt(es);
|
||||
|
||||
sin_olat = sin(_latitudeOrigin);
|
||||
_scaleFactor = 1.0 / (sqrt(1.e0 - _es * sin_olat * sin_olat)
|
||||
_scaleFactor = 1.0 / (sqrt(1.e0 - es * sin_olat * sin_olat)
|
||||
/ cos(_latitudeOrigin));
|
||||
es2 = _es * _es;
|
||||
es3 = es2 * _es;
|
||||
es4 = es3 * _es;
|
||||
_ab = _es / 2.e0 + 5.e0 * es2 / 24.e0 + es3 / 12.e0 + 13.e0 * es4 / 360.e0;
|
||||
es2 = es * es;
|
||||
es3 = es2 * es;
|
||||
es4 = es3 * es;
|
||||
_ab = es / 2.e0 + 5.e0 * es2 / 24.e0 + es3 / 12.e0 + 13.e0 * es4 / 360.e0;
|
||||
_bb = 7.e0 * es2 / 48.e0 + 29.e0 * es3 / 240.e0 + 811.e0 * es4 / 11520.e0;
|
||||
_cb = 7.e0 * es3 / 120.e0 + 81.e0 * es4 / 1120.e0;
|
||||
_db = 4279.e0 * es4 / 161280.e0;
|
||||
|
||||
@ -17,7 +17,7 @@ public:
|
||||
virtual Coordinates xy2ll(const PointD &p) const;
|
||||
|
||||
private:
|
||||
double _a, _es, _e;
|
||||
double _a, _e;
|
||||
double _latitudeOrigin;
|
||||
double _longitudeOrigin;
|
||||
double _falseNorthing;
|
||||
|
||||
@ -72,11 +72,9 @@ TransverseMercator::TransverseMercator(const Ellipsoid *ellipsoid,
|
||||
_falseEasting = falseEasting;
|
||||
_falseNorthing = falseNorthing;
|
||||
|
||||
_es = 2 * ellipsoid->flattening() - ellipsoid->flattening()
|
||||
* ellipsoid->flattening();
|
||||
_es = ellipsoid->es();
|
||||
_ebs = (1 / (1 - _es)) - 1;
|
||||
|
||||
b = _a * (1 - ellipsoid->flattening());
|
||||
b = ellipsoid->b();
|
||||
|
||||
tn = (_a - b) / (_a + b);
|
||||
tn2 = tn * tn;
|
||||
|
||||
@ -24,7 +24,6 @@ private:
|
||||
double _falseEasting;
|
||||
double _falseNorthing;
|
||||
double _a;
|
||||
|
||||
double _es;
|
||||
double _ebs;
|
||||
double _ap, _bp, _cp, _dp, _ep;
|
||||
|
||||
Loading…
Reference in New Issue
Block a user