576 lines
17 KiB
C++
576 lines
17 KiB
C++
/*
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PIP - Platform Independent Primitives
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Class for geo position storage and conversions
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Andrey Bychkov work.a.b@yandex.ru
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "pigeoposition.h"
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const double PIGeoPosition::one_cm_tolerance = 0.01; // One centimeter tolerance.
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const double PIGeoPosition::one_mm_tolerance = 0.001; // One milimeter tolerance.
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const double PIGeoPosition::one_um_tolerance = 0.000001; // One micron tolerance.
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double PIGeoPosition::position_tolerance = PIGeoPosition::one_mm_tolerance; // Default tolerance in meters.
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PIGeoPosition::PIGeoPosition() {
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initialize(PIMathVectorT3d());
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}
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PIGeoPosition::PIGeoPosition(double a, double b, double c, PIGeoPosition::CoordinateSystem s, PIEllipsoidModel ell) {
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PIMathVectorT3d v;
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v[0] = a;
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v[1] = b;
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v[2] = c;
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initialize(v, s, ell);
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}
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PIGeoPosition::PIGeoPosition(PIMathVectorT3d v, PIGeoPosition::CoordinateSystem s, PIEllipsoidModel ell) {
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initialize(v, s, ell);
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}
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PIGeoPosition & PIGeoPosition::transformTo(PIGeoPosition::CoordinateSystem sys) {
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if (sys == Unknown || sys == s) return *this;
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PIGeoPosition tmp(*this);
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switch (s) {
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case Unknown: return *this;
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case Geodetic:
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switch (sys) {
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case Unknown:
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case Geodetic: return *this;
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case Geocentric:
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convertGeodeticToGeocentric(*this, tmp, el);
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tmp.s = Geocentric;
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break;
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case Cartesian:
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convertGeodeticToCartesian(*this, tmp, el);
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tmp.s = Cartesian;
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break;
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case Spherical:
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convertGeodeticToGeocentric(*this, tmp, el);
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tmp[0] = 90 - tmp[0]; // geocen -> sph
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tmp.s = Spherical;
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break;
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}
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break;
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case Geocentric:
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switch (sys) {
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case Unknown:
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case Geocentric: return *this;
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case Geodetic:
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convertGeocentricToGeodetic(*this, tmp, el);
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tmp.s = Geodetic;
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break;
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case Cartesian:
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convertGeocentricToCartesian(*this, tmp);
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tmp.s = Cartesian;
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break;
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case Spherical:
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tmp[0] = 90 - tmp[0]; // geocen -> sph
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tmp.s = Spherical;
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break;
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}
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break;
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case Cartesian:
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switch (sys) {
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case Unknown:
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case Cartesian: return *this;
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case Geodetic:
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convertCartesianToGeodetic(*this, tmp, el);
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tmp.s = Geodetic;
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break;
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case Geocentric:
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convertCartesianToGeocentric(*this, tmp);
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tmp.s = Geocentric;
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break;
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case Spherical:
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convertCartesianToSpherical(*this, tmp);
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tmp.s = Spherical;
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break;
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}
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break;
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case Spherical:
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switch (sys) {
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case Unknown:
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case Spherical: return *this;
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case Geodetic:
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(*this)[0] = 90 - (*this)[0]; // sph -> geocen
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convertGeocentricToGeodetic(*this, tmp, el);
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tmp.s = Geodetic;
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break;
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case Geocentric:
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tmp[0] = 90 - tmp[0]; // sph -> geocen
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tmp.s = Geocentric;
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break;
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case Cartesian:
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convertSphericalToCartesian(*this, tmp);
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tmp.s = Cartesian;
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break;
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}
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break;
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}
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*this = tmp;
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return *this;
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}
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double PIGeoPosition::x() const {
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if (s == Cartesian) return (*this)[0];
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PIGeoPosition t(*this);
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t.transformTo(Cartesian);
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return t[0];
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}
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double PIGeoPosition::y() const {
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if (s == Cartesian) return (*this)[1];
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PIGeoPosition t(*this);
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t.transformTo(Cartesian);
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return t[1];
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}
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double PIGeoPosition::z() const {
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if (s == Cartesian) return (*this)[2];
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PIGeoPosition t(*this);
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t.transformTo(Cartesian);
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return t[2];
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}
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double PIGeoPosition::latitudeGeodetic() const {
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if (s == Geodetic) return (*this)[0];
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PIGeoPosition t(*this);
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t.transformTo(Geodetic);
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return t[0];
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}
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double PIGeoPosition::latitudeGeocentric() const {
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if (s == Geocentric) return (*this)[0];
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PIGeoPosition t(*this);
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t.transformTo(Geocentric);
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return t[0];
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}
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double PIGeoPosition::longitude() const {
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if (s != Cartesian) return (*this)[1];
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PIGeoPosition t(*this);
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t.transformTo(Spherical);
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return t[1];
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}
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double PIGeoPosition::theta() const {
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if (s == Spherical) return (*this)[0];
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PIGeoPosition t(*this);
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t.transformTo(Spherical);
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return t[0];
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}
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double PIGeoPosition::phi() const {
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return longitude();
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}
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double PIGeoPosition::radius() const {
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if (s == Spherical || s == Geocentric) return (*this)[2];
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PIGeoPosition t(*this);
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t.transformTo(Spherical);
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return t[2];
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}
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double PIGeoPosition::height() const {
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if (s == Geodetic) return (*this)[2];
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PIGeoPosition t(*this);
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t.transformTo(Geodetic);
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return t[2];
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}
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PIGeoPosition & PIGeoPosition::setGeodetic(double lat, double lon, double ht, PIEllipsoidModel ell) {
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assertm(lat <= 90 && lat >= -90, "Achtung! Invalid latitude in setGeodetic");
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(*this)[0] = lat;
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(*this)[1] = lon;
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if ((*this)[1] < 0)
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(*this)[1] += 360 * (1 + (unsigned long)((*this)[1] / 360));
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else if ((*this)[1] >= 360)
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(*this)[1] -= 360 * (unsigned long)((*this)[1] / 360);
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(*this)[2] = ht;
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el = ell;
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s = Geodetic;
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return *this;
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}
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PIGeoPosition & PIGeoPosition::setGeocentric(double lat, double lon, double rad) {
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assertm(lat <= 90 && lat >= -90, "Achtung! Invalid latitude in setGeocentric");
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assertm(rad >= 0, "Achtung! Invalid radius in setGeocentric");
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(*this)[0] = lat;
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(*this)[1] = lon;
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(*this)[2] = rad;
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if ((*this)[1] < 0)
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(*this)[1] += 360 * (1 + (unsigned long)((*this)[1] / 360));
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else if ((*this)[1] >= 360)
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(*this)[1] -= 360 * (unsigned long)((*this)[1] / 360);
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s = Geocentric;
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return *this;
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}
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PIGeoPosition & PIGeoPosition::setSpherical(double theta, double phi, double rad) {
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assertm(theta <= 180 && theta >= 0, "Achtung! Invalid theta in setSpherical");
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assertm(rad >= 0, "Achtung! Invalid radius in setSpherical");
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(*this)[0] = theta;
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(*this)[1] = phi;
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(*this)[2] = rad;
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if ((*this)[1] < 0)
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(*this)[1] += 360 * (1 + (unsigned long)((*this)[1] / 360));
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else if ((*this)[1] >= 360)
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(*this)[1] -= 360 * (unsigned long)((*this)[1] / 360);
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s = Spherical;
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return *this;
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}
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PIGeoPosition & PIGeoPosition::setECEF(double x, double y, double z) {
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(*this)[0] = x;
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(*this)[1] = y;
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(*this)[2] = z;
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s = Cartesian;
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return *this;
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}
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void PIGeoPosition::convertSphericalToCartesian(const PIMathVectorT3d & tpr, PIMathVectorT3d & xyz) {
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double st = sin(toRad(tpr[0]));
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xyz[0] = tpr[2] * st * cos(toRad(tpr[1]));
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xyz[1] = tpr[2] * st * sin(toRad(tpr[1]));
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xyz[2] = tpr[2] * cos(toRad(tpr[0]));
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}
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void PIGeoPosition::convertCartesianToSpherical(const PIMathVectorT3d & xyz, PIMathVectorT3d & tpr) {
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tpr[2] = xyz.length();
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if (tpr[2] <= PIGeoPosition::position_tolerance / 5) { // zero-length Cartesian vector
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tpr[0] = 90.0;
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tpr[1] = 0.0;
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return;
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}
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tpr[0] = acos(xyz[2] / tpr[2]) * rad2deg;
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if (sqrt(xyz[0] * xyz[0] + xyz[1] * xyz[1]) < PIGeoPosition::position_tolerance / 5) { // pole
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tpr[1] = 0.0;
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return;
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}
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tpr[1] = atan2(xyz[1], xyz[0]) * rad2deg;
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if (tpr[1] < 0.0) tpr[1] += 360.0;
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}
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void PIGeoPosition::convertCartesianToGeodetic(const PIMathVectorT3d & xyz, PIMathVectorT3d & llh, PIEllipsoidModel ell) {
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double p, slat, nn, htold, latold;
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p = sqrt(xyz[0] * xyz[0] + xyz[1] * xyz[1]);
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if (p < PIGeoPosition::position_tolerance / 5) { // pole or origin
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llh[0] = (xyz[2] > 0.0 ? 90.0 : -90.0);
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llh[1] = 0.0; // lon undefined, really
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llh[2] = piAbsd(xyz[2]) - ell.a * sqrt(1.0 - ell.eccSquared());
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return;
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}
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llh[0] = atan2(xyz[2], p * (1.0 - ell.eccSquared()));
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llh[2] = 0;
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for (int i = 0; i < 5; i++) {
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slat = sin(llh[0]);
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nn = ell.a / sqrt(1.0 - ell.eccSquared() * slat * slat);
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htold = llh[2];
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llh[2] = p / cos(llh[0]) - nn;
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latold = llh[0];
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llh[0] = atan2(xyz[2], p * (1.0 - ell.eccSquared() * (nn / (nn + llh[2]))));
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if (piAbsd(llh[0] - latold) < 1.0e-9 && piAbsd(llh[2] - htold) < 1.0e-9 * ell.a) break;
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}
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llh[1] = atan2(xyz[1], xyz[0]);
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if (llh[1] < 0.0) llh[1] += M_2PI;
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llh[0] *= rad2deg;
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llh[1] *= rad2deg;
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}
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void PIGeoPosition::convertGeodeticToCartesian(const PIMathVectorT3d & llh, PIMathVectorT3d & xyz, PIEllipsoidModel ell) {
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double slat = sin(toRad(llh[0]));
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double clat = cos(toRad(llh[0]));
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double nn = ell.a / sqrt(1.0 - ell.eccSquared() * slat * slat);
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xyz[0] = (nn + llh[2]) * clat * cos(toRad(llh[1]));
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xyz[1] = (nn + llh[2]) * clat * sin(toRad(llh[1]));
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xyz[2] = (nn * (1.0 - ell.eccSquared()) + llh[2]) * slat;
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}
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void PIGeoPosition::convertCartesianToGeocentric(const PIMathVectorT3d & xyz, PIMathVectorT3d & llr) {
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convertCartesianToSpherical(xyz, llr);
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llr[0] = 90.0 - llr[0]; // convert theta to latitude
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}
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void PIGeoPosition::convertGeocentricToCartesian(const PIMathVectorT3d & llr, PIMathVectorT3d & xyz) {
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PIMathVectorT3d llh(llr);
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llh[0] = 90.0 - llh[0]; // convert latitude to theta
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convertSphericalToCartesian(llh, xyz);
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}
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void PIGeoPosition::convertGeocentricToGeodetic(const PIMathVectorT3d & llr, PIMathVectorT3d & llh, PIEllipsoidModel ell) {
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double cl, p, sl, slat, nn, htold, latold;
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llh[1] = llr[1]; // longitude is unchanged
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cl = sin(toRad(90.0 - llr[0]));
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sl = cos(toRad(90.0 - llr[0]));
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if (llr[2] <= PIGeoPosition::position_tolerance /
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5) { // radius is below tolerance, hence assign zero-length, arbitrarily set latitude = longitude = 0
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llh[0] = llh[1] = 0.0;
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llh[2] = -ell.a;
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return;
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} else if (cl < 1.e-10) { // near pole ... note that 1mm/radius(Earth) = 1.5e-10
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if (llr[0] < 0.0)
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llh[0] = -90.0;
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else
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llh[0] = 90.0;
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llh[1] = 0.0;
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llh[2] = llr[2] - ell.a * sqrt(1.0 - ell.eccSquared());
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return;
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}
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llh[0] = atan2(sl, cl * (1.0 - ell.eccSquared()));
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p = cl * llr[2];
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llh[2] = 0.0;
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for (int i = 0; i < 5; i++) {
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slat = sin(llh[0]);
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nn = ell.a / sqrt(1.0 - ell.eccSquared() * slat * slat);
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htold = llh[2];
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llh[2] = p / cos(llh[0]) - nn;
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latold = llh[0];
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llh[0] = atan2(sl, cl * (1.0 - ell.eccSquared() * (nn / (nn + llh[2]))));
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if (piAbsd(llh[0] - latold) < 1.0e-9 && piAbsd(llh[2] - htold) < 1.0e-9 * ell.a) break;
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}
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llh[0] *= rad2deg;
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}
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void PIGeoPosition::convertGeodeticToGeocentric(const PIMathVectorT3d & llh, PIMathVectorT3d & llr, PIEllipsoidModel ell) {
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double slat = sin(toRad(llh[0]));
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double nn = ell.a / sqrt(1.0 - ell.eccSquared() * slat * slat);
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llr[1] = llh[1]; // longitude is unchanged
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llr[2] =
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sqrt((nn + llh[2]) * (nn + llh[2]) + nn * ell.eccSquared() * (nn * ell.eccSquared() - 2 * (nn + llh[2])) * slat * slat); // radius
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if (llr[2] <= PIGeoPosition::position_tolerance / 5) { // radius is below tolerance, hence assign zero-length
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llr[0] = llr[1] = llr[2] = 0; // arbitrarily set latitude = longitude = 0
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return;
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}
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if (1 - piAbsd(slat) < 1.e-10) { // at the pole
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if (slat < 0)
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llr[0] = -90.0;
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else
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llr[0] = 90.0;
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llr[1] = 0.0;
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return;
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}
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llr[0] = acos((nn * (1.0 - ell.eccSquared()) + llh[2]) * slat / llr[2]); // theta
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llr[0] *= rad2deg;
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llr[0] = 90.0 - llr[0];
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}
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double PIGeoPosition::radiusEarth(double geolat, PIEllipsoidModel ell) {
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double slat = sin(toRad(geolat));
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double e = (1.0 - ell.eccSquared());
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double f = (1.0 + (e * e - 1.0) * slat * slat) / (1.0 - ell.eccSquared() * slat * slat);
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return (ell.a * sqrt(f));
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}
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PIGeoPosition & PIGeoPosition::operator=(const PIMathVectorT3d & v) {
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*((PIMathVectorT3d *)(this)) = v;
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return *this;
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}
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PIGeoPosition & PIGeoPosition::operator-=(const PIGeoPosition & right) {
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PIGeoPosition r(right);
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CoordinateSystem saves = s;
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transformTo(Cartesian);
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r.transformTo(Cartesian);
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(*(PIMathVectorT3d *)(this)) -= r;
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transformTo(saves);
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return *this;
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}
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PIGeoPosition & PIGeoPosition::operator+=(const PIGeoPosition & right) {
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PIGeoPosition r(right);
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CoordinateSystem saves = s;
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transformTo(Cartesian);
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r.transformTo(Cartesian);
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(*(PIMathVectorT3d *)(this)) += r;
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transformTo(saves);
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return *this;
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}
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bool PIGeoPosition::operator==(const PIGeoPosition & right) const {
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if (el.a != right.el.a || el.eccSquared() != right.el.eccSquared()) return false;
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if (range(*this, right) < position_tolerance)
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return true;
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else
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return false;
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}
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void PIGeoPosition::initialize(PIMathVectorT3d v, PIGeoPosition::CoordinateSystem sys, PIEllipsoidModel ell) {
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double a(v[0]), b(v[1]), c(v[2]);
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if (sys == Geodetic || sys == Geocentric) {
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assertm(a <= 90 && a >= -90, "Achtung! Invalid latitude in constructor");
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if (b < 0)
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b += 360 * (1 + (unsigned long)(b / 360));
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else if (b >= 360)
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b -= 360 * (unsigned long)(b / 360);
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}
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if (sys == Geocentric || sys == Spherical) {
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assertm(c >= 0, "Achtung! Invalid radius in constructor");
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}
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if (sys == Spherical) {
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assertm(a >= 0 && a <= 180, "Achtung! Invalid theta in constructor");
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if (b < 0)
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b += 360 * (1 + (unsigned long)(b / 360));
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else if (b >= 360)
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b -= 360 * (unsigned long)(b / 360);
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}
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(*this)[0] = a;
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(*this)[1] = b;
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(*this)[2] = c;
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el = ell;
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s = sys;
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|
}
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|
|
|
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double PIGeoPosition::range(const PIGeoPosition & a, const PIGeoPosition & b) {
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PIGeoPosition l(a), r(b);
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l.transformTo(PIGeoPosition::Cartesian);
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|
r.transformTo(PIGeoPosition::Cartesian);
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return (l - r).length();
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|
}
|
|
|
|
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double PIGeoPosition::elevation(const PIGeoPosition & p) const {
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PIGeoPosition r(*this), s(p);
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r.transformTo(Cartesian);
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|
s.transformTo(Cartesian);
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return r.angleElevation(s);
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|
}
|
|
|
|
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double PIGeoPosition::elevationGeodetic(const PIGeoPosition & p) const {
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|
PIGeoPosition r(*this), s(p);
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double lat = toRad(r.latitudeGeodetic());
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|
double lng = toRad(r.longitude());
|
|
double local_up;
|
|
double cos_up;
|
|
r.transformTo(Cartesian);
|
|
s.transformTo(Cartesian);
|
|
PIMathVectorT3d z = s - r;
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|
assertm(z.length() > 1e-4, "Positions are within .1 millimeter");
|
|
PIMathVectorT3d kv; // Compute k vector in local North-East-Up (NEU) system
|
|
kv[0] = cos(lat) * cos(lng);
|
|
kv[1] = cos(lat) * sin(lng);
|
|
kv[2] = sin(lat);
|
|
local_up = z.dot(kv); // Take advantage of dot method to get Up coordinate in local NEU system
|
|
cos_up = local_up / z.length(); // Let's get cos(z), being z the angle with respect to local vertical (Up);
|
|
return 90.0 - toDeg(acos(cos_up));
|
|
}
|
|
|
|
|
|
double PIGeoPosition::azimuth(const PIGeoPosition & p) const {
|
|
PIGeoPosition r(*this), s(p);
|
|
r.transformTo(Cartesian);
|
|
s.transformTo(Cartesian);
|
|
double xy, xyz, cosl, sinl, sint, xn1, xn2, xn3, xe1, xe2;
|
|
double z1, z2, z3, p1, p2, alpha;
|
|
xy = r[0] * r[0] + r[1] * r[1];
|
|
xyz = xy + r[2] * r[2];
|
|
xy = sqrt(xy);
|
|
xyz = sqrt(xyz);
|
|
assertm(xy > 1e-14 && xyz > 1e-14, "Divide by Zero Error");
|
|
cosl = r[0] / xy;
|
|
sinl = r[1] / xy;
|
|
sint = r[2] / xyz;
|
|
xn1 = -sint * cosl;
|
|
xn2 = -sint * sinl;
|
|
xn3 = xy / xyz;
|
|
xe1 = -sinl;
|
|
xe2 = cosl;
|
|
z1 = s[0] - r[0];
|
|
z2 = s[1] - r[1];
|
|
z3 = s[2] - r[2];
|
|
p1 = (xn1 * z1) + (xn2 * z2) + (xn3 * z3);
|
|
p2 = (xe1 * z1) + (xe2 * z2);
|
|
assertm((piAbsd(p1) + piAbsd(p2)) >= 1.0e-16, "azAngle(), failed p1+p2 test");
|
|
alpha = 90 - toDeg(atan2(p1, p2));
|
|
if (alpha < 0)
|
|
return alpha + 360;
|
|
else
|
|
return alpha;
|
|
}
|
|
|
|
|
|
double PIGeoPosition::azimuthGeodetic(const PIGeoPosition & p) const {
|
|
PIGeoPosition r(*this), s(p);
|
|
double lat = toRad(r.latitudeGeodetic());
|
|
double lng = toRad(r.longitude());
|
|
r.transformTo(Cartesian);
|
|
s.transformTo(Cartesian);
|
|
PIMathVectorT3d z;
|
|
z = s - r;
|
|
assertm(z.length() > 1e-4, "Positions are within 0.1 millimeter");
|
|
PIMathVectorT3d iv; // Compute i vector in local North-East-Up (NEU) system
|
|
iv[0] = -sin(lat) * cos(lng);
|
|
iv[1] = -sin(lat) * sin(lng);
|
|
iv[2] = cos(lat);
|
|
PIMathVectorT3d jv; // Compute j vector in local North-East-Up (NEU) system
|
|
jv[0] = -sin(lng);
|
|
jv[1] = cos(lng);
|
|
jv[2] = 0.0;
|
|
double local_n = z.dot(iv) / z.length(); // Now, let's use dot product to get localN unitary vectors
|
|
double local_e = z.dot(jv) / z.length(); // Now, let's use dot product to get localE unitary vector
|
|
double test = piAbsd(local_n) + piAbsd(local_e); // Let's test if computing azimuth has any sense
|
|
if (test < 1.0e-16) return 0.0; // Warning: If elevation is very close to 90 degrees, we will return azimuth = 0.0
|
|
double alpha = toDeg(atan2(local_e, local_n));
|
|
if (alpha < 0.0)
|
|
return alpha + 360.0;
|
|
else
|
|
return alpha;
|
|
}
|
|
|
|
double PIGeoPosition::getCurvMeridian() const {
|
|
double slat = sin(toRad(latitudeGeodetic()));
|
|
double w = 1.0 / sqrt(1.0 - el.eccSquared() * slat * slat);
|
|
return el.a * (1.0 - el.eccSquared()) * w * w * w;
|
|
}
|
|
|
|
|
|
double PIGeoPosition::getCurvPrimeVertical() const {
|
|
double slat = sin(toRad(latitudeGeodetic()));
|
|
return el.a / sqrt(1.0 - el.eccSquared() * slat * slat);
|
|
}
|