553 lines
16 KiB
C++
553 lines
16 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:
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return *this;
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case Geodetic:
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switch(sys) {
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case Unknown: 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: 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: 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: 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) (*this)[1] += 360 * (1 + (unsigned long)((*this)[1]/360));
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else if((*this)[1] >= 360) (*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) (*this)[1] += 360*(1+(unsigned long)((*this)[1]/360));
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else if((*this)[1] >= 360) (*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) (*this)[1] += 360*(1+(unsigned long)((*this)[1]/360));
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else if((*this)[1] >= 360) (*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(tpr[0] * deg2rad);
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xyz[0] = tpr[2] * st * cos(tpr[1] * deg2rad);
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xyz[1] = tpr[2] * st * sin(tpr[1] * deg2rad);
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xyz[2] = tpr[2] * cos(tpr[0] * deg2rad);
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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(llh[0] * deg2rad);
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double clat = cos(llh[0] * deg2rad);
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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(llh[1] * deg2rad);
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xyz[1] = (nn + llh[2]) * clat * sin(llh[1] * deg2rad);
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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((90.0 - llr[0]) * deg2rad);
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sl = cos((90.0 - llr[0]) * deg2rad);
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if(llr[2] <= PIGeoPosition::position_tolerance / 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) llh[0] = -90.0;
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else 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(llh[0] * deg2rad);
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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] = 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) llr[0] = -90.0;
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else 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(geolat * deg2rad);
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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) return true;
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else 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) b += 360*(1+(unsigned long)(b/360));
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else if(b >= 360) 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) b += 360*(1+(unsigned long)(b/360));
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else if(b >= 360) 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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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 = r.latitudeGeodetic() * deg2rad;
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double lng = r.longitude() * deg2rad;
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double local_up;
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double cos_up;
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r.transformTo(Cartesian);
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s.transformTo(Cartesian);
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PIMathVectorT3d z = s - r;
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assertm(z.length() > 1e-4, "Positions are within .1 millimeter");
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PIMathVectorT3d kv; // Compute k vector in local North-East-Up (NEU) system
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kv[0] = cos(lat) * cos(lng);
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kv[1] = cos(lat) * sin(lng);
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kv[2] = sin(lat);
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local_up = z.dot(kv); // Take advantage of dot method to get Up coordinate in local NEU system
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cos_up = local_up / z.length(); // Let's get cos(z), being z the angle with respect to local vertical (Up);
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return 90.0 - ((acos(cos_up)) * rad2deg);
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}
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double PIGeoPosition::azimuth(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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double xy, xyz, cosl, sinl, sint, xn1, xn2, xn3, xe1, xe2;
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double z1, z2, z3, p1, p2, test, alpha;
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xy = r[0] * r[0] + r[1] * r[1];
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xyz = xy + r[2] * r[2];
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xy = sqrt(xy);
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xyz = sqrt(xyz);
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assertm(xy > 1e-14 && xyz > 1e-14, "Divide by Zero Error");
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cosl = r[0] / xy;
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sinl = r[1] / xy;
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sint = r[2] / xyz;
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xn1 = -sint * cosl;
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xn2 = -sint * sinl;
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xn3 = xy / xyz;
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xe1 = -sinl;
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xe2 = cosl;
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z1 = s[0] - r[0];
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z2 = s[1] - r[1];
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z3 = s[2] - r[2];
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p1 = (xn1 * z1) + (xn2 * z2) + (xn3 * z3) ;
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p2 = (xe1 * z1) + (xe2 * z2) ;
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test = piAbsd(p1) + piAbsd(p2);
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assertm(test >= 1.0e-16, "azAngle(), failed p1+p2 test");
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alpha = 90 - atan2(p1, p2) * rad2deg;
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if (alpha < 0) return alpha + 360;
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else return alpha;
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}
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|
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|
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double PIGeoPosition::azimuthGeodetic(const PIGeoPosition &p) const {
|
|
PIGeoPosition r(*this), s(p);
|
|
double lat = r.latitudeGeodetic() * deg2rad;
|
|
double lng = r.longitude() * deg2rad;
|
|
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 = atan2(local_e, local_n) * rad2deg;
|
|
if (alpha < 0.0) return alpha + 360.0;
|
|
else return alpha;
|
|
}
|
|
|
|
double PIGeoPosition::getCurvMeridian() const {
|
|
double slat = sin(latitudeGeodetic() * deg2rad);
|
|
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(latitudeGeodetic() * deg2rad);
|
|
return el.a / sqrt(1.0 - el.eccSquared() * slat * slat);
|
|
}
|
|
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