std::pair<LatLonAlt,Velocity> KinematicsLatLon::vsAccel(const LatLonAlt& so, const Velocity& vo, double t, double a) {
double dist = vo.gs()*t;
double currentTrk = vo.trk();
LatLonAlt sn = GreatCircle::linear_initial(so, currentTrk, dist);
double nsz = so.alt() + vo.z*t + 0.5*a*t*t;
sn = sn.mkAlt(nsz);
Velocity vn = vo.mkVs(vo.z + a*t);
return std::pair<LatLonAlt,Velocity>(sn,vn);
}
std::pair<LatLonAlt,Velocity> KinematicsLatLon::gsAccel(const LatLonAlt& so, const Velocity& vo, double t, double a) {
double dist = vo.gs()*t + 0.5*a*t*t;
double currentTrk = vo.trk();
LatLonAlt sn = GreatCircle::linear_initial(so, currentTrk, dist);
sn = sn.mkAlt(so.alt() + vo.z*t);
double vnGs = vo.gs() + a*t;
Velocity vn = vo.mkGs(vnGs);
//fpln(" $$$$$ gsAccel: sn = "+sn+" vn = "+vn);
return std::pair<LatLonAlt,Velocity>(sn,vn);
}
std::pair<LatLonAlt,Velocity> KinematicsLatLon::turnOmegaAlt(const LatLonAlt& so, const Velocity& vo, double t, double omega) {
double currentTrk = vo.trk();
double perpTrk;
if (omega > 0.0) {
perpTrk = currentTrk+M_PI/2;
} else {
perpTrk = currentTrk-M_PI/2;
}
double radius = turnRadiusByRate(vo.gs(), omega);
LatLonAlt center = GreatCircle::linear_initial(so, perpTrk, radius);
//f.pln("center="+center);
LatLonAlt sn = GreatCircle::small_circle_rotation(so,center,omega*t).mkAlt(so.alt()+vo.z*t);
double finalPerpTrk = GreatCircle::initial_course(sn,center);
double nTrk = finalPerpTrk - M_PI/2 * Util::sign(omega);
Velocity vn = vo.mkTrk(nTrk);
return std::pair<LatLonAlt,Velocity>(sn,vn);
}
std::pair<LatLonAlt,Velocity> KinematicsLatLon::turnOmega(const LatLonAlt& so, const Velocity& vo, double t, double omega) {
double currentTrk = vo.trk();
double perpTrk;
if (omega > 0) perpTrk = currentTrk+M_PI/2;
else perpTrk = currentTrk-M_PI/2;
double radius = Kinematics::turnRadiusByRate(vo.gs(), omega);
LatLonAlt center = GreatCircle::linear_initial(so, perpTrk, radius);
double alpha = omega*t;
double vFinalTrk = GreatCircle::initial_course(center,so);
double nTrk = vFinalTrk + alpha;
LatLonAlt sn = GreatCircle::linear_initial(center, nTrk, radius);
sn = sn.mkAlt(so.alt() + vo.z*t);
//double finalTrk = currentTrk+theta;
double final_course = GreatCircle::final_course(center,sn); // TODO: THIS IS PROBABLY BETTER
double finalTrk = final_course + Util::sign(omega)*M_PI/2;
Velocity vn = vo.mkTrk(finalTrk);
return std::pair<LatLonAlt,Velocity>(sn,vn);
}
std::pair<LatLonAlt,Velocity> KinematicsLatLon::turnByDist(const LatLonAlt& so, const Velocity& vo, double signedRadius, double d) {
double currentTrk = vo.trk();
double perpTrk;
if (signedRadius > 0) perpTrk = currentTrk+M_PI/2;
else perpTrk = currentTrk-M_PI/2;
double radius = std::abs(signedRadius);
LatLonAlt center = GreatCircle::linear_initial(so, perpTrk, radius);
double alpha = d/signedRadius;
double vFinalTrk = GreatCircle::initial_course(center,so);
double nTrk = vFinalTrk + alpha;
LatLonAlt sn = GreatCircle::linear_initial(center, nTrk, radius);
double t = d/vo.gs();
sn = sn.mkAlt(so.alt() + vo.z*t);
double final_course = GreatCircle::final_course(center,sn);
//double finalTrk = currentTrk+alpha;
double finalTrk = final_course + Util::sign(d)*M_PI/2;
Velocity vn = vo.mkTrk(finalTrk);
return std::pair<LatLonAlt,Velocity>(sn,vn);
}
std::pair<LatLonAlt,Velocity> KinematicsLatLon::turnRadius(const LatLonAlt& so, const Velocity& vo, double t, double signedRadius) {
double currentTrk = vo.trk();
double dir = Util::sign(signedRadius);
double perpTrk = currentTrk+dir*M_PI/2;
double radius = std::abs(signedRadius);
LatLonAlt center = GreatCircle::linear_initial(so, perpTrk, radius);
double pathDist = vo.gs()*t;
double theta = pathDist/radius;
//TODO: theta = pathDist/radius, assumes radius is a chord radius, when it is actually a great circle radius.
// for small distances the difference is not that big, but still...
//Note: The other problem is that this assumes a constant speed and constant ground speed through the turn.
// this may or may not be true.
double vFinalTrk = GreatCircle::initial_course(center,so);
double nTrk = vFinalTrk + dir*theta;
LatLonAlt sn = GreatCircle::linear_initial(center, nTrk, radius);
sn = sn.mkAlt(so.alt() + vo.z*t);
double final_course = GreatCircle::final_course(center,sn);
double finalTrk = final_course + dir*M_PI/2;
Velocity vn = vo.mkTrk(finalTrk);
return std::pair<LatLonAlt,Velocity>(sn,vn);
}
AziEquiProjection::AziEquiProjection(const LatLonAlt& lla) {
projAlt = lla.alt();
ref = spherical2xyz(lla.lat(),lla.lon());
llaRef = lla;
}
Vect3 AziEquiProjection::project(const LatLonAlt& lla) const {
return Vect3(project2(lla),lla.alt() - projAlt);
}