double KinematicsLatLon::closestDistOnTurn(const LatLonAlt& s0, const Velocity& v0, double R, int dir, const LatLonAlt& x, double maxDist) {
LatLonAlt cent = center(s0, v0.trk(), R, dir);
if (x.mkAlt(0).almostEquals(cent.mkAlt(0))) return -1.0;
double ang1 = GreatCircle::initial_course(cent,s0);
double ang2 = GreatCircle::initial_course(cent,x);
double delta = Util::turnDelta(ang1, ang2, dir);
double t = GreatCircle::small_circle_arc_length(R, delta);
if (maxDist > 0 && (t < 0 || t > maxDist)) {
double maxD = 2*M_PI*R;
if (t > (maxD + maxDist) / 2) {
return 0.0;
} else {
return maxDist;
}
}
return t;
}
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);
}
double KinematicsLatLon::closestTimeOnTurn(const LatLonAlt& s0, const Velocity& v0, double omega, const LatLonAlt& x, double endTime) {
LatLonAlt cent = center(s0,v0,omega);
if (x.mkAlt(0).almostEquals(cent.mkAlt(0))) return -1.0;
double ang1 = GreatCircle::initial_course(cent,s0);
double ang2 = GreatCircle::initial_course(cent,x);
double delta = Util::turnDelta(ang1, ang2, Util::sign(omega));
double t = std::abs(delta/omega);
if (endTime > 0 && (t < 0 || t > endTime)) {
double maxTime = 2*M_PI/std::abs(omega);
if (t > (maxTime + endTime) / 2) {
return 0.0;
} else {
return endTime;
}
}
return t;
}
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::turnByDist2D(const LatLonAlt& so, const LatLonAlt& center, int dir, double d, double gsAtd) {
double R = GreatCircle::distance(so, center);
double alpha = dir*d/R;
double vFinalTrk = GreatCircle::initial_course(center,so);
double nTrk = vFinalTrk + alpha;
LatLonAlt sn = GreatCircle::linear_initial(center, nTrk, R);
sn = sn.mkAlt(0.0);
double final_course = GreatCircle::final_course(center,sn);
double finalTrk = final_course + dir*M_PI/2;
Velocity vn = Velocity::mkTrkGsVs(finalTrk,gsAtd,0.0);
//double finalTrk = vo.trk()+alpha;
//double finalTrk = final_course + Util.sign(d)*Math.PI/2;
//Velocity vn = vo.mkTrk(finalTrk); // TODO: THIS IS WRONG -- cannot assume gs is constant!!!!
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);
}