36 real lat1, real lon1, real azi1,
39 , _lat1(
Math::LatFix(lat1))
41 , _azi1(
Math::AngNormalize(azi1))
48 , _caps(caps | LATITUDE | AZIMUTH | LONG_UNROLL)
55 Math::norm(sbet1, cbet1); cbet1 = max(tiny_, cbet1);
56 _dn1 = sqrt(1 + g._ep2 *
Math::sq(sbet1));
59 _salp0 = _salp1 * cbet1;
72 _ssig1 = sbet1; _somg1 = _salp0 * sbet1;
73 _csig1 = _comg1 = sbet1 != 0 || _calp1 != 0 ? cbet1 * _calp1 : 1;
78 real eps = _k2 / (2 * (1 + sqrt(1 + _k2)) + _k2);
81 _A1m1 = Geodesic::A1m1f(eps);
82 Geodesic::C1f(eps, _C1a);
83 _B11 = Geodesic::SinCosSeries(
true, _ssig1, _csig1, _C1a, nC1_);
84 real s = sin(_B11), c = cos(_B11);
86 _stau1 = _ssig1 * c + _csig1 * s;
87 _ctau1 = _csig1 * c - _ssig1 * s;
93 Geodesic::C1pf(eps, _C1pa);
96 _A2m1 = Geodesic::A2m1f(eps);
97 Geodesic::C2f(eps, _C2a);
98 _B21 = Geodesic::SinCosSeries(
true, _ssig1, _csig1, _C2a, nC2_);
101 if (_caps & CAP_C3) {
103 _A3c = -_f * _salp0 * g.A3f(eps);
104 _B31 = Geodesic::SinCosSeries(
true, _ssig1, _csig1, _C3a, nC3_-1);
107 if (_caps & CAP_C4) {
110 _A4 =
Math::sq(_a) * _calp0 * _salp0 * g._e2;
111 _B41 = Geodesic::SinCosSeries(
false, _ssig1, _csig1, _C4a, nC4_);
117 real& lat2, real& lon2, real& azi2,
118 real& s12, real& m12,
119 real& M12, real& M21,
122 outmask &= _caps & OUT_MASK;
128 real sig12, ssig12, csig12, B12 = 0, AB1 = 0;
136 tau12 = s12_a12 / (_b * (1 + _A1m1)),
140 B12 = - Geodesic::SinCosSeries(
true,
141 _stau1 * c + _ctau1 * s,
142 _ctau1 * c - _stau1 * s,
144 sig12 = tau12 - (B12 - _B11);
145 ssig12 = sin(sig12); csig12 = cos(sig12);
146 if (abs(_f) > 0.01) {
169 ssig2 = _ssig1 * csig12 + _csig1 * ssig12,
170 csig2 = _csig1 * csig12 - _ssig1 * ssig12;
171 B12 = Geodesic::SinCosSeries(
true, ssig2, csig2, _C1a, nC1_);
172 real serr = (1 + _A1m1) * (sig12 + (B12 - _B11)) - s12_a12 / _b;
173 sig12 = sig12 - serr / sqrt(1 + _k2 *
Math::sq(ssig2));
174 ssig12 = sin(sig12); csig12 = cos(sig12);
179 real ssig2, csig2, sbet2, cbet2, salp2, calp2;
181 ssig2 = _ssig1 * csig12 + _csig1 * ssig12;
182 csig2 = _csig1 * csig12 - _ssig1 * ssig12;
183 real dn2 = sqrt(1 + _k2 *
Math::sq(ssig2));
185 if (arcmode || abs(_f) > 0.01)
186 B12 = Geodesic::SinCosSeries(
true, ssig2, csig2, _C1a, nC1_);
187 AB1 = (1 + _A1m1) * (B12 - _B11);
190 sbet2 = _calp0 * ssig2;
195 cbet2 = csig2 = tiny_;
197 salp2 = _salp0; calp2 = _calp0 * csig2;
200 s12 = arcmode ? _b * ((1 + _A1m1) * sig12 + AB1) : s12_a12;
204 real somg2 = _salp0 * ssig2, comg2 = csig2;
205 int E = _salp0 < 0 ? -1 : 1;
209 - (atan2( ssig2, csig2) - atan2( _ssig1, _csig1))
210 + (atan2(E * somg2, comg2) - atan2(E * _somg1, _comg1)))
211 : atan2(somg2 * _comg1 - comg2 * _somg1,
212 comg2 * _comg1 + somg2 * _somg1);
213 real lam12 = omg12 + _A3c *
214 ( sig12 + (Geodesic::SinCosSeries(
true, ssig2, csig2, _C3a, nC3_-1)
230 B22 = Geodesic::SinCosSeries(
true, ssig2, csig2, _C2a, nC2_),
231 AB2 = (1 + _A2m1) * (B22 - _B21),
232 J12 = (_A1m1 - _A2m1) * sig12 + (AB1 - AB2);
236 m12 = _b * ((dn2 * (_csig1 * ssig2) - _dn1 * (_ssig1 * csig2))
237 - _csig1 * csig2 * J12);
239 real t = _k2 * (ssig2 - _ssig1) * (ssig2 + _ssig1) / (_dn1 + dn2);
240 M12 = csig12 + (t * ssig2 - csig2 * J12) * _ssig1 / _dn1;
241 M21 = csig12 - (t * _ssig1 - _csig1 * J12) * ssig2 / dn2;
245 if (outmask &
AREA) {
247 B42 = Geodesic::SinCosSeries(
false, ssig2, csig2, _C4a, nC4_);
249 if (_calp0 == 0 || _salp0 == 0) {
251 salp12 = salp2 * _calp1 - calp2 * _salp1;
252 calp12 = calp2 * _calp1 + salp2 * _salp1;
256 if (salp12 == 0 && calp12 < 0) {
257 salp12 = tiny_ * _calp1;
269 salp12 = _calp0 * _salp0 *
270 (csig12 <= 0 ? _csig1 * (1 - csig12) + ssig12 * _ssig1 :
271 ssig12 * (_csig1 * ssig12 / (1 + csig12) + _ssig1));
274 S12 = _c2 * atan2(salp12, calp12) + _A4 * (B42 - _B41);
static T AngNormalize(T x)
Header for GeographicLib::GeodesicLine class.
Mathematical functions needed by GeographicLib.
static void sincosd(T x, T &sinx, T &cosx)
static void norm(T &x, T &y)
Math::real GenPosition(bool arcmode, real s12_a12, unsigned outmask, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21, real &S12) const
static T atan2d(T y, T x)
Namespace for GeographicLib.