31 namespace GeographicLib {
36 real lat1, real lon1, real azi1,
45 , _caps(caps | LATITUDE | AZIMUTH)
57 _salp1 = azi1 == -180 ? 0 : sin(alp1);
58 _calp1 = abs(azi1) == 90 ? 0 : cos(alp1);
59 real cbet1, sbet1, phi;
62 sbet1 = _f1 * sin(phi);
63 cbet1 = abs(lat1) == 90 ? tiny_ : cos(phi);
64 Geodesic::SinCosNorm(sbet1, cbet1);
65 _dn1 = sqrt(1 + g._ep2 *
Math::sq(sbet1));
68 _salp0 = _salp1 * cbet1;
81 _ssig1 = sbet1; _somg1 = _salp0 * sbet1;
82 _csig1 = _comg1 = sbet1 != 0 || _calp1 != 0 ? cbet1 * _calp1 : 1;
83 Geodesic::SinCosNorm(_ssig1, _csig1);
87 real eps = _k2 / (2 * (1 + sqrt(1 + _k2)) + _k2);
90 _A1m1 = Geodesic::A1m1f(eps);
91 Geodesic::C1f(eps, _C1a);
92 _B11 = Geodesic::SinCosSeries(
true, _ssig1, _csig1, _C1a, nC1_);
93 real s = sin(_B11), c = cos(_B11);
95 _stau1 = _ssig1 * c + _csig1 * s;
96 _ctau1 = _csig1 * c - _ssig1 * s;
102 Geodesic::C1pf(eps, _C1pa);
104 if (_caps & CAP_C2) {
105 _A2m1 = Geodesic::A2m1f(eps);
106 Geodesic::C2f(eps, _C2a);
107 _B21 = Geodesic::SinCosSeries(
true, _ssig1, _csig1, _C2a, nC2_);
110 if (_caps & CAP_C3) {
112 _A3c = -_f * _salp0 * g.A3f(eps);
113 _B31 = Geodesic::SinCosSeries(
true, _ssig1, _csig1, _C3a, nC3_-1);
116 if (_caps & CAP_C4) {
119 _A4 =
Math::sq(_a) * _calp0 * _salp0 * g._e2;
120 _B41 = Geodesic::SinCosSeries(
false, _ssig1, _csig1, _C4a, nC4_);
126 real& lat2, real& lon2, real& azi2,
127 real& s12, real& m12,
128 real& M12, real& M21,
131 outmask &= _caps & OUT_ALL;
137 real sig12, ssig12, csig12, B12 = 0, AB1 = 0;
141 real s12a = abs(s12_a12);
142 s12a -= 180 * floor(s12a / 180);
143 ssig12 = s12a == 0 ? 0 : sin(sig12);
144 csig12 = s12a == 90 ? 0 : cos(sig12);
148 tau12 = s12_a12 / (_b * (1 + _A1m1)),
152 B12 = - Geodesic::SinCosSeries(
true,
153 _stau1 * c + _ctau1 * s,
154 _ctau1 * c - _stau1 * s,
156 sig12 = tau12 - (B12 - _B11);
157 ssig12 = sin(sig12); csig12 = cos(sig12);
158 if (abs(_f) > 0.01) {
181 ssig2 = _ssig1 * csig12 + _csig1 * ssig12,
182 csig2 = _csig1 * csig12 - _ssig1 * ssig12;
183 B12 = Geodesic::SinCosSeries(
true, ssig2, csig2, _C1a, nC1_);
184 real serr = (1 + _A1m1) * (sig12 + (B12 - _B11)) - s12_a12 / _b;
185 sig12 = sig12 - serr / sqrt(1 + _k2 *
Math::sq(ssig2));
186 ssig12 = sin(sig12); csig12 = cos(sig12);
191 real omg12, lam12, lon12;
192 real ssig2, csig2, sbet2, cbet2, somg2, comg2, salp2, calp2;
194 ssig2 = _ssig1 * csig12 + _csig1 * ssig12;
195 csig2 = _csig1 * csig12 - _ssig1 * ssig12;
196 real dn2 = sqrt(1 + _k2 *
Math::sq(ssig2));
198 if (arcmode || abs(_f) > 0.01)
199 B12 = Geodesic::SinCosSeries(
true, ssig2, csig2, _C1a, nC1_);
200 AB1 = (1 + _A1m1) * (B12 - _B11);
203 sbet2 = _calp0 * ssig2;
208 cbet2 = csig2 = tiny_;
210 somg2 = _salp0 * ssig2; comg2 = csig2;
212 salp2 = _salp0; calp2 = _calp0 * csig2;
214 omg12 = atan2(somg2 * _comg1 - comg2 * _somg1,
215 comg2 * _comg1 + somg2 * _somg1);
218 s12 = arcmode ? _b * ((1 + _A1m1) * sig12 + AB1) : s12_a12;
221 lam12 = omg12 + _A3c *
222 ( sig12 + (Geodesic::SinCosSeries(
true, ssig2, csig2, _C3a, nC3_-1)
240 B22 = Geodesic::SinCosSeries(
true, ssig2, csig2, _C2a, nC2_),
241 AB2 = (1 + _A2m1) * (B22 - _B21),
242 J12 = (_A1m1 - _A2m1) * sig12 + (AB1 - AB2);
246 m12 = _b * ((dn2 * (_csig1 * ssig2) - _dn1 * (_ssig1 * csig2))
247 - _csig1 * csig2 * J12);
249 real t = _k2 * (ssig2 - _ssig1) * (ssig2 + _ssig1) / (_dn1 + dn2);
250 M12 = csig12 + (t * ssig2 - csig2 * J12) * _ssig1 / _dn1;
251 M21 = csig12 - (t * _ssig1 - _csig1 * J12) * ssig2 / dn2;
255 if (outmask &
AREA) {
257 B42 = Geodesic::SinCosSeries(
false, ssig2, csig2, _C4a, nC4_);
259 if (_calp0 == 0 || _salp0 == 0) {
261 salp12 = salp2 * _calp1 - calp2 * _salp1;
262 calp12 = calp2 * _calp1 + salp2 * _salp1;
266 if (salp12 == 0 && calp12 < 0) {
267 salp12 = tiny_ * _calp1;
279 salp12 = _calp0 * _salp0 *
280 (csig12 <= 0 ? _csig1 * (1 - csig12) + ssig12 * _ssig1 :
281 ssig12 * (_csig1 * ssig12 / (1 + csig12) + _ssig1));
284 S12 = _c2 * atan2(salp12, calp12) + _A4 * (B42 - _B41);