31 namespace GeographicLib {
36 real lat1, real lon1, real azi1,
37 unsigned caps)
throw()
44 , _caps(caps | LATITUDE | AZIMUTH)
53 real alp1 = azi1 * Math::degree<real>();
56 _salp1 = azi1 == -180 ? 0 : sin(alp1);
57 _calp1 = abs(azi1) == 90 ? 0 : cos(alp1);
58 real cbet1, sbet1, phi;
59 phi = lat1 * Math::degree<real>();
61 sbet1 = _f1 * sin(phi);
62 cbet1 = abs(lat1) == 90 ? Geodesic::tiny_ : cos(phi);
63 Geodesic::SinCosNorm(sbet1, cbet1);
64 _dn1 = sqrt(1 + g._ep2 *
Math::sq(sbet1));
67 _salp0 = _salp1 * cbet1;
80 _ssig1 = sbet1; _somg1 = _salp0 * sbet1;
81 _csig1 = _comg1 = sbet1 != 0 || _calp1 != 0 ? cbet1 * _calp1 : 1;
82 Geodesic::SinCosNorm(_ssig1, _csig1);
86 real eps = _k2 / (2 * (1 + sqrt(1 + _k2)) + _k2);
89 _A1m1 = Geodesic::A1m1f(eps);
90 Geodesic::C1f(eps, _C1a);
91 _B11 = Geodesic::SinCosSeries(
true, _ssig1, _csig1, _C1a, nC1_);
92 real s = sin(_B11), c = cos(_B11);
94 _stau1 = _ssig1 * c + _csig1 * s;
95 _ctau1 = _csig1 * c - _ssig1 * s;
101 Geodesic::C1pf(eps, _C1pa);
103 if (_caps & CAP_C2) {
104 _A2m1 = Geodesic::A2m1f(eps);
105 Geodesic::C2f(eps, _C2a);
106 _B21 = Geodesic::SinCosSeries(
true, _ssig1, _csig1, _C2a, nC2_);
109 if (_caps & CAP_C3) {
111 _A3c = -_f * _salp0 * g.A3f(eps);
112 _B31 = Geodesic::SinCosSeries(
true, _ssig1, _csig1, _C3a, nC3_-1);
115 if (_caps & CAP_C4) {
118 _A4 =
Math::sq(_a) * _calp0 * _salp0 * g._e2;
119 _B41 = Geodesic::SinCosSeries(
false, _ssig1, _csig1, _C4a, nC4_);
125 real& lat2, real& lon2, real& azi2,
126 real& s12, real& m12,
127 real& M12, real& M21,
130 outmask &= _caps & OUT_ALL;
131 if (!( Init() && (arcmode || (_caps & DISTANCE_IN & OUT_ALL)) ))
133 return Math::NaN<real>();
136 real sig12, ssig12, csig12, B12 = 0, AB1 = 0;
139 sig12 = s12_a12 * Math::degree<real>();
140 real s12a = abs(s12_a12);
141 s12a -= 180 * floor(s12a / 180);
142 ssig12 = s12a == 0 ? 0 : sin(sig12);
143 csig12 = s12a == 90 ? 0 : cos(sig12);
147 tau12 = s12_a12 / (_b * (1 + _A1m1)),
151 B12 = - Geodesic::SinCosSeries(
true,
152 _stau1 * c + _ctau1 * s,
153 _ctau1 * c - _stau1 * s,
155 sig12 = tau12 - (B12 - _B11);
156 ssig12 = sin(sig12); csig12 = cos(sig12);
157 if (abs(_f) > 0.01) {
180 ssig2 = _ssig1 * csig12 + _csig1 * ssig12,
181 csig2 = _csig1 * csig12 - _ssig1 * ssig12;
182 B12 = Geodesic::SinCosSeries(
true, ssig2, csig2, _C1a, nC1_);
183 real serr = (1 + _A1m1) * (sig12 + (B12 - _B11)) - s12_a12 / _b;
184 sig12 = sig12 - serr / sqrt(1 + _k2 *
Math::sq(ssig2));
185 ssig12 = sin(sig12); csig12 = cos(sig12);
190 real omg12, lam12, lon12;
191 real ssig2, csig2, sbet2, cbet2, somg2, comg2, salp2, calp2;
193 ssig2 = _ssig1 * csig12 + _csig1 * ssig12;
194 csig2 = _csig1 * csig12 - _ssig1 * ssig12;
195 real dn2 = sqrt(1 + _k2 *
Math::sq(ssig2));
196 if (outmask & (DISTANCE | REDUCEDLENGTH | GEODESICSCALE)) {
197 if (arcmode || abs(_f) > 0.01)
198 B12 = Geodesic::SinCosSeries(
true, ssig2, csig2, _C1a, nC1_);
199 AB1 = (1 + _A1m1) * (B12 - _B11);
202 sbet2 = _calp0 * ssig2;
207 cbet2 = csig2 = Geodesic::tiny_;
209 somg2 = _salp0 * ssig2; comg2 = csig2;
211 salp2 = _salp0; calp2 = _calp0 * csig2;
213 omg12 = atan2(somg2 * _comg1 - comg2 * _somg1,
214 comg2 * _comg1 + somg2 * _somg1);
216 if (outmask & DISTANCE)
217 s12 = arcmode ? _b * ((1 + _A1m1) * sig12 + AB1) : s12_a12;
219 if (outmask & LONGITUDE) {
220 lam12 = omg12 + _A3c *
221 ( sig12 + (Geodesic::SinCosSeries(
true, ssig2, csig2, _C3a, nC3_-1)
223 lon12 = lam12 / Math::degree<real>();
230 if (outmask & LATITUDE)
231 lat2 = atan2(sbet2, _f1 * cbet2) / Math::degree<real>();
233 if (outmask & AZIMUTH)
235 azi2 = 0 - atan2(-salp2, calp2) / Math::degree<real>();
237 if (outmask & (REDUCEDLENGTH | GEODESICSCALE)) {
239 B22 = Geodesic::SinCosSeries(
true, ssig2, csig2, _C2a, nC2_),
240 AB2 = (1 + _A2m1) * (B22 - _B21),
241 J12 = (_A1m1 - _A2m1) * sig12 + (AB1 - AB2);
242 if (outmask & REDUCEDLENGTH)
245 m12 = _b * ((dn2 * (_csig1 * ssig2) - _dn1 * (_ssig1 * csig2))
246 - _csig1 * csig2 * J12);
247 if (outmask & GEODESICSCALE) {
248 real t = _k2 * (ssig2 - _ssig1) * (ssig2 + _ssig1) / (_dn1 + dn2);
249 M12 = csig12 + (t * ssig2 - csig2 * J12) * _ssig1 / _dn1;
250 M21 = csig12 - (t * _ssig1 - _csig1 * J12) * ssig2 / dn2;
254 if (outmask & AREA) {
256 B42 = Geodesic::SinCosSeries(
false, ssig2, csig2, _C4a, nC4_);
258 if (_calp0 == 0 || _salp0 == 0) {
260 salp12 = salp2 * _calp1 - calp2 * _salp1;
261 calp12 = calp2 * _calp1 + salp2 * _salp1;
265 if (salp12 == 0 && calp12 < 0) {
266 salp12 = Geodesic::tiny_ * _calp1;
278 salp12 = _calp0 * _salp0 *
279 (csig12 <= 0 ? _csig1 * (1 - csig12) + ssig12 * _ssig1 :
280 ssig12 * (_csig1 * ssig12 / (1 + csig12) + _ssig1));
283 S12 = _c2 * atan2(salp12, calp12) + _A4 * (B42 - _B41);
286 return arcmode ? s12_a12 : sig12 / Math::degree<real>();
static T AngNormalize(T x)
Header for GeographicLib::GeodesicLine class.
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 AngNormalize2(T x)