31 namespace GeographicLib {
36 real lat1, real lon1, real azi1,
37 unsigned caps)
throw()
46 , _caps(caps | LATITUDE | AZIMUTH)
54 real alp1 = azi1 * Math::degree<real>();
57 _salp1 = azi1 == -180 ? 0 : sin(alp1);
58 _calp1 = abs(azi1) == 90 ? 0 : cos(alp1);
59 real cbet1, sbet1, phi;
60 phi = lat1 * Math::degree<real>();
62 sbet1 = _f1 * sin(phi);
63 cbet1 = abs(lat1) == 90 ? GeodesicExact::tiny_ : cos(phi);
64 GeodesicExact::SinCosNorm(sbet1, cbet1);
65 _dn1 = (_f >= 0 ? sqrt(1 + g._ep2 *
Math::sq(sbet1)) :
66 sqrt(1 - _e2 *
Math::sq(cbet1)) / _f1);
69 _salp0 = _salp1 * cbet1;
82 _ssig1 = sbet1; _somg1 = _salp0 * sbet1;
83 _csig1 = _comg1 = sbet1 != 0 || _calp1 != 0 ? cbet1 * _calp1 : 1;
85 _cchi1 = _f1 * _dn1 * _comg1;
86 GeodesicExact::SinCosNorm(_ssig1, _csig1);
91 _E.Reset(-_k2, -g._ep2, 1 + _k2, 1 + g._ep2);
94 _E0 = _E.E() / (Math::pi<real>() / 2);
95 _E1 = _E.deltaE(_ssig1, _csig1, _dn1);
96 real s = sin(_E1), c = cos(_E1);
98 _stau1 = _ssig1 * c + _csig1 * s;
99 _ctau1 = _csig1 * c - _ssig1 * s;
105 _D0 = _E.D() / (Math::pi<real>() / 2);
106 _D1 = _E.deltaD(_ssig1, _csig1, _dn1);
110 _H0 = _E.H() / (Math::pi<real>() / 2);
111 _H1 = _E.deltaH(_ssig1, _csig1, _dn1);
114 if (_caps & CAP_C4) {
115 real eps = _k2 / (2 * (1 + sqrt(1 + _k2)) + _k2);
118 _A4 =
Math::sq(_a) * _calp0 * _salp0 * _e2;
119 _B41 = GeodesicExact::CosSeries(_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, E2 = 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 * _E0),
151 E2 = - _E.deltaEinv(_stau1 * c + _ctau1 * s, _ctau1 * c - _stau1 * s);
152 sig12 = tau12 - (E2 - _E1);
158 real ssig2, csig2, sbet2, cbet2, salp2, calp2;
160 ssig2 = _ssig1 * csig12 + _csig1 * ssig12;
161 csig2 = _csig1 * csig12 - _ssig1 * ssig12;
162 real dn2 = _E.Delta(ssig2, csig2);
163 if (outmask & (DISTANCE | REDUCEDLENGTH | GEODESICSCALE)) {
165 E2 = _E.deltaE(ssig2, csig2, dn2);
167 AB1 = _E0 * (E2 - _E1);
170 sbet2 = _calp0 * ssig2;
175 cbet2 = csig2 = GeodesicExact::tiny_;
177 salp2 = _salp0; calp2 = _calp0 * csig2;
179 if (outmask & DISTANCE)
180 s12 = arcmode ? _b * (_E0 * sig12 + AB1) : s12_a12;
182 if (outmask & LONGITUDE) {
183 real somg2 = _salp0 * ssig2, comg2 = csig2;
185 real cchi2 = _f1 * dn2 * comg2;
186 lam12 = atan2(somg2 * _cchi1 - cchi2 * _somg1,
187 cchi2 * _cchi1 + somg2 * _somg1) -
188 _e2/_f1 * _salp0 * _H0 * (sig12 + _E.deltaH(ssig2, csig2, dn2) - _H1 );
189 lon12 = lam12 / Math::degree<real>();
196 if (outmask & LATITUDE)
197 lat2 = atan2(sbet2, _f1 * cbet2) / Math::degree<real>();
199 if (outmask & AZIMUTH)
201 azi2 = 0 - atan2(-salp2, calp2) / Math::degree<real>();
203 if (outmask & (REDUCEDLENGTH | GEODESICSCALE)) {
204 real J12 = _k2 * _D0 * (sig12 + _E.deltaD(ssig2, csig2, dn2) - _D1);
205 if (outmask & REDUCEDLENGTH)
208 m12 = _b * ((dn2 * (_csig1 * ssig2) - _dn1 * (_ssig1 * csig2))
209 - _csig1 * csig2 * J12);
210 if (outmask & GEODESICSCALE) {
211 real t = _k2 * (ssig2 - _ssig1) * (ssig2 + _ssig1) / (_dn1 + dn2);
212 M12 = csig12 + (t * ssig2 - csig2 * J12) * _ssig1 / _dn1;
213 M21 = csig12 - (t * _ssig1 - _csig1 * J12) * ssig2 / dn2;
217 if (outmask & AREA) {
219 B42 = GeodesicExact::CosSeries(ssig2, csig2, _C4a, nC4_);
221 if (_calp0 == 0 || _salp0 == 0) {
223 salp12 = salp2 * _calp1 - calp2 * _salp1;
224 calp12 = calp2 * _calp1 + salp2 * _salp1;
228 if (salp12 == 0 && calp12 < 0) {
229 salp12 = GeodesicExact::tiny_ * _calp1;
241 salp12 = _calp0 * _salp0 *
242 (csig12 <= 0 ? _csig1 * (1 - csig12) + ssig12 * _ssig1 :
243 ssig12 * (_csig1 * ssig12 / (1 + csig12) + _ssig1));
246 S12 = _c2 * atan2(salp12, calp12) + _A4 * (B42 - _B41);
249 return arcmode ? s12_a12 : sig12 / Math::degree<real>();
static T AngNormalize(T x)
Header for GeographicLib::GeodesicLineExact class.
Exact geodesic calculations.
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)