36 real lat1, real lon1, real azi1,
42 , _azi1(
Math::AngRound(
Math::AngNormalize(azi1)))
51 , _caps(caps | LATITUDE | AZIMUTH)
56 _salp1 = _azi1 == -180 ? 0 : sin(alp1);
57 _calp1 = abs(_azi1) == 90 ? 0 : cos(alp1);
58 real cbet1, sbet1, phi;
61 sbet1 = _f1 * sin(phi);
62 cbet1 = abs(lat1) == 90 ? tiny_ : cos(phi);
64 _dn1 = (_f >= 0 ? sqrt(1 + g._ep2 *
Math::sq(sbet1)) :
65 sqrt(1 - _e2 *
Math::sq(cbet1)) / _f1);
68 _salp0 = _salp1 * cbet1;
81 _ssig1 = sbet1; _somg1 = _salp0 * sbet1;
82 _csig1 = _comg1 = sbet1 != 0 || _calp1 != 0 ? cbet1 * _calp1 : 1;
84 _cchi1 = _f1 * _dn1 * _comg1;
90 _E.
Reset(-_k2, -g._ep2, 1 + _k2, 1 + g._ep2);
94 _E1 = _E.
deltaE(_ssig1, _csig1, _dn1);
95 real s = sin(_E1), c = cos(_E1);
97 _stau1 = _ssig1 * c + _csig1 * s;
98 _ctau1 = _csig1 * c - _ssig1 * s;
105 _D1 = _E.
deltaD(_ssig1, _csig1, _dn1);
110 _H1 = _E.
deltaH(_ssig1, _csig1, _dn1);
113 if (_caps & CAP_C4) {
114 real eps = _k2 / (2 * (1 + sqrt(1 + _k2)) + _k2);
117 _A4 =
Math::sq(_a) * _calp0 * _salp0 * _e2;
118 _B41 = GeodesicExact::CosSeries(_ssig1, _csig1, _C4a, nC4_);
124 real& lat2, real& lon2, real& azi2,
125 real& s12, real& m12,
126 real& M12, real& M21,
129 outmask &= _caps & OUT_MASK;
135 real sig12, ssig12, csig12, E2 = 0, AB1 = 0;
139 real s12a = abs(s12_a12);
140 s12a -= 180 * floor(s12a / 180);
141 ssig12 = s12a == 0 ? 0 : sin(sig12);
142 csig12 = s12a == 90 ? 0 : cos(sig12);
146 tau12 = s12_a12 / (_b * _E0),
150 E2 = - _E.
deltaEinv(_stau1 * c + _ctau1 * s, _ctau1 * c - _stau1 * s);
151 sig12 = tau12 - (E2 - _E1);
156 real ssig2, csig2, sbet2, cbet2, salp2, calp2;
158 ssig2 = _ssig1 * csig12 + _csig1 * ssig12;
159 csig2 = _csig1 * csig12 - _ssig1 * ssig12;
160 real dn2 = _E.
Delta(ssig2, csig2);
163 E2 = _E.
deltaE(ssig2, csig2, dn2);
165 AB1 = _E0 * (E2 - _E1);
168 sbet2 = _calp0 * ssig2;
173 cbet2 = csig2 = tiny_;
175 salp2 = _salp0; calp2 = _calp0 * csig2;
178 s12 = arcmode ? _b * (_E0 * sig12 + AB1) : s12_a12;
181 real somg2 = _salp0 * ssig2, comg2 = csig2;
183 real cchi2 = _f1 * dn2 * comg2;
185 - (atan2(ssig2, csig2) - atan2(_ssig1, _csig1))
186 + (atan2(somg2, cchi2) - atan2(_somg1, _cchi1))
187 : atan2(somg2 * _cchi1 - cchi2 * _somg1,
188 cchi2 * _cchi1 + somg2 * _somg1);
190 _e2/_f1 * _salp0 * _H0 * (sig12 + _E.
deltaH(ssig2, csig2, dn2) - _H1 );
207 real J12 = _k2 * _D0 * (sig12 + _E.
deltaD(ssig2, csig2, dn2) - _D1);
211 m12 = _b * ((dn2 * (_csig1 * ssig2) - _dn1 * (_ssig1 * csig2))
212 - _csig1 * csig2 * J12);
214 real t = _k2 * (ssig2 - _ssig1) * (ssig2 + _ssig1) / (_dn1 + dn2);
215 M12 = csig12 + (t * ssig2 - csig2 * J12) * _ssig1 / _dn1;
216 M21 = csig12 - (t * _ssig1 - _csig1 * J12) * ssig2 / dn2;
220 if (outmask &
AREA) {
222 B42 = GeodesicExact::CosSeries(ssig2, csig2, _C4a, nC4_);
224 if (_calp0 == 0 || _salp0 == 0) {
226 salp12 = salp2 * _calp1 - calp2 * _salp1;
227 calp12 = calp2 * _calp1 + salp2 * _salp1;
231 if (salp12 == 0 && calp12 < 0) {
232 salp12 = tiny_ * _calp1;
244 salp12 = _calp0 * _salp0 *
245 (csig12 <= 0 ? _csig1 * (1 - csig12) + ssig12 * _ssig1 :
246 ssig12 * (_csig1 * ssig12 / (1 + csig12) + _ssig1));
249 S12 = _c2 * atan2(salp12, calp12) + _A4 * (B42 - _B41);
static T AngNormalize(T x)
Math::real deltaEinv(real stau, real ctau) const
void Reset(real k2=0, real alpha2=0)
Mathematical functions needed by GeographicLib.
Math::real Delta(real sn, real cn) const
static void norm(T &x, T &y)
Header for GeographicLib::GeodesicLineExact class.
static T atan2d(T y, T x)
Namespace for GeographicLib.
Exact geodesic calculations.
Math::real deltaE(real sn, real cn, real dn) const
Math::real deltaH(real sn, real cn, real dn) const
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)
Math::real deltaD(real sn, real cn, real dn) const