35 void GeodesicLine::LineInit(
const Geodesic& g,
56 Math::norm(sbet1, cbet1); cbet1 = max(tiny_, cbet1);
57 _dn1 = sqrt(1 + g._ep2 *
Math::sq(sbet1));
60 _salp0 = _salp1 * cbet1;
63 _calp0 = hypot(_calp1, _salp1 * sbet1);
73 _ssig1 = sbet1; _somg1 = _salp0 * sbet1;
74 _csig1 = _comg1 = sbet1 != 0 || _calp1 != 0 ? cbet1 * _calp1 : 1;
79 real eps = _k2 / (2 * (1 + sqrt(1 + _k2)) + _k2);
82 _A1m1 = Geodesic::A1m1f(eps);
83 Geodesic::C1f(eps, _C1a);
84 _B11 = Geodesic::SinCosSeries(
true, _ssig1, _csig1, _C1a, nC1_);
85 real s = sin(_B11), c = cos(_B11);
87 _stau1 = _ssig1 * c + _csig1 * s;
88 _ctau1 = _csig1 * c - _ssig1 * s;
94 Geodesic::C1pf(eps, _C1pa);
97 _A2m1 = Geodesic::A2m1f(eps);
98 Geodesic::C2f(eps, _C2a);
99 _B21 = Geodesic::SinCosSeries(
true, _ssig1, _csig1, _C2a, nC2_);
102 if (_caps & CAP_C3) {
104 _A3c = -_f * _salp0 * g.A3f(eps);
105 _B31 = Geodesic::SinCosSeries(
true, _ssig1, _csig1, _C3a, nC3_-1);
108 if (_caps & CAP_C4) {
111 _A4 =
Math::sq(_a) * _calp0 * _salp0 * g._e2;
112 _B41 = Geodesic::SinCosSeries(
false, _ssig1, _csig1, _C4a, nC4_);
119 real lat1, real lon1, real azi1,
125 LineInit(g, lat1, lon1, azi1, salp1, calp1, caps);
131 unsigned caps,
bool arcmode,
real s13_a13) {
132 LineInit(g, lat1, lon1, azi1, salp1, calp1, caps);
138 real& lat2, real& lon2, real& azi2,
139 real& s12, real& m12,
140 real& M12, real& M21,
142 outmask &= _caps & OUT_MASK;
148 real sig12, ssig12, csig12, B12 = 0, AB1 = 0;
156 tau12 = s12_a12 / (_b * (1 + _A1m1)),
160 B12 = - Geodesic::SinCosSeries(
true,
161 _stau1 * c + _ctau1 * s,
162 _ctau1 * c - _stau1 * s,
164 sig12 = tau12 - (B12 - _B11);
165 ssig12 = sin(sig12); csig12 = cos(sig12);
166 if (abs(_f) > 0.01) {
190 ssig2 = _ssig1 * csig12 + _csig1 * ssig12,
191 csig2 = _csig1 * csig12 - _ssig1 * ssig12;
192 B12 = Geodesic::SinCosSeries(
true, ssig2, csig2, _C1a, nC1_);
193 real serr = (1 + _A1m1) * (sig12 + (B12 - _B11)) - s12_a12 / _b;
194 sig12 = sig12 - serr / sqrt(1 + _k2 *
Math::sq(ssig2));
195 ssig12 = sin(sig12); csig12 = cos(sig12);
200 real ssig2, csig2, sbet2, cbet2, salp2, calp2;
202 ssig2 = _ssig1 * csig12 + _csig1 * ssig12;
203 csig2 = _csig1 * csig12 - _ssig1 * ssig12;
204 real dn2 = sqrt(1 + _k2 *
Math::sq(ssig2));
206 if (arcmode || abs(_f) > 0.01)
207 B12 = Geodesic::SinCosSeries(
true, ssig2, csig2, _C1a, nC1_);
208 AB1 = (1 + _A1m1) * (B12 - _B11);
211 sbet2 = _calp0 * ssig2;
213 cbet2 = hypot(_salp0, _calp0 * csig2);
216 cbet2 = csig2 = tiny_;
218 salp2 = _salp0; calp2 = _calp0 * csig2;
221 s12 = arcmode ? _b * ((1 + _A1m1) * sig12 + AB1) : s12_a12;
225 real somg2 = _salp0 * ssig2, comg2 = csig2,
226 E = copysign(real(1), _salp0);
230 - (atan2( ssig2, csig2) - atan2( _ssig1, _csig1))
231 + (atan2(E * somg2, comg2) - atan2(E * _somg1, _comg1)))
232 : atan2(somg2 * _comg1 - comg2 * _somg1,
233 comg2 * _comg1 + somg2 * _somg1);
234 real lam12 = omg12 + _A3c *
235 ( sig12 + (Geodesic::SinCosSeries(
true, ssig2, csig2, _C3a, nC3_-1)
251 B22 = Geodesic::SinCosSeries(
true, ssig2, csig2, _C2a, nC2_),
252 AB2 = (1 + _A2m1) * (B22 - _B21),
253 J12 = (_A1m1 - _A2m1) * sig12 + (AB1 - AB2);
257 m12 = _b * ((dn2 * (_csig1 * ssig2) - _dn1 * (_ssig1 * csig2))
258 - _csig1 * csig2 * J12);
260 real t = _k2 * (ssig2 - _ssig1) * (ssig2 + _ssig1) / (_dn1 + dn2);
261 M12 = csig12 + (t * ssig2 - csig2 * J12) * _ssig1 / _dn1;
262 M21 = csig12 - (t * _ssig1 - _csig1 * J12) * ssig2 / dn2;
266 if (outmask &
AREA) {
268 B42 = Geodesic::SinCosSeries(
false, ssig2, csig2, _C4a, nC4_);
270 if (_calp0 == 0 || _salp0 == 0) {
272 salp12 = salp2 * _calp1 - calp2 * _salp1;
273 calp12 = calp2 * _calp1 + salp2 * _salp1;
290 salp12 = _calp0 * _salp0 *
291 (csig12 <= 0 ? _csig1 * (1 - csig12) + ssig12 * _ssig1 :
292 ssig12 * (_csig1 * ssig12 / (1 + csig12) + _ssig1));
295 S12 = _c2 * atan2(salp12, calp12) + _A4 * (B42 - _B41);
306 _a13 =
GenPosition(
false, _s13, 0u, t, t, t, t, t, t, t, t);
314 GenPosition(
true, _a13,
DISTANCE, t, t, t, _s13, t, t, t, t);
GeographicLib::Math::real real
Header for GeographicLib::GeodesicLine class.
void GenSetDistance(bool arcmode, real s13_a13)
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
void SetDistance(real s13)
static T AngNormalize(T x)
static void sincosd(T x, T &sinx, T &cosx)
static T atan2d(T y, T x)
static void norm(T &x, T &y)
Namespace for GeographicLib.