35 void GeodesicLineExact::LineInit(
const GeodesicExact& g,
52 _caps = caps | LATITUDE | AZIMUTH | LONG_UNROLL;
57 Math::norm(sbet1, cbet1); cbet1 = max(tiny_, cbet1);
58 _dn1 = (_f >= 0 ? sqrt(1 + g._ep2 *
Math::sq(sbet1)) :
59 sqrt(1 - _e2 * Math::sq(cbet1)) / _f1);
62 _salp0 = _salp1 * cbet1;
75 _ssig1 = sbet1; _somg1 = _salp0 * sbet1;
76 _csig1 = _comg1 = sbet1 != 0 || _calp1 != 0 ? cbet1 * _calp1 : 1;
78 _cchi1 = _f1 * _dn1 * _comg1;
84 _E.Reset(-_k2, -g._ep2, 1 + _k2, 1 + g._ep2);
88 _E1 = _E.deltaE(_ssig1, _csig1, _dn1);
89 real s = sin(_E1), c = cos(_E1);
91 _stau1 = _ssig1 * c + _csig1 * s;
92 _ctau1 = _csig1 * c - _ssig1 * s;
99 _D1 = _E.deltaD(_ssig1, _csig1, _dn1);
104 _H1 = _E.deltaH(_ssig1, _csig1, _dn1);
107 if (_caps & CAP_C4) {
108 real eps = _k2 / (2 * (1 + sqrt(1 + _k2)) + _k2);
111 _A4 =
Math::sq(_a) * _calp0 * _salp0 * _e2;
112 _B41 = GeodesicExact::CosSeries(_ssig1, _csig1, _C4a, nC4_);
119 real lat1, real lon1, real azi1,
125 LineInit(g, lat1, lon1, azi1, salp1, calp1, caps);
132 bool arcmode,
real s13_a13) {
133 LineInit(g, lat1, lon1, azi1, salp1, calp1, caps);
134 GenSetDistance(arcmode, s13_a13);
139 real& lat2, real& lon2, real& azi2,
140 real& s12, real& m12,
141 real& M12, real& M21,
144 outmask &= _caps & OUT_MASK;
145 if (!( Init() && (arcmode || (_caps & (OUT_MASK & DISTANCE_IN))) ))
150 real sig12, ssig12, csig12, E2 = 0, AB1 = 0;
154 real s12a = abs(s12_a12);
155 s12a -= 180 * floor(s12a / 180);
156 ssig12 = s12a == 0 ? 0 : sin(sig12);
157 csig12 = s12a == 90 ? 0 : cos(sig12);
161 tau12 = s12_a12 / (_b * _E0),
165 E2 = - _E.deltaEinv(_stau1 * c + _ctau1 * s, _ctau1 * c - _stau1 * s);
166 sig12 = tau12 - (E2 - _E1);
171 real ssig2, csig2, sbet2, cbet2, salp2, calp2;
173 ssig2 = _ssig1 * csig12 + _csig1 * ssig12;
174 csig2 = _csig1 * csig12 - _ssig1 * ssig12;
175 real dn2 = _E.Delta(ssig2, csig2);
176 if (outmask & (DISTANCE | REDUCEDLENGTH | GEODESICSCALE)) {
178 E2 = _E.deltaE(ssig2, csig2, dn2);
180 AB1 = _E0 * (E2 - _E1);
183 sbet2 = _calp0 * ssig2;
188 cbet2 = csig2 = tiny_;
190 salp2 = _salp0; calp2 = _calp0 * csig2;
192 if (outmask & DISTANCE)
193 s12 = arcmode ? _b * (_E0 * sig12 + AB1) : s12_a12;
195 if (outmask & LONGITUDE) {
196 real somg2 = _salp0 * ssig2, comg2 = csig2,
199 real cchi2 = _f1 * dn2 * comg2;
200 real chi12 = outmask & LONG_UNROLL
202 - (atan2( ssig2, csig2) - atan2( _ssig1, _csig1))
203 + (atan2(E * somg2, cchi2) - atan2(E * _somg1, _cchi1)))
204 : atan2(somg2 * _cchi1 - cchi2 * _somg1,
205 cchi2 * _cchi1 + somg2 * _somg1);
207 _e2/_f1 * _salp0 * _H0 * (sig12 + (_E.deltaH(ssig2, csig2, dn2) - _H1));
209 lon2 = outmask & LONG_UNROLL ? _lon1 + lon12 :
214 if (outmask & LATITUDE)
217 if (outmask & AZIMUTH)
220 if (outmask & (REDUCEDLENGTH | GEODESICSCALE)) {
221 real J12 = _k2 * _D0 * (sig12 + (_E.deltaD(ssig2, csig2, dn2) - _D1));
222 if (outmask & REDUCEDLENGTH)
225 m12 = _b * ((dn2 * (_csig1 * ssig2) - _dn1 * (_ssig1 * csig2))
226 - _csig1 * csig2 * J12);
227 if (outmask & GEODESICSCALE) {
228 real t = _k2 * (ssig2 - _ssig1) * (ssig2 + _ssig1) / (_dn1 + dn2);
229 M12 = csig12 + (t * ssig2 - csig2 * J12) * _ssig1 / _dn1;
230 M21 = csig12 - (t * _ssig1 - _csig1 * J12) * ssig2 / dn2;
234 if (outmask & AREA) {
236 B42 = GeodesicExact::CosSeries(ssig2, csig2, _C4a, nC4_);
238 if (_calp0 == 0 || _salp0 == 0) {
240 salp12 = salp2 * _calp1 - calp2 * _salp1;
241 calp12 = calp2 * _calp1 + salp2 * _salp1;
258 salp12 = _calp0 * _salp0 *
259 (csig12 <= 0 ? _csig1 * (1 - csig12) + ssig12 * _ssig1 :
260 ssig12 * (_csig1 * ssig12 / (1 + csig12) + _ssig1));
263 S12 = _c2 * atan2(salp12, calp12) + _A4 * (B42 - _B41);
274 _a13 = GenPosition(
false, _s13, 0u, t, t, t, t, t, t, t, t);
282 GenPosition(
true, _a13, DISTANCE, t, t, t, _s13, t, t, t, t);
286 arcmode ? SetArc(s13_a13) : SetDistance(s13_a13);
static T AngNormalize(T x)
GeographicLib::Math::real real
static void sincosd(T x, T &sinx, T &cosx)
void SetDistance(real s13)
static void norm(T &x, T &y)
void GenSetDistance(bool arcmode, real s13_a13)
Header for GeographicLib::GeodesicLineExact class.
static T atan2d(T y, T x)
Namespace for GeographicLib.
Exact geodesic calculations.
static T copysign(T x, T y)
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