GeographicLib  1.44
CassiniSoldner.cpp
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1 /**
2  * \file CassiniSoldner.cpp
3  * \brief Implementation for GeographicLib::CassiniSoldner class
4  *
5  * Copyright (c) Charles Karney (2009-2015) <charles@karney.com> and licensed
6  * under the MIT/X11 License. For more information, see
7  * http://geographiclib.sourceforge.net/
8  **********************************************************************/
9 
11 
12 namespace GeographicLib {
13 
14  using namespace std;
15 
17  : _earth(earth) {}
18 
19  CassiniSoldner::CassiniSoldner(real lat0, real lon0, const Geodesic& earth)
20  : _earth(earth)
21  { Reset(lat0, lon0); }
22 
23  void CassiniSoldner::Reset(real lat0, real lon0) {
24  _meridian = _earth.Line(lat0, lon0, real(0),
28  real f = _earth.Flattening();
29  Math::sincosd(LatitudeOrigin(), _sbet0, _cbet0);
30  _sbet0 *= (1 - f);
31  Math::norm(_sbet0, _cbet0);
32  }
33 
34  void CassiniSoldner::Forward(real lat, real lon, real& x, real& y,
35  real& azi, real& rk) const {
36  if (!Init())
37  return;
38  real dlon = Math::AngDiff(LongitudeOrigin(), lon);
39  real sig12, s12, azi1, azi2;
40  sig12 = _earth.Inverse(lat, -abs(dlon), lat, abs(dlon), s12, azi1, azi2);
41  sig12 *= real(0.5);
42  s12 *= real(0.5);
43  if (s12 == 0) {
44  real da = Math::AngDiff(azi1, azi2)/2;
45  if (abs(dlon) <= 90) {
46  azi1 = 90 - da;
47  azi2 = 90 + da;
48  } else {
49  azi1 = -90 - da;
50  azi2 = -90 + da;
51  }
52  }
53  if (dlon < 0) {
54  azi2 = azi1;
55  s12 = -s12;
56  sig12 = -sig12;
57  }
58  x = s12;
59  azi = Math::AngNormalize(azi2);
60  GeodesicLine perp(_earth.Line(lat, dlon, azi, Geodesic::GEODESICSCALE));
61  real t;
62  perp.GenPosition(true, -sig12,
64  t, t, t, t, t, t, rk, t);
65 
66  real salp0, calp0;
67  Math::sincosd(perp.EquatorialAzimuth(), salp0, calp0);
68  real
69  sbet1 = lat >=0 ? calp0 : -calp0,
70  cbet1 = abs(dlon) <= 90 ? abs(salp0) : -abs(salp0),
71  sbet01 = sbet1 * _cbet0 - cbet1 * _sbet0,
72  cbet01 = cbet1 * _cbet0 + sbet1 * _sbet0,
73  sig01 = atan2(sbet01, cbet01) / Math::degree();
74  _meridian.GenPosition(true, sig01,
76  t, t, t, y, t, t, t, t);
77  }
78 
79  void CassiniSoldner::Reverse(real x, real y, real& lat, real& lon,
80  real& azi, real& rk) const {
81  if (!Init())
82  return;
83  real lat1, lon1;
84  real azi0, t;
85  _meridian.Position(y, lat1, lon1, azi0);
86  _earth.Direct(lat1, lon1, azi0 + 90, x, lat, lon, azi, rk, t);
87  }
88 
89 } // namespace GeographicLib
static T AngNormalize(T x)
Definition: Math.hpp:451
CassiniSoldner(const Geodesic &earth=Geodesic::WGS84())
Math::real LatitudeOrigin() const
Header for GeographicLib::CassiniSoldner class.
Math::real Direct(real lat1, real lon1, real azi1, real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21, real &S12) const
Definition: Geodesic.hpp:380
GeodesicLine Line(real lat1, real lon1, real azi1, unsigned caps=ALL) const
Definition: Geodesic.cpp:118
void Forward(real lat, real lon, real &x, real &y, real &azi, real &rk) const
Math::real Inverse(real lat1, real lon1, real lat2, real lon2, real &s12, real &azi1, real &azi2, real &m12, real &M12, real &M21, real &S12) const
Definition: Geodesic.hpp:675
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21, real &S12) const
static void sincosd(T x, T &sinx, T &cosx)
Definition: Math.hpp:559
static void norm(T &x, T &y)
Definition: Math.hpp:398
void Reverse(real x, real y, real &lat, real &lon, real &azi, real &rk) 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
Namespace for GeographicLib.
Definition: Accumulator.cpp:12
static T degree()
Definition: Math.hpp:230
static T AngDiff(T x, T y)
Definition: Math.hpp:499
Math::real Flattening() const
Definition: Geodesic.hpp:858
Geodesic calculations
Definition: Geodesic.hpp:171
void Reset(real lat0, real lon0)
Math::real LongitudeOrigin() const