GeographicLib  1.51
Gnomonic.cpp
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1 /**
2  * \file Gnomonic.cpp
3  * \brief Implementation for GeographicLib::Gnomonic class
4  *
5  * Copyright (c) Charles Karney (2010-2020) <charles@karney.com> and licensed
6  * under the MIT/X11 License. For more information, see
7  * https://geographiclib.sourceforge.io/
8  **********************************************************************/
9 
11 
12 #if defined(_MSC_VER)
13 // Squelch warnings about potentially uninitialized local variables and
14 // constant conditional expressions
15 # pragma warning (disable: 4701 4127)
16 #endif
17 
18 namespace GeographicLib {
19 
20  using namespace std;
21 
23  : eps0_(numeric_limits<real>::epsilon())
24  , eps_(real(0.01) * sqrt(eps0_))
25  , _earth(earth)
26  , _a(_earth.EquatorialRadius())
27  , _f(_earth.Flattening())
28  {}
29 
30  void Gnomonic::Forward(real lat0, real lon0, real lat, real lon,
31  real& x, real& y, real& azi, real& rk) const {
32  real azi0, m, M, t;
33  _earth.GenInverse(lat0, lon0, lat, lon,
36  t, azi0, azi, m, M, t, t);
37  rk = M;
38  if (M <= 0)
39  x = y = Math::NaN();
40  else {
41  real rho = m/M;
42  Math::sincosd(azi0, x, y);
43  x *= rho; y *= rho;
44  }
45  }
46 
47  void Gnomonic::Reverse(real lat0, real lon0, real x, real y,
48  real& lat, real& lon, real& azi, real& rk) const {
49  real
50  azi0 = Math::atan2d(x, y),
51  rho = hypot(x, y),
52  s = _a * atan(rho/_a);
53  bool little = rho <= _a;
54  if (!little)
55  rho = 1/rho;
56  GeodesicLine line(_earth.Line(lat0, lon0, azi0,
61  int count = numit_, trip = 0;
62  real lat1, lon1, azi1, M;
63  while (count-- || GEOGRAPHICLIB_PANIC) {
64  real m, t;
65  line.Position(s, lat1, lon1, azi1, m, M, t);
66  if (trip)
67  break;
68  // If little, solve rho(s) = rho with drho(s)/ds = 1/M^2
69  // else solve 1/rho(s) = 1/rho with d(1/rho(s))/ds = -1/m^2
70  real ds = little ? (m - rho * M) * M : (rho * m - M) * m;
71  s -= ds;
72  // Reversed test to allow escape with NaNs
73  if (!(abs(ds) >= eps_ * _a))
74  ++trip;
75  }
76  if (trip) {
77  lat = lat1; lon = lon1; azi = azi1; rk = M;
78  } else
79  lat = lon = azi = rk = Math::NaN();
80  return;
81  }
82 
83 } // namespace GeographicLib
GeodesicLine Line(real lat1, real lon1, real azi1, unsigned caps=ALL) const
Definition: Geodesic.cpp:118
Header for GeographicLib::Gnomonic class.
static T atan2d(T y, T x)
Definition: Math.cpp:189
void Forward(real lat0, real lon0, real lat, real lon, real &x, real &y, real &azi, real &rk) const
Definition: Gnomonic.cpp:30
Namespace for GeographicLib.
Definition: Accumulator.cpp:12
static T NaN()
Definition: Math.cpp:268
void Reverse(real lat0, real lon0, real x, real y, real &lat, real &lon, real &azi, real &rk) const
Definition: Gnomonic.cpp:47
static void sincosd(T x, T &sinx, T &cosx)
Definition: Math.cpp:126
Gnomonic(const Geodesic &earth=Geodesic::WGS84())
Definition: Gnomonic.cpp:22
Geodesic calculations
Definition: Geodesic.hpp:172
#define GEOGRAPHICLIB_PANIC
Definition: Math.hpp:61