GeographicLib 2.3

Gnomonic.cpp
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1/**
2 * \file Gnomonic.cpp
3 * \brief Implementation for GeographicLib::Gnomonic class
4 *
5 * Copyright (c) Charles Karney (2010-2022) <karney@alum.mit.edu> and licensed
6 * under the MIT/X11 License. For more information, see
7 * https://geographiclib.sourceforge.io/
8 **********************************************************************/
9
10#include <GeographicLib/Gnomonic.hpp>
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
22 Gnomonic::Gnomonic(const Geodesic& earth)
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,
34 Geodesic::AZIMUTH | Geodesic::REDUCEDLENGTH |
35 Geodesic::GEODESICSCALE,
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,
57 Geodesic::LATITUDE | Geodesic::LONGITUDE |
58 Geodesic::AZIMUTH | Geodesic::DISTANCE_IN |
59 Geodesic::REDUCEDLENGTH |
60 Geodesic::GEODESICSCALE));
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 (!(fabs(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
Gnomonic.hpp
Header for GeographicLib::Gnomonic class.
GEOGRAPHICLIB_PANIC
#define GEOGRAPHICLIB_PANIC
Definition: Math.hpp:62
GeographicLib::GeodesicLine
A geodesic line.
Definition: GeodesicLine.hpp:74
GeographicLib::GeodesicLine::Position
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21, real &S12) const
Definition: GeodesicLine.hpp:298
GeographicLib::Geodesic
Geodesic calculations
Definition: Geodesic.hpp:175
GeographicLib::Geodesic::Line
GeodesicLine Line(real lat1, real lon1, real azi1, unsigned caps=ALL) const
Definition: Geodesic.cpp:124
GeographicLib::Geodesic::REDUCEDLENGTH
@ REDUCEDLENGTH
Definition: Geodesic.hpp:313
GeographicLib::Geodesic::LATITUDE
@ LATITUDE
Definition: Geodesic.hpp:279
GeographicLib::Geodesic::LONGITUDE
@ LONGITUDE
Definition: Geodesic.hpp:284
GeographicLib::Geodesic::AZIMUTH
@ AZIMUTH
Definition: Geodesic.hpp:291
GeographicLib::Geodesic::DISTANCE_IN
@ DISTANCE_IN
Definition: Geodesic.hpp:308
GeographicLib::Geodesic::GEODESICSCALE
@ GEODESICSCALE
Definition: Geodesic.hpp:318
GeographicLib::Gnomonic::Gnomonic
Gnomonic(const Geodesic &earth=Geodesic::WGS84())
Definition: Gnomonic.cpp:22
GeographicLib::Gnomonic::Forward
void Forward(real lat0, real lon0, real lat, real lon, real &x, real &y, real &azi, real &rk) const
Definition: Gnomonic.cpp:30
GeographicLib::Gnomonic::Reverse
void Reverse(real lat0, real lon0, real x, real y, real &lat, real &lon, real &azi, real &rk) const
Definition: Gnomonic.cpp:47
GeographicLib::Math::sincosd
static void sincosd(T x, T &sinx, T &cosx)
Definition: Math.cpp:106
GeographicLib::Math::atan2d
static T atan2d(T y, T x)
Definition: Math.cpp:183
GeographicLib::Math::NaN
static T NaN()
Definition: Math.cpp:250
GeographicLib
Namespace for GeographicLib.
Definition: Accumulator.cpp:12
std
Definition: NearestNeighbor.hpp:812