GeographicLib 2.5.2

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PolarStereographic.cpp
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1/**
2 * \file PolarStereographic.cpp
3 * \brief Implementation for GeographicLib::PolarStereographic class
4 *
5 * Copyright (c) Charles Karney (2008-2022) <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/PolarStereographic.hpp>
11
12 namespace GeographicLib {
13
14 using namespace std;
15
16 PolarStereographic::PolarStereographic(real a, real f, real k0)
17 : _a(a)
18 , _f(f)
19 , _e2(_f * (2 - _f))
20 , _es((_f < 0 ? -1 : 1) * sqrt(fabs(_e2)))
21 , _e2m(1 - _e2)
22 , _c( (1 - _f) * exp(Math::eatanhe(real(1), _es)) )
23 , _k0(k0)
24 {
25 if (!(isfinite(_a) && _a > 0))
26 throw GeographicErr("Equatorial radius is not positive");
27 if (!(isfinite(_f) && _f < 1))
28 throw GeographicErr("Polar semi-axis is not positive");
29 if (!(isfinite(_k0) && _k0 > 0))
30 throw GeographicErr("Scale is not positive");
31 }
32
33 const PolarStereographic& PolarStereographic::UPS() {
34 static const PolarStereographic ups(Constants::WGS84_a(),
35 Constants::WGS84_f(),
36 Constants::UPS_k0());
37 return ups;
38 }
39
40 // This formulation converts to conformal coordinates by tau = tan(phi) and
41 // tau' = tan(phi') where phi' is the conformal latitude. The formulas are:
42 // tau = tan(phi)
43 // secphi = hypot(1, tau)
44 // sig = sinh(e * atanh(e * tau / secphi))
45 // taup = tan(phip) = tau * hypot(1, sig) - sig * hypot(1, tau)
46 // c = (1 - f) * exp(e * atanh(e))
47 //
48 // Forward:
49 // rho = (2*k0*a/c) / (hypot(1, taup) + taup) (taup >= 0)
50 // = (2*k0*a/c) * (hypot(1, taup) - taup) (taup < 0)
51 //
52 // Reverse:
53 // taup = ((2*k0*a/c) / rho - rho / (2*k0*a/c))/2
54 //
55 // Scale:
56 // k = (rho/a) * secphi * sqrt((1-e2) + e2 / secphi^2)
57 //
58 // In limit rho -> 0, tau -> inf, taup -> inf, secphi -> inf, secphip -> inf
59 // secphip = taup = exp(-e * atanh(e)) * tau = exp(-e * atanh(e)) * secphi
60
61 void PolarStereographic::Forward(bool northp, real lat, real lon,
62 real& x, real& y,
63 real& gamma, real& k) const {
64 lat = Math::LatFix(lat);
65 lat *= northp ? 1 : -1;
66 real
67 tau = Math::tand(lat),
68 secphi = hypot(real(1), tau),
69 taup = Math::taupf(tau, _es),
70 rho = hypot(real(1), taup) + fabs(taup);
71 rho = taup >= 0 ? (lat != Math::qd ? 1/rho : 0) : rho;
72 rho *= 2 * _k0 * _a / _c;
73 k = lat != Math::qd ?
74 (rho / _a) * secphi * sqrt(_e2m + _e2 / Math::sq(secphi)) : _k0;
75 Math::sincosd(lon, x, y);
76 x *= rho;
77 y *= (northp ? -rho : rho);
78 gamma = Math::AngNormalize(northp ? lon : -lon);
79 }
80
81 void PolarStereographic::Reverse(bool northp, real x, real y,
82 real& lat, real& lon,
83 real& gamma, real& k) const {
84 real
85 rho = hypot(x, y),
86 t = rho != 0 ? rho / (2 * _k0 * _a / _c) :
87 Math::sq(numeric_limits<real>::epsilon()),
88 taup = (1 / t - t) / 2,
89 tau = Math::tauf(taup, _es),
90 secphi = hypot(real(1), tau);
91 k = rho != 0 ? (rho / _a) * secphi * sqrt(_e2m + _e2 / Math::sq(secphi)) :
92 _k0;
93 lat = (northp ? 1 : -1) * Math::atand(tau);
94 lon = Math::atan2d(x, northp ? -y : y );
95 gamma = Math::AngNormalize(northp ? lon : -lon);
96 }
97
98 void PolarStereographic::SetScale(real lat, real k) {
99 if (!(isfinite(k) && k > 0))
100 throw GeographicErr("Scale is not positive");
101 if (!(-Math::qd < lat && lat <= Math::qd))
102 throw GeographicErr("Latitude must be in (-" + to_string(Math::qd)
103 + "d, " + to_string(Math::qd) + "d]");
104 real x, y, gamma, kold;
105 _k0 = 1;
106 Forward(true, lat, 0, x, y, gamma, kold);
107 _k0 *= k/kold;
108 }
109
110} // namespace GeographicLib
PolarStereographic.hpp
Header for GeographicLib::PolarStereographic class.
GeographicLib::Constants::UPS_k0
static T UPS_k0()
Definition Constants.hpp:205
GeographicLib::Constants::WGS84_f
static T WGS84_f()
Definition Constants.hpp:141
GeographicLib::Constants::WGS84_a
static T WGS84_a()
Definition Constants.hpp:135
GeographicLib::GeographicErr
Exception handling for GeographicLib.
Definition Constants.hpp:316
GeographicLib::Math
Mathematical functions needed by GeographicLib.
Definition Math.hpp:82
GeographicLib::Math::tand
static T tand(T x)
Definition Math.cpp:191
GeographicLib::Math::LatFix
static T LatFix(T x)
Definition Math.hpp:315
GeographicLib::Math::sincosd
static void sincosd(T x, T &sinx, T &cosx)
Definition Math.cpp:104
GeographicLib::Math::atan2d
static T atan2d(T y, T x)
Definition Math.cpp:202
GeographicLib::Math::sq
static T sq(T x)
Definition Math.hpp:227
GeographicLib::Math::qd
static constexpr int qd
degrees per quarter turn
Definition Math.hpp:150
GeographicLib::Math::tauf
static T tauf(T taup, T es)
Definition Math.cpp:241
GeographicLib::Math::AngNormalize
static T AngNormalize(T x)
Definition Math.cpp:69
GeographicLib::Math::atand
static T atand(T x)
Definition Math.cpp:224
GeographicLib::Math::taupf
static T taupf(T tau, T es)
Definition Math.cpp:231
GeographicLib::PolarStereographic
Polar stereographic projection.
Definition PolarStereographic.hpp:36
GeographicLib::PolarStereographic::Reverse
void Reverse(bool northp, real x, real y, real &lat, real &lon, real &gamma, real &k) const
Definition PolarStereographic.cpp:81
GeographicLib::PolarStereographic::PolarStereographic
PolarStereographic(real a, real f, real k0)
Definition PolarStereographic.cpp:16
GeographicLib::PolarStereographic::SetScale
void SetScale(real lat, real k=real(1))
Definition PolarStereographic.cpp:98
GeographicLib::PolarStereographic::UPS
static const PolarStereographic & UPS()
Definition PolarStereographic.cpp:33
GeographicLib::PolarStereographic::Forward
void Forward(bool northp, real lat, real lon, real &x, real &y, real &gamma, real &k) const
Definition PolarStereographic.cpp:61
GeographicLib
Namespace for GeographicLib.
Definition Accumulator.cpp:12
std
Definition NearestNeighbor.hpp:806