GeographicLib 2.3

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#if defined(_MSC_VER)
13// Squelch warnings about enum-float expressions
14# pragma warning (disable: 5055)
15#endif
16
17 namespace GeographicLib {
18
19 using namespace std;
20
21 PolarStereographic::PolarStereographic(real a, real f, real k0)
22 : _a(a)
23 , _f(f)
24 , _e2(_f * (2 - _f))
25 , _es((_f < 0 ? -1 : 1) * sqrt(fabs(_e2)))
26 , _e2m(1 - _e2)
27 , _c( (1 - _f) * exp(Math::eatanhe(real(1), _es)) )
28 , _k0(k0)
29 {
30 if (!(isfinite(_a) && _a > 0))
31 throw GeographicErr("Equatorial radius is not positive");
32 if (!(isfinite(_f) && _f < 1))
33 throw GeographicErr("Polar semi-axis is not positive");
34 if (!(isfinite(_k0) && _k0 > 0))
35 throw GeographicErr("Scale is not positive");
36 }
37
38 const PolarStereographic& PolarStereographic::UPS() {
39 static const PolarStereographic ups(Constants::WGS84_a(),
40 Constants::WGS84_f(),
41 Constants::UPS_k0());
42 return ups;
43 }
44
45 // This formulation converts to conformal coordinates by tau = tan(phi) and
46 // tau' = tan(phi') where phi' is the conformal latitude. The formulas are:
47 // tau = tan(phi)
48 // secphi = hypot(1, tau)
49 // sig = sinh(e * atanh(e * tau / secphi))
50 // taup = tan(phip) = tau * hypot(1, sig) - sig * hypot(1, tau)
51 // c = (1 - f) * exp(e * atanh(e))
52 //
53 // Forward:
54 // rho = (2*k0*a/c) / (hypot(1, taup) + taup) (taup >= 0)
55 // = (2*k0*a/c) * (hypot(1, taup) - taup) (taup < 0)
56 //
57 // Reverse:
58 // taup = ((2*k0*a/c) / rho - rho / (2*k0*a/c))/2
59 //
60 // Scale:
61 // k = (rho/a) * secphi * sqrt((1-e2) + e2 / secphi^2)
62 //
63 // In limit rho -> 0, tau -> inf, taup -> inf, secphi -> inf, secphip -> inf
64 // secphip = taup = exp(-e * atanh(e)) * tau = exp(-e * atanh(e)) * secphi
65
66 void PolarStereographic::Forward(bool northp, real lat, real lon,
67 real& x, real& y,
68 real& gamma, real& k) const {
69 lat = Math::LatFix(lat);
70 lat *= northp ? 1 : -1;
71 real
72 tau = Math::tand(lat),
73 secphi = hypot(real(1), tau),
74 taup = Math::taupf(tau, _es),
75 rho = hypot(real(1), taup) + fabs(taup);
76 rho = taup >= 0 ? (lat != Math::qd ? 1/rho : 0) : rho;
77 rho *= 2 * _k0 * _a / _c;
78 k = lat != Math::qd ?
79 (rho / _a) * secphi * sqrt(_e2m + _e2 / Math::sq(secphi)) : _k0;
80 Math::sincosd(lon, x, y);
81 x *= rho;
82 y *= (northp ? -rho : rho);
83 gamma = Math::AngNormalize(northp ? lon : -lon);
84 }
85
86 void PolarStereographic::Reverse(bool northp, real x, real y,
87 real& lat, real& lon,
88 real& gamma, real& k) const {
89 real
90 rho = hypot(x, y),
91 t = rho != 0 ? rho / (2 * _k0 * _a / _c) :
92 Math::sq(numeric_limits<real>::epsilon()),
93 taup = (1 / t - t) / 2,
94 tau = Math::tauf(taup, _es),
95 secphi = hypot(real(1), tau);
96 k = rho != 0 ? (rho / _a) * secphi * sqrt(_e2m + _e2 / Math::sq(secphi)) :
97 _k0;
98 lat = (northp ? 1 : -1) * Math::atand(tau);
99 lon = Math::atan2d(x, northp ? -y : y );
100 gamma = Math::AngNormalize(northp ? lon : -lon);
101 }
102
103 void PolarStereographic::SetScale(real lat, real k) {
104 if (!(isfinite(k) && k > 0))
105 throw GeographicErr("Scale is not positive");
106 if (!(-Math::qd < lat && lat <= Math::qd))
107 throw GeographicErr("Latitude must be in (-" + to_string(Math::qd)
108 + "d, " + to_string(Math::qd) + "d]");
109 real x, y, gamma, kold;
110 _k0 = 1;
111 Forward(true, lat, 0, x, y, gamma, kold);
112 _k0 *= k/kold;
113 }
114
115} // 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:77
GeographicLib::Math::tand
static T tand(T x)
Definition: Math.cpp:172
GeographicLib::Math::LatFix
static T LatFix(T x)
Definition: Math.hpp:293
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::sq
static T sq(T x)
Definition: Math.hpp:205
GeographicLib::Math::tauf
static T tauf(T taup, T es)
Definition: Math.cpp:219
GeographicLib::Math::AngNormalize
static T AngNormalize(T x)
Definition: Math.cpp:71
GeographicLib::Math::atand
static T atand(T x)
Definition: Math.cpp:202
GeographicLib::Math::taupf
static T taupf(T tau, T es)
Definition: Math.cpp:209
GeographicLib::Math::qd
@ qd
degrees per quarter turn
Definition: Math.hpp:138
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:86
GeographicLib::PolarStereographic::PolarStereographic
PolarStereographic(real a, real f, real k0)
Definition: PolarStereographic.cpp:21
GeographicLib::PolarStereographic::SetScale
void SetScale(real lat, real k=real(1))
Definition: PolarStereographic.cpp:103
GeographicLib::PolarStereographic::UPS
static const PolarStereographic & UPS()
Definition: PolarStereographic.cpp:38
GeographicLib::PolarStereographic::Forward
void Forward(bool northp, real lat, real lon, real &x, real &y, real &gamma, real &k) const
Definition: PolarStereographic.cpp:66
GeographicLib
Namespace for GeographicLib.
Definition: Accumulator.cpp:12
std
Definition: NearestNeighbor.hpp:812