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PolarStereographic.cpp
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/**
* \file PolarStereographic.cpp
* \brief Implementation for GeographicLib::PolarStereographic class
*
* Copyright (c) Charles Karney (2008-2022) <karney@alum.mit.edu> and licensed
* under the MIT/X11 License. For more information, see
* https://geographiclib.sourceforge.io/
**********************************************************************/
#include <GeographicLib/PolarStereographic.hpp>
namespace GeographicLib {
using namespace std;
PolarStereographic::PolarStereographic(real a, real f, real k0)
: _a(a)
, _f(f)
, _e2(_f * (2 - _f))
, _es((_f < 0 ? -1 : 1) * sqrt(fabs(_e2)))
, _e2m(1 - _e2)
, _c( (1 - _f) * exp(Math::eatanhe(real(1), _es)) )
, _k0(k0)
{
if (!(isfinite(_a) && _a > 0))
throw GeographicErr("Equatorial radius is not positive");
if (!(isfinite(_f) && _f < 1))
throw GeographicErr("Polar semi-axis is not positive");
if (!(isfinite(_k0) && _k0 > 0))
throw GeographicErr("Scale is not positive");
}
const PolarStereographic& PolarStereographic::UPS() {
static const PolarStereographic ups(Constants::WGS84_a(),
Constants::WGS84_f(),
Constants::UPS_k0());
return ups;
}
// This formulation converts to conformal coordinates by tau = tan(phi) and
// tau' = tan(phi') where phi' is the conformal latitude. The formulas are:
// tau = tan(phi)
// secphi = hypot(1, tau)
// sig = sinh(e * atanh(e * tau / secphi))
// taup = tan(phip) = tau * hypot(1, sig) - sig * hypot(1, tau)
// c = (1 - f) * exp(e * atanh(e))
//
// Forward:
// rho = (2*k0*a/c) / (hypot(1, taup) + taup) (taup >= 0)
// = (2*k0*a/c) * (hypot(1, taup) - taup) (taup < 0)
//
// Reverse:
// taup = ((2*k0*a/c) / rho - rho / (2*k0*a/c))/2
//
// Scale:
// k = (rho/a) * secphi * sqrt((1-e2) + e2 / secphi^2)
//
// In limit rho -> 0, tau -> inf, taup -> inf, secphi -> inf, secphip -> inf
// secphip = taup = exp(-e * atanh(e)) * tau = exp(-e * atanh(e)) * secphi
void PolarStereographic::Forward(bool northp, real lat, real lon,
real& x, real& y,
real& gamma, real& k) const {
lat = Math::LatFix(lat);
lat *= northp ? 1 : -1;
real
tau = Math::tand(lat),
secphi = hypot(real(1), tau),
taup = Math::taupf(tau, _es),
rho = hypot(real(1), taup) + fabs(taup);
rho = taup >= 0 ? (lat != Math::qd ? 1/rho : 0) : rho;
rho *= 2 * _k0 * _a / _c;
k = lat != Math::qd ?
(rho / _a) * secphi * sqrt(_e2m + _e2 / Math::sq(secphi)) : _k0;
Math::sincosd(lon, x, y);
x *= rho;
y *= (northp ? -rho : rho);
gamma = Math::AngNormalize(northp ? lon : -lon);
}
void PolarStereographic::Reverse(bool northp, real x, real y,
real& lat, real& lon,
real& gamma, real& k) const {
real
rho = hypot(x, y),
t = rho != 0 ? rho / (2 * _k0 * _a / _c) :
Math::sq(numeric_limits<real>::epsilon()),
taup = (1 / t - t) / 2,
tau = Math::tauf(taup, _es),
secphi = hypot(real(1), tau);
k = rho != 0 ? (rho / _a) * secphi * sqrt(_e2m + _e2 / Math::sq(secphi)) :
_k0;
lat = (northp ? 1 : -1) * Math::atand(tau);
lon = Math::atan2d(x, northp ? -y : y );
gamma = Math::AngNormalize(northp ? lon : -lon);
}
void PolarStereographic::SetScale(real lat, real k) {
if (!(isfinite(k) && k > 0))
throw GeographicErr("Scale is not positive");
if (!(-Math::qd < lat && lat <= Math::qd))
throw GeographicErr("Latitude must be in (-" + to_string(Math::qd)
+ "d, " + to_string(Math::qd) + "d]");
real x, y, gamma, kold;
_k0 = 1;
Forward(true, lat, 0, x, y, gamma, kold);
_k0 *= k/kold;
}
} // 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:188
GeographicLib::Math::LatFix
static T LatFix(T x)
Definition Math.hpp:309
GeographicLib::Math::sincosd
static void sincosd(T x, T &sinx, T &cosx)
Definition Math.cpp:101
GeographicLib::Math::atan2d
static T atan2d(T y, T x)
Definition Math.cpp:199
GeographicLib::Math::sq
static T sq(T x)
Definition Math.hpp:221
GeographicLib::Math::qd
static constexpr int qd
degrees per quarter turn
Definition Math.hpp:145
GeographicLib::Math::tauf
static T tauf(T taup, T es)
Definition Math.cpp:235
GeographicLib::Math::AngNormalize
static T AngNormalize(T x)
Definition Math.cpp:66
GeographicLib::Math::atand
static T atand(T x)
Definition Math.cpp:218
GeographicLib::Math::taupf
static T taupf(T tau, T es)
Definition Math.cpp:225
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