Ellipsoid.cpp

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/**
 * \file Ellipsoid.cpp
 * \brief Implementation for GeographicLib::Ellipsoid class
 *
 * Copyright (c) Charles Karney (2012-2022) <charles@karney.com> and licensed
 * under the MIT/X11 License.  For more information, see
 * https://geographiclib.sourceforge.io/
 **********************************************************************/
 
#include <GeographicLib/Ellipsoid.hpp>
 
#if defined(_MSC_VER)
// Squelch warnings about enum-float expressions
#  pragma warning (disable: 5055)
#endif
 
namespace GeographicLib {
 
  using namespace std;
 
  Ellipsoid::Ellipsoid(real a, real f)
    : stol_(real(0.01) * sqrt(numeric_limits<real>::epsilon()))
    , _a(a)
    , _f(f)
    , _f1(1 - _f)
    , _f12(Math::sq(_f1))
    , _e2(_f * (2 - _f))
    , _es((_f < 0 ? -1 : 1) * sqrt(fabs(_e2)))
    , _e12(_e2 / (1 - _e2))
    , _n(_f / (2  - _f))
    , _b(_a * _f1)
    , _tm(_a, _f, real(1))
    , _ell(-_e12)
    , _au(_a, _f, real(0), real(1), real(0), real(1), real(1))
  {}
 
  const Ellipsoid& Ellipsoid::WGS84() {
    static const Ellipsoid wgs84(Constants::WGS84_a(), Constants::WGS84_f());
    return wgs84;
  }
 
  Math::real Ellipsoid::QuarterMeridian() const
  { return _b * _ell.E(); }
 
  Math::real Ellipsoid::Area() const {
    return 4 * Math::pi() *
      ((Math::sq(_a) + Math::sq(_b) *
        (_e2 == 0 ? 1 :
         (_e2 > 0 ? atanh(sqrt(_e2)) : atan(sqrt(-_e2))) /
         sqrt(fabs(_e2))))/2);
  }
 
  Math::real Ellipsoid::ParametricLatitude(real phi) const
  { return Math::atand(_f1 * Math::tand(Math::LatFix(phi))); }
 
  Math::real Ellipsoid::InverseParametricLatitude(real beta) const
  { return Math::atand(Math::tand(Math::LatFix(beta)) / _f1); }
 
  Math::real Ellipsoid::GeocentricLatitude(real phi) const
  { return Math::atand(_f12 * Math::tand(Math::LatFix(phi))); }
 
  Math::real Ellipsoid::InverseGeocentricLatitude(real theta) const
  { return Math::atand(Math::tand(Math::LatFix(theta)) / _f12); }
 
  Math::real Ellipsoid::RectifyingLatitude(real phi) const {
    return fabs(phi) == Math::qd ? phi:
      Math::qd * MeridianDistance(phi) / QuarterMeridian();
  }
 
  Math::real Ellipsoid::InverseRectifyingLatitude(real mu) const {
    if (fabs(mu) == Math::qd)
      return mu;
    return InverseParametricLatitude(_ell.Einv(mu * _ell.E() / Math::qd) /
                                     Math::degree());
  }
 
  Math::real Ellipsoid::AuthalicLatitude(real phi) const
  { return Math::atand(_au.txif(Math::tand(Math::LatFix(phi)))); }
 
  Math::real Ellipsoid::InverseAuthalicLatitude(real xi) const
  { return Math::atand(_au.tphif(Math::tand(Math::LatFix(xi)))); }
 
  Math::real Ellipsoid::ConformalLatitude(real phi) const
  { return Math::atand(Math::taupf(Math::tand(Math::LatFix(phi)), _es)); }
 
  Math::real Ellipsoid::InverseConformalLatitude(real chi) const
  { return Math::atand(Math::tauf(Math::tand(Math::LatFix(chi)), _es)); }
 
  Math::real Ellipsoid::IsometricLatitude(real phi) const
  { return asinh(Math::taupf(Math::tand(Math::LatFix(phi)), _es)) /
      Math::degree(); }
 
  Math::real Ellipsoid::InverseIsometricLatitude(real psi) const
  { return Math::atand(Math::tauf(sinh(psi * Math::degree()), _es)); }
 
  Math::real Ellipsoid::CircleRadius(real phi) const {
    return fabs(phi) == Math::qd ? 0 :
      // a * cos(beta)
      _a / hypot(real(1), _f1 * Math::tand(Math::LatFix(phi)));
  }
 
  Math::real Ellipsoid::CircleHeight(real phi) const {
    real tbeta = _f1 * Math::tand(phi);
    // b * sin(beta)
    return _b * tbeta / hypot(real(1),
                              _f1 * Math::tand(Math::LatFix(phi)));
  }
 
  Math::real Ellipsoid::MeridianDistance(real phi) const
  { return _b * _ell.Ed( ParametricLatitude(phi) ); }
 
  Math::real Ellipsoid::MeridionalCurvatureRadius(real phi) const {
    real v = 1 - _e2 * Math::sq(Math::sind(Math::LatFix(phi)));
    return _a * (1 - _e2) / (v * sqrt(v));
  }
 
  Math::real Ellipsoid::TransverseCurvatureRadius(real phi) const {
    real v = 1 - _e2 * Math::sq(Math::sind(Math::LatFix(phi)));
    return _a / sqrt(v);
  }
 
  Math::real Ellipsoid::NormalCurvatureRadius(real phi, real azi) const {
    real calp, salp,
      v = 1 - _e2 * Math::sq(Math::sind(Math::LatFix(phi)));
    Math::sincosd(azi, salp, calp);
    return _a / (sqrt(v) * (Math::sq(calp) * v / (1 - _e2) + Math::sq(salp)));
  }
 
} // namespace GeographicLib