Ellipsoid.hpp

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#if !defined(GEOGRAPHICLIB_ELLIPSOID_HPP)
#define GEOGRAPHICLIB_ELLIPSOID_HPP 1

#include <GeographicLib/Constants.hpp>
#include <GeographicLib/TransverseMercator.hpp>
#include <GeographicLib/EllipticFunction.hpp>
#include <GeographicLib/AlbersEqualArea.hpp>

namespace GeographicLib {

  class GEOGRAPHICLIB_EXPORT Ellipsoid {
  private:
    typedef Math::real real;
    static const int numit_ = 10;
    real stol_;
    real _a, _f, _f1, _f12, _e2, _es, _e12, _n, _b;
    TransverseMercator _tm;
    EllipticFunction _ell;
    AlbersEqualArea _au;

    // These are the alpha and beta coefficients in the Krueger series from
    // TransverseMercator.  Thy are used by RhumbSolve to compute
    // (psi2-psi1)/(mu2-mu1).
    const Math::real* ConformalToRectifyingCoeffs() const { return _tm._alp; }
    const Math::real* RectifyingToConformalCoeffs() const { return _tm._bet; }
    friend class Rhumb; friend class RhumbLine;
  public:

    Ellipsoid(real a, real f);


    Math::real MajorRadius() const { return _a; }

    Math::real MinorRadius() const { return _b; }

    Math::real QuarterMeridian() const;

    Math::real Area() const;

    Math::real Volume() const
    { return (4 * Math::pi()) * Math::sq(_a) * _b / 3; }


    Math::real Flattening() const { return _f; }

    Math::real SecondFlattening() const { return _f / (1 - _f); }

    Math::real ThirdFlattening() const { return _n; }

    Math::real EccentricitySq() const { return _e2; }

    Math::real SecondEccentricitySq() const { return _e12; }

    Math::real ThirdEccentricitySq() const { return _e2 / (2 - _e2); }


    Math::real ParametricLatitude(real phi) const;

    Math::real InverseParametricLatitude(real beta) const;

    Math::real GeocentricLatitude(real phi) const;

    Math::real InverseGeocentricLatitude(real theta) const;

    Math::real RectifyingLatitude(real phi) const;

    Math::real InverseRectifyingLatitude(real mu) const;

    Math::real AuthalicLatitude(real phi) const;

    Math::real InverseAuthalicLatitude(real xi) const;

    Math::real ConformalLatitude(real phi) const;

    Math::real InverseConformalLatitude(real chi) const;

    Math::real IsometricLatitude(real phi) const;

    Math::real InverseIsometricLatitude(real psi) const;


    Math::real CircleRadius(real phi) const;

    Math::real CircleHeight(real phi) const;

    Math::real MeridianDistance(real phi) const;

    Math::real MeridionalCurvatureRadius(real phi) const;

    Math::real TransverseCurvatureRadius(real phi) const;

    Math::real NormalCurvatureRadius(real phi, real azi) const;


    static Math::real SecondFlatteningToFlattening(real fp)
    { return fp / (1 + fp); }

    static Math::real FlatteningToSecondFlattening(real f)
    { return f / (1 - f); }

    static Math::real ThirdFlatteningToFlattening(real n)
    { return 2 * n / (1 + n); }

    static Math::real FlatteningToThirdFlattening(real f)
    { return f / (2 - f); }

    static Math::real EccentricitySqToFlattening(real e2)
    { using std::sqrt; return e2 / (sqrt(1 - e2) + 1); }

    static Math::real FlatteningToEccentricitySq(real f)
    { return f * (2 - f); }

    static Math::real SecondEccentricitySqToFlattening(real ep2)
    { using std::sqrt; return ep2 / (sqrt(1 + ep2) + 1 + ep2); }

    static Math::real FlatteningToSecondEccentricitySq(real f)
    { return f * (2 - f) / Math::sq(1 - f); }

    static Math::real ThirdEccentricitySqToFlattening(real epp2) {
      using std::sqrt;
      return 2 * epp2 / (sqrt((1 - epp2) * (1 + epp2)) + 1 + epp2);
    }

    static Math::real FlatteningToThirdEccentricitySq(real f)
    { return f * (2 - f) / (1 + Math::sq(1 - f)); }


    static const Ellipsoid& WGS84();
  };

} // namespace GeographicLib

#endif  // GEOGRAPHICLIB_ELLIPSOID_HPP