EllipticFunction.hpp

Go to the documentation of this file.

#if !defined(GEOGRAPHICLIB_ELLIPTICFUNCTION_HPP)
#define GEOGRAPHICLIB_ELLIPTICFUNCTION_HPP 1

#include <GeographicLib/Constants.hpp>

namespace GeographicLib {

  class GEOGRAPHICLIB_EXPORT EllipticFunction {
  private:
    typedef Math::real real;

    enum { num_ = 13 }; // Max depth required for sncndn; probably 5 is enough.
    real _k2, _kp2, _alpha2, _alphap2, _eps;
    real _Kc, _Ec, _Dc, _Pic, _Gc, _Hc;
  public:

    EllipticFunction(real k2 = 0, real alpha2 = 0)
      { Reset(k2, alpha2); }

    EllipticFunction(real k2, real alpha2, real kp2, real alphap2)
      { Reset(k2, alpha2, kp2, alphap2); }

    void Reset(real k2 = 0, real alpha2 = 0)
    { Reset(k2, alpha2, 1 - k2, 1 - alpha2); }

    void Reset(real k2, real alpha2, real kp2, real alphap2);



    Math::real k2() const { return _k2; }

    Math::real kp2() const { return _kp2; }

    Math::real alpha2() const { return _alpha2; }

    Math::real alphap2() const { return _alphap2; }


    Math::real K() const { return _Kc; }

    Math::real E() const { return _Ec; }

    Math::real D() const { return _Dc; }

    Math::real KE() const { return _k2 * _Dc; }

    Math::real Pi() const { return _Pic; }

    Math::real G() const { return _Gc; }

    Math::real H() const { return _Hc; }


    Math::real F(real phi) const;

    Math::real E(real phi) const;

    Math::real Ed(real ang) const;

    Math::real Einv(real x) const;

    Math::real Pi(real phi) const;

    Math::real D(real phi) const;

    Math::real G(real phi) const;

    Math::real H(real phi) const;

    Math::real F(real sn, real cn, real dn) const;

    Math::real E(real sn, real cn, real dn) const;

    Math::real Pi(real sn, real cn, real dn) const;

    Math::real D(real sn, real cn, real dn) const;

    Math::real G(real sn, real cn, real dn) const;

    Math::real H(real sn, real cn, real dn) const;


    Math::real deltaF(real sn, real cn, real dn) const;

    Math::real deltaE(real sn, real cn, real dn) const;

    Math::real deltaEinv(real stau, real ctau) const;

    Math::real deltaPi(real sn, real cn, real dn) const;

    Math::real deltaD(real sn, real cn, real dn) const;

    Math::real deltaG(real sn, real cn, real dn) const;

    Math::real deltaH(real sn, real cn, real dn) const;


    void sncndn(real x, real& sn, real& cn, real& dn) const;

    Math::real Delta(real sn, real cn) const {
      using std::sqrt;
      return sqrt(_k2 < 0 ? 1 - _k2 * sn*sn : _kp2 + _k2 * cn*cn);
    }


    static real RF(real x, real y, real z);

    static real RF(real x, real y);

    static real RC(real x, real y);

    static real RG(real x, real y, real z);

    static real RG(real x, real y);

    static real RJ(real x, real y, real z, real p);

    static real RD(real x, real y, real z);

  };

} // namespace GeographicLib

#endif  // GEOGRAPHICLIB_ELLIPTICFUNCTION_HPP