TransformUTMTo4326 Class Reference

#include <Utm.h>

Public Member Functions
DEVICE ALWAYS_INLINE	TransformUTMTo4326 (unsigned const srid, double const x, double const y)
DEVICE ALWAYS_INLINE double	calculateX () const
DEVICE ALWAYS_INLINE double	calculateY () const

Private Attributes
unsigned const	srid_
double	eta_
double	xi_
bool	small_eta_

Detailed Description

Definition at line 211 of file Utm.h.

Constructor & Destructor Documentation

DEVICE ALWAYS_INLINE TransformUTMTo4326::TransformUTMTo4326 ( unsigned const  srid, double const  x, double const  y  )

inline

Definition at line 224 of file Utm.h.

References anonymous_namespace{Utm.h}::betas, anonymous_namespace{Utm.h}::E0, eta_, shared::fastCosh(), shared::fastSinh(), anonymous_namespace{Utm.h}::k0_A, anonymous_namespace{Utm.h}::N, small_eta_, srid_, and xi_.

      : srid_(srid) {
    double const eta = (x - E0) / k0_A;
    small_eta_ = -1.0 / 12 <= eta && eta <= 1.0 / 12;
    double const N0 = (32700 < srid_) * 10e6;  // UTM False northing (m)
    double const xi = (y - N0) / k0_A;

    double eta_sum = 0;
    double xi_sum = 0;
    if (small_eta_) {
      for (unsigned j = N; j; --j) {
        eta_sum += betas[j] * cos(2 * j * xi) * shared::fastSinh(2 * j * eta);
      }
      for (unsigned j = N; j; --j) {
        xi_sum += betas[j] * sin(2 * j * xi) * shared::fastCosh(2 * j * eta);
      }
    } else {
      for (unsigned j = N; j; --j) {
        eta_sum += betas[j] * cos(2 * j * xi) * sinh(2 * j * eta);
      }
      for (unsigned j = N; j; --j) {
        xi_sum += betas[j] * sin(2 * j * xi) * cosh(2 * j * eta);
      }
    }
    eta_ = eta - eta_sum;
    xi_ = xi - xi_sum;
  }

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Member Function Documentation

DEVICE ALWAYS_INLINE double TransformUTMTo4326::calculateX ( ) const

inline

Definition at line 255 of file Utm.h.

References math_consts::deg_div_rad, eta_, shared::fastSinh(), small_eta_, srid_, and xi_.

Referenced by conv_utm_4326(), and transform_utm_4326_x().

                                                 {
    unsigned const zone = srid_ % 100u;
    double const lambda0 = zone * 6.0 - 183;
    double const sinh_eta = small_eta_ ? shared::fastSinh(eta_) : sinh(eta_);
    return lambda0 + atan(sinh_eta / cos(xi_)) * math_consts::deg_div_rad;
  }

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DEVICE ALWAYS_INLINE double TransformUTMTo4326::calculateY ( ) const

inline

Definition at line 263 of file Utm.h.

References math_consts::deg_div_rad, anonymous_namespace{Utm.h}::deltas, eta_, f(), shared::fastCosh(), anonymous_namespace{Utm.h}::N, small_eta_, and xi_.

Referenced by conv_utm_4326(), and transform_utm_4326_y().

                                                 {
#if 1
    // https://en.wikipedia.org/wiki/Universal_Transverse_Mercator_coordinate_system#Simplified_formulae
    double const cosh_eta = small_eta_ ? shared::fastCosh(eta_) : cosh(eta_);
    double const chi = asin(sin(xi_) / cosh_eta);
    double sum = 0;
    for (unsigned j = N; j; --j) {
      sum += deltas[j] * sin(2 * j * chi);
    }
    return (chi + sum) * math_consts::deg_div_rad;
#else
    // Heavier calculation from Transverse Mercator with an accuracy of a few nanometers
    // by Karney 3 Feb 2011.  This does not make use of the constexpr delta Fourier
    // coefficients used by Kawase 2011 above which appears to be more accurate and
    // probably faster.
    double const e = std::sqrt(f * (2 - f));
    double const taup =
        std::sin(xi_) / std::sqrt(sq(std::sinh(eta_)) + sq(std::cos(xi_)));

    double tau[2]{taup, 0.0 / 0.0};
    unsigned i = 0;
    for (; tau[0] != tau[1]; ++i) {
      double const tau_i = tau[i & 1];
      double const sigma_i =
          std::sinh(e * std::tanh(e * tau_i / std::sqrt(1 + sq(tau_i))));
      double const taup_i =
          tau_i * std::sqrt(1 + sq(sigma_i)) - sigma_i * std::sqrt(1 + sq(tau_i));
      double const dtau_i = (taup - taup_i) * (1 + (1 - e * e) * sq(tau_i)) /
                            ((1 - e * e) * std::sqrt((1 + sq(taup_i)) * (1 + sq(tau_i))));
      tau[~i & 1] = tau_i + dtau_i;
    }
    return std::atan(tau[0]) * deg_div_rad;
#endif
  }

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Member Data Documentation

double TransformUTMTo4326::eta_

private

Definition at line 214 of file Utm.h.

Referenced by calculateX(), calculateY(), and TransformUTMTo4326().

bool TransformUTMTo4326::small_eta_

private

Definition at line 216 of file Utm.h.

Referenced by calculateX(), calculateY(), and TransformUTMTo4326().

unsigned const TransformUTMTo4326::srid_

private

Definition at line 213 of file Utm.h.

Referenced by calculateX(), and TransformUTMTo4326().

double TransformUTMTo4326::xi_

private

Definition at line 215 of file Utm.h.

Referenced by calculateX(), calculateY(), and TransformUTMTo4326().

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The documentation for this class was generated from the following file:

• /home/jenkins-slave/workspace/core-os-doxygen/Geospatial/Utm.h