Function UTMtoLatLon

libs/platform/utm_mgrs_utils.cpp:233–295

Convert UTM parameters to lat,lon for WSG 84 ellipsoid. If UTM parameters are valid lat and lon references are used to output calculated coordinates. Otherwise function returns empty optional.

// If UTM parameters are valid lat and lon references are used to output calculated coordinates.
// Otherwise function returns empty optional.
std::optional<ms::LatLon> UTMtoLatLon(int easting, int northing, int zoneNumber, char zoneLetter)
{
  if (zoneNumber < 1 || zoneNumber > 60)
    return {};

  if (easting < 100000 || easting >= 1000000)
    return {};

  if (northing < 0 || northing > 10000000)
    return {};

  if (zoneLetter < 'C' || zoneLetter > 'X' || zoneLetter == 'I' || zoneLetter == 'O')
    return {};

  bool const northern = (zoneLetter >= 'N');
  double const x = easting - 500000.0;
  double y = northing;

  if (!northern)
    y -= 10000000.0;

  double const m = y / K0;
  double const mu = m / (R * M1);

  double const p_rad = (mu + P2 * sin(2.0 * mu) + P3 * sin(4.0 * mu) + P4 * sin(6.0 * mu) + P5 * sin(8.0 * mu));

  double const p_sin = sin(p_rad);
  double const p_sin2 = p_sin * p_sin;

  double const p_cos = cos(p_rad);

  double const p_tan = p_sin / p_cos;
  double const p_tan2 = p_tan * p_tan;
  double const p_tan4 = p_tan2 * p_tan2;

  double const ep_sin = 1 - E * p_sin2;
  double const ep_sin_sqrt = sqrt(1 - E * p_sin2);

  double const n = R / ep_sin_sqrt;
  double const r = (1 - E) / ep_sin;

  double const c = E_P2 * p_cos * p_cos;
  double const c2 = c * c;

  double const d = x / (n * K0);
  double const d2 = d * d;
  double const d3 = d2 * d;
  double const d4 = d3 * d;
  double const d5 = d4 * d;
  double const d6 = d5 * d;

  double const latitude =
      (p_rad - (p_tan / r) * (d2 / 2.0 - d4 / 24.0 * (5.0 + 3.0 * p_tan2 + 10.0 * c - 4.0 * c2 - 9.0 * E_P2)) +
       d6 / 720.0 * (61.0 + 90.0 * p_tan2 + 298.0 * c + 45.0 * p_tan4 - 252.0 * E_P2 - 3.0 * c2));

  double longitude = (d - d3 / 6.0 * (1.0 + 2.0 * p_tan2 + c) +
                      d5 / 120.0 * (5.0 - 2.0 * c + 28.0 * p_tan2 - 3.0 * c2 + 8.0 * E_P2 + 24.0 * p_tan4)) /
                     p_cos;