OSGB.hpp

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/**
 * \file OSGB.hpp
 * \brief Header for GeographicLib::OSGB class
 *
 * Copyright (c) Charles Karney (2010-2024) <karney@alum.mit.edu> and licensed
 * under the MIT/X11 License.  For more information, see
 * https://geographiclib.sourceforge.io/
 **********************************************************************/

#if !defined(GEOGRAPHICLIB_OSGB_HPP)
#define GEOGRAPHICLIB_OSGB_HPP 1

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

namespace GeographicLib {

  /**
   * \brief Ordnance Survey grid system for Great Britain
   *
   * The class implements the coordinate system used by the Ordnance Survey for
   * maps of Great Britain and conversions to the grid reference system.
   *
   * See
   * - <a href="https://www.ordnancesurvey.co.uk/documents/resources/guide-coordinate-systems-great-britain.pdf">
   *   A guide to coordinate systems in Great Britain</a>
   * - <a href="https://www.ordnancesurvey.co.uk/documents/resources/guide-to-nationalgrid.pdf">
   *   Using the National Grid</a>
   *
   * \warning the latitudes and longitudes for the Ordnance Survey grid
   * system do not use the WGS84 datum.  Do not use the values returned by this
   * class in the UTMUPS, MGRS, or Geoid classes without first converting the
   * datum (and vice versa).
   *
   * Example of use:
   * \include example-OSGB.cpp
   **********************************************************************/
  class GEOGRAPHICLIB_EXPORT OSGB {
  private:
    typedef Math::real real;
    static const char* const letters_;
    static const char* const digits_;
    static const TransverseMercator& OSGBTM();
    static constexpr int base_ = 10;
    static constexpr int tile_ = 100000;
    static constexpr int tilelevel_ = 5;
    static constexpr int tilegrid_ = 5;
    static constexpr int tileoffx_ = 2 * tilegrid_;
    static constexpr int tileoffy_ = 1 * tilegrid_;
    static constexpr int minx_ = - tileoffx_ * tile_;
    static constexpr int miny_ = - tileoffy_ * tile_;
    static constexpr int maxx_ = (tilegrid_*tilegrid_ - tileoffx_) * tile_;
    static constexpr int maxy_ = (tilegrid_*tilegrid_ - tileoffy_) * tile_;
    // Maximum precision is um
    static constexpr int maxprec_ = 5 + 6;
    static real computenorthoffset();
    static void CheckCoords(real x, real y);
    OSGB() = delete;            // Disable constructor
  public:

    /**
     * Forward projection, from geographic to OSGB coordinates.
     *
     * @param[in] lat latitude of point (degrees).
     * @param[in] lon longitude of point (degrees).
     * @param[out] x easting of point (meters).
     * @param[out] y northing of point (meters).
     * @param[out] gamma meridian convergence at point (degrees).
     * @param[out] k scale of projection at point.
     *
     * \e lat should be in the range [&minus;90&deg;, 90&deg;].
     **********************************************************************/
    static void Forward(real lat, real lon,
                        real& x, real& y, real& gamma, real& k) {
      OSGBTM().Forward(OriginLongitude(), lat, lon, x, y, gamma, k);
      x += FalseEasting();
      y += computenorthoffset();
    }

    /**
     * Reverse projection, from OSGB coordinates to geographic.
     *
     * @param[in] x easting of point (meters).
     * @param[in] y northing of point (meters).
     * @param[out] lat latitude of point (degrees).
     * @param[out] lon longitude of point (degrees).
     * @param[out] gamma meridian convergence at point (degrees).
     * @param[out] k scale of projection at point.
     *
     * The value of \e lon returned is in the range [&minus;180&deg;,
     * 180&deg;].
     **********************************************************************/

    static void Reverse(real x, real y,
                        real& lat, real& lon, real& gamma, real& k) {
      x -= FalseEasting();
      y -= computenorthoffset();
      OSGBTM().Reverse(OriginLongitude(), x, y, lat, lon, gamma, k);
    }

    /**
     * OSGB::Forward without returning the convergence and scale.
     **********************************************************************/
    static void Forward(real lat, real lon, real& x, real& y) {
      real gamma, k;
      Forward(lat, lon, x, y, gamma, k);
    }

    /**
     * OSGB::Reverse without returning the convergence and scale.
     **********************************************************************/
    static void Reverse(real x, real y, real& lat, real& lon) {
      real gamma, k;
      Reverse(x, y, lat, lon, gamma, k);
    }

    /**
     * Convert OSGB coordinates to a grid reference.
     *
     * @param[in] x easting of point (meters).
     * @param[in] y northing of point (meters).
     * @param[in] prec precision relative to 100 km.
     * @param[out] gridref National Grid reference.
     * @exception GeographicErr if \e prec, \e x, or \e y is outside its
     *   allowed range.
     * @exception std::bad_alloc if the memory for \e gridref can't be
     *   allocatied.
     *
     * \e prec specifies the precision of the grid reference string as follows:
     * - prec = 0 (min), 100km
     * - prec = 1, 10km
     * - prec = 2, 1km
     * - prec = 3, 100m
     * - prec = 4, 10m
     * - prec = 5, 1m
     * - prec = 6, 0.1m
     * - prec = 11 (max), 1&mu;m
     *
     * The easting must be in the range [&minus;1000 km, 1500 km) and the
     * northing must be in the range [&minus;500 km, 2000 km).  These bounds
     * are consistent with rules for the letter designations for the grid
     * system.
     *
     * If \e x or \e y is NaN, the returned grid reference is "INVALID".
     **********************************************************************/
    static void GridReference(real x, real y, int prec, std::string& gridref);

    /**
     * Convert OSGB grid reference to coordinates.
     *
     * @param[in] gridref National Grid reference.
     * @param[out] x easting of point (meters).
     * @param[out] y northing of point (meters).
     * @param[out] prec precision relative to 100 km.
     * @param[in] centerp if true (default), return center of the grid square,
     *   else return SW (lower left) corner.
     * @exception GeographicErr if \e gridref is illegal.
     *
     * The grid reference must be of the form: two letters (not including I)
     * followed by an even number of digits (up to 22).
     *
     * If the first 2 characters of \e gridref are "IN", then \e x and \e y are
     * set to NaN and \e prec is set to &minus;2.
     **********************************************************************/
    static void GridReference(const std::string& gridref,
                              real& x, real& y, int& prec,
                              bool centerp = true);

    /** \name Inspector functions
     **********************************************************************/
    ///@{
    /**
     * @return \e a the equatorial radius of the Airy 1830 ellipsoid (meters).
     *
     * This is 20923713 ft converted to meters using the rule 1 ft =
     * 10<sup>9.48401603&minus;10</sup> m.  The Airy 1830 value is returned
     * because the OSGB projection is based on this ellipsoid.  The conversion
     * factor from feet to meters is the one used for the 1936 retriangulation
     * of Britain; see Section A.1 (footnote 10 on p. 44) of <i>A guide to
     * coordinate systems in Great Britain</i>, v3.6 (2020).
     **********************************************************************/
    static Math::real EquatorialRadius() {
      // result is about 6377563.3960320664406 m
      using std::pow;
      return pow(real(10), real(48401603 - 100000000) / 100000000)
        * real(20923713);
    }

    /**
     * @return \e f the inverse flattening of the Airy 1830 ellipsoid.
     *
     * For the Airy 1830 ellipsoid, \e a = 20923713 ft and \e b = 20853810 ft;
     * thus the flattening = (20923713 &minus; 20853810)/20923713 =
     * 7767/2324857 = 1/299.32496459...  (The Airy 1830 value is returned
     * because the OSGB projection is based on this ellipsoid.)
     **********************************************************************/
    static Math::real Flattening()
    { return real(20923713 - 20853810) / real(20923713); }

    /**
     * @return \e k0 central scale for the OSGB projection (0.9996012717...).
     *
     * C. J. Mugnier, Grids &amp; Datums, PE&amp;RS, Oct. 2003, states that
     * this is defined as 10<sup>9.9998268&minus;10</sup>.
     **********************************************************************/
    static Math::real CentralScale() {
      using std::pow;
      return pow(real(10), real(9998268 - 10000000) / 10000000);
    }

    /**
     * @return latitude of the origin for the OSGB projection (49 degrees).
     **********************************************************************/
    static Math::real OriginLatitude() { return real(49); }

    /**
     * @return longitude of the origin for the OSGB projection (&minus;2
     *   degrees).
     **********************************************************************/
    static Math::real OriginLongitude() { return real(-2); }

    /**
     * @return false northing the OSGB projection (&minus;100000 meters).
     **********************************************************************/
    static Math::real FalseNorthing() { return real(-100000); }

    /**
     * @return false easting the OSGB projection (400000 meters).
     **********************************************************************/
    static Math::real FalseEasting() { return real(400000); }
    ///@}

  };

} // namespace GeographicLib

#endif  // GEOGRAPHICLIB_OSGB_HPP