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MGRS.hpp
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/**
* \file MGRS.hpp
* \brief Header for GeographicLib::MGRS class
*
* Copyright (c) Charles Karney (2008-2024) <karney@alum.mit.edu> and licensed
* under the MIT/X11 License. For more information, see
* https://geographiclib.sourceforge.io/
**********************************************************************/
#if !defined(GEOGRAPHICLIB_MGRS_HPP)
#define GEOGRAPHICLIB_MGRS_HPP 1
#include <GeographicLib/Constants.hpp>
#include <GeographicLib/UTMUPS.hpp>
namespace GeographicLib {
/**
* \brief Convert between UTM/UPS and %MGRS
*
* MGRS is defined in Chapter 3 of
* - J. W. Hager, L. L. Fry, S. S. Jacks, D. R. Hill,
* <a href="https://web.archive.org/web/20161214054445/http://earth-info.nga.mil/GandG/publications/tm8358.1/pdf/TM8358_1.pdf">
* Datums, Ellipsoids, Grids, and Grid Reference Systems</a>,
* Defense Mapping Agency, Technical Manual TM8358.1 (1990).
* .
* This document has been updated by the two NGA documents
* - <a href="https://earth-info.nga.mil/php/download.php?file=coord-grids">
* Universal Grids and Grid Reference Systems</a>,
* NGA.STND.0037 (2014).
* - <a href="https://earth-info.nga.mil/php/download.php?file=coord-utmups">
* The Universal Grids and the Transverse Mercator and Polar Stereographic
* Map Projections</a>, NGA.SIG.0012 (2014).
*
* This implementation has the following properties:
* - The conversions are closed, i.e., output from Forward is legal input for
* Reverse and vice versa. Conversion in both directions preserve the
* UTM/UPS selection and the UTM zone.
* - Forward followed by Reverse and vice versa is approximately the
* identity. (This is affected in predictable ways by errors in
* determining the latitude band and by loss of precision in the MGRS
* coordinates.)
* - The trailing digits produced by Forward are consistent as the precision
* is varied. Specifically, the digits are obtained by operating on the
* easting with &lfloor;10<sup>6</sup> <i>x</i>&rfloor; and extracting the
* required digits from the resulting number (and similarly for the
* northing).
* - All MGRS coordinates truncate to legal 100 km blocks. All MGRS
* coordinates with a legal 100 km block prefix are legal (even though the
* latitude band letter may now belong to a neighboring band).
* - The range of UTM/UPS coordinates allowed for conversion to MGRS
* coordinates is the maximum consistent with staying within the letter
* ranges of the MGRS scheme.
* - All the transformations are implemented as static methods in the MGRS
* class.
*
* The <a href="http://www.nga.mil">NGA</a> software package
* <a href="https://earth-info.nga.mil/index.php?dir=wgs84&action=wgs84#tab_geotrans">geotrans</a>
* also provides conversions to and from MGRS. Version 3.0 (and earlier)
* suffers from some drawbacks:
* - Inconsistent rules are used to determine the whether a particular MGRS
* coordinate is legal. A more systematic approach is taken here.
* - The underlying projections are not very accurately implemented.
*
* Example of use:
* \include example-MGRS.cpp
**********************************************************************/
class GEOGRAPHICLIB_EXPORT MGRS {
private:
typedef Math::real real;
static const char* const hemispheres_;
static const char* const utmcols_[3];
static const char* const utmrow_;
static const char* const upscols_[4];
static const char* const upsrows_[2];
static const char* const latband_;
static const char* const upsband_;
static const char* const digits_;
static const char* const alpha_;
static const int mineasting_[4];
static const int maxeasting_[4];
static const int minnorthing_[4];
static const int maxnorthing_[4];
static constexpr int base_ = 10;
// Top-level tiles are 10^5 m = 100 km on a side
static constexpr int tilelevel_ = 5;
// Period of UTM row letters
static constexpr int utmrowperiod_ = 20;
// Row letters are shifted by 5 for even zones
static constexpr int utmevenrowshift_ = 5;
// Maximum precision is um
static constexpr int maxprec_ = 5 + 6;
// For generating digits at maxprec
static constexpr int mult_ = 1000000;
static void CheckCoords(bool utmp, bool& northp, real& x, real& y);
static int UTMRow(int iband, int icol, int irow);
friend class UTMUPS; // UTMUPS::StandardZone calls LatitudeBand
// Return latitude band number [-10, 10) for the given latitude (degrees).
// The bands are reckoned in include their southern edges.
static int LatitudeBand(real lat) {
using std::floor;
int ilat = int(floor(lat));
return (std::max)(-10, (std::min)(9, (ilat + 80)/8 - 10));
}
// Return approximate latitude band number [-10, 10) for the given northing
// (meters). With this rule, each 100km tile would have a unique band
// letter corresponding to the latitude at the center of the tile. This
// function isn't currently used.
static int ApproxLatitudeBand(real y) {
// northing at tile center in units of tile = 100km
using std::floor, std::fabs, std::fmin;
real ya = floor( fmin(real(88), fabs(y / real(tile_))) ) + real(0.5);
// convert to lat (mult by 90/100) and then to band (divide by 8)
// the +1 fine tunes the boundary between bands 3 and 4
int b = int(floor( ((ya * 9 + 1) / 10) / 8 ));
// For the northern hemisphere we have
// band rows num
// N 0 0:8 9
// P 1 9:17 9
// Q 2 18:26 9
// R 3 27:34 8
// S 4 35:43 9
// T 5 44:52 9
// U 6 53:61 9
// V 7 62:70 9
// W 8 71:79 9
// X 9 80:94 15
return y >= 0 ? b : -(b + 1);
}
// UTMUPS accesses these constants
static constexpr int tile_ = 100000; // Size MGRS blocks
static constexpr int minutmcol_ = 1;
static constexpr int maxutmcol_ = 9;
static constexpr int minutmSrow_ = 10;
static constexpr int maxutmSrow_ = 100; // Also used for UTM S false northing
static constexpr int minutmNrow_ = 0; // Also used for UTM N false northing
static constexpr int maxutmNrow_ = 95;
static constexpr int minupsSind_ = 8; // These 4 ind's apply to easting and northing
static constexpr int maxupsSind_ = 32;
static constexpr int minupsNind_ = 13;
static constexpr int maxupsNind_ = 27;
static constexpr int upseasting_ = 20; // Also used for UPS false northing
static constexpr int utmeasting_ = 5; // UTM false easting
// Difference between S hemisphere northing and N hemisphere northing
static constexpr int utmNshift_ = (maxutmSrow_ - minutmNrow_) * tile_;
MGRS() = delete; // Disable constructor
public:
/**
* Convert UTM or UPS coordinate to an MGRS coordinate.
*
* @param[in] zone UTM zone (zero means UPS).
* @param[in] northp hemisphere (true means north, false means south).
* @param[in] x easting of point (meters).
* @param[in] y northing of point (meters).
* @param[in] prec precision relative to 100 km.
* @param[out] mgrs MGRS string.
* @exception GeographicErr if \e zone, \e x, or \e y is outside its
* allowed range.
* @exception GeographicErr if the memory for the MGRS string can't be
* allocated.
*
* \e prec specifies the precision of the MGRS string as follows:
* - \e prec = &minus;1 (min), only the grid zone is returned
* - \e prec = 0, 100 km
* - \e prec = 1, 10 km
* - \e prec = 2, 1 km
* - \e prec = 3, 100 m
* - \e prec = 4, 10 m
* - \e prec = 5, 1 m
* - \e prec = 6, 0.1 m
* - &hellip;
* - \e prec = 11 (max), 1 &mu;m
*
* UTM eastings are allowed to be in the range [100 km, 900 km], northings
* are allowed to be in in [0 km, 9500 km] for the northern hemisphere and
* in [1000 km, 10000 km] for the southern hemisphere. (However UTM
* northings can be continued across the equator. So the actual limits on
* the northings are [&minus;9000 km, 9500 km] for the "northern"
* hemisphere and [1000 km, 19500 km] for the "southern" hemisphere.)
*
* UPS eastings/northings are allowed to be in the range [1300 km, 2700 km]
* in the northern hemisphere and in [800 km, 3200 km] in the southern
* hemisphere.
*
* The ranges are 100 km more restrictive than for the conversion between
* geographic coordinates and UTM and UPS given by UTMUPS. These
* restrictions are dictated by the allowed letters in MGRS coordinates.
* The choice of 9500 km for the maximum northing for northern hemisphere
* and of 1000 km as the minimum northing for southern hemisphere provide
* at least 0.5 degree extension into standard UPS zones. The upper ends
* of the ranges for the UPS coordinates is dictated by requiring symmetry
* about the meridians 0E and 90E.
*
* All allowed UTM and UPS coordinates may now be converted to legal MGRS
* coordinates with the proviso that eastings and northings on the upper
* boundaries are silently reduced by about 4 nm (4 nanometers) to place
* them \e within the allowed range. (This includes reducing a southern
* hemisphere northing of 10000 km by 4 nm so that it is placed in latitude
* band M.) The UTM or UPS coordinates are truncated to requested
* precision to determine the MGRS coordinate. Thus in UTM zone 38n, the
* square area with easting in [444 km, 445 km) and northing in [3688 km,
* 3689 km) maps to MGRS coordinate 38SMB4488 (at \e prec = 2, 1 km),
* Khulani Sq., Baghdad.
*
* The UTM/UPS selection and the UTM zone is preserved in the conversion to
* MGRS coordinate. Thus for \e zone > 0, the MGRS coordinate begins with
* the zone number followed by one of [C--M] for the southern
* hemisphere and [N--X] for the northern hemisphere. For \e zone =
* 0, the MGRS coordinates begins with one of [AB] for the southern
* hemisphere and [XY] for the northern hemisphere.
*
* The conversion to the MGRS is exact for prec in [0, 5] except that a
* neighboring latitude band letter may be given if the point is within 5nm
* of a band boundary. For prec in [6, 11], the conversion is accurate to
* roundoff.
*
* If \e prec = &minus;1, then the "grid zone designation", e.g., 18T, is
* returned. This consists of the UTM zone number (absent for UPS) and the
* first letter of the MGRS string which labels the latitude band for UTM
* and the hemisphere for UPS.
*
* If \e x or \e y is NaN or if \e zone is UTMUPS::INVALID, the returned
* MGRS string is "INVALID".
*
* Return the result via a reference argument to avoid the overhead of
* allocating a potentially large number of small strings. If an error is
* thrown, then \e mgrs is unchanged.
**********************************************************************/
static void Forward(int zone, bool northp, real x, real y,
int prec, std::string& mgrs);
/**
* Convert UTM or UPS coordinate to an MGRS coordinate when the latitude is
* known.
*
* @param[in] zone UTM zone (zero means UPS).
* @param[in] northp hemisphere (true means north, false means south).
* @param[in] x easting of point (meters).
* @param[in] y northing of point (meters).
* @param[in] lat latitude (degrees).
* @param[in] prec precision relative to 100 km.
* @param[out] mgrs MGRS string.
* @exception GeographicErr if \e zone, \e x, or \e y is outside its
* allowed range.
* @exception GeographicErr if \e lat is inconsistent with the given UTM
* coordinates.
* @exception std::bad_alloc if the memory for \e mgrs can't be allocated.
*
* The latitude is ignored for \e zone = 0 (UPS); otherwise the latitude is
* used to determine the latitude band and this is checked for consistency
* using the same tests as Reverse.
**********************************************************************/
static void Forward(int zone, bool northp, real x, real y, real lat,
int prec, std::string& mgrs);
/**
* Convert a MGRS coordinate to UTM or UPS coordinates.
*
* @param[in] mgrs MGRS string.
* @param[out] zone UTM zone (zero means UPS).
* @param[out] northp hemisphere (true means north, false means south).
* @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 MGRS square,
* else return SW (lower left) corner.
* @exception GeographicErr if \e mgrs is illegal.
*
* All conversions from MGRS to UTM/UPS are permitted provided the MGRS
* coordinate is a possible result of a conversion in the other direction.
* (The leading 0 may be dropped from an input MGRS coordinate for UTM
* zones 1--9.) In addition, MGRS coordinates with a neighboring
* latitude band letter are permitted provided that some portion of the
* 100 km block is within the given latitude band. Thus
* - 38VLS and 38WLS are allowed (latitude 64N intersects the square
* 38[VW]LS); but 38VMS is not permitted (all of 38WMS is north of 64N)
* - 38MPE and 38NPF are permitted (they straddle the equator); but 38NPE
* and 38MPF are not permitted (the equator does not intersect either
* block).
* - Similarly ZAB and YZB are permitted (they straddle the prime
* meridian); but YAB and ZZB are not (the prime meridian does not
* intersect either block).
*
* The UTM/UPS selection and the UTM zone is preserved in the conversion
* from MGRS coordinate. The conversion is exact for prec in [0, 5]. With
* \e centerp = true, the conversion from MGRS to geographic and back is
* stable. This is not assured if \e centerp = false.
*
* If a "grid zone designation" (for example, 18T or A) is given, then some
* suitable (but essentially arbitrary) point within that grid zone is
* returned. The main utility of the conversion is to allow \e zone and \e
* northp to be determined. In this case, the \e centerp parameter is
* ignored and \e prec is set to &minus;1.
*
* If the first 3 characters of \e mgrs are "INV", then \e x and \e y are
* set to NaN, \e zone is set to UTMUPS::INVALID, and \e prec is set to
* &minus;2.
*
* If an exception is thrown, then the arguments are unchanged.
**********************************************************************/
static void Reverse(const std::string& mgrs,
int& zone, bool& northp, real& x, real& y,
int& prec, bool centerp = true);
/**
* Split a MGRS grid reference into its components.
*
* @param[in] mgrs MGRS string, e.g., 38SMB4488.
* @param[out] gridzone the grid zone, e.g., 38S.
* @param[out] block the 100km block id, e.g., MB.
* @param[out] easting the leading digits of the block easting, e.g., 44.
* @param[out] northing the leading digits of the block easting, e.g., 88.
* @exception GeographicErr if \e mgrs is illegal.
*
* Only the most rudimentary checking of MGRS grid ref is done: it is
* expected to consist of 0-2 digits followed by 1 or 3 letters, followed
* (in the case of 3 letters) by an even number (possibly 0) of digits. In
* reporting errors, the letters I and O (illegal in MSRS) are regarded as
* non-alphabetic. The returned \e gridzone will always be non-empty. The
* other output arguments may be empty strings.
*
* If the first 3 characters of \e mgrs are "INV", then \e gridzone is set
* to those 3 characters and the other return arguments are set to empty
* strings..
*
* If an exception is thrown, then the arguments are unchanged.
**********************************************************************/
static void Decode(const std::string& mgrs,
std::string& gridzone, std::string& block,
std::string& easting, std::string& northing);
/** \name Inspector functions
**********************************************************************/
///@{
/**
* @return \e a the equatorial radius of the WGS84 ellipsoid (meters).
*
* (The WGS84 value is returned because the UTM and UPS projections are
* based on this ellipsoid.)
**********************************************************************/
static Math::real EquatorialRadius() { return UTMUPS::EquatorialRadius(); }
/**
* @return \e f the flattening of the WGS84 ellipsoid.
*
* (The WGS84 value is returned because the UTM and UPS projections are
* based on this ellipsoid.)
**********************************************************************/
static Math::real Flattening() { return UTMUPS::Flattening(); }
///@}
/**
* Perform some checks on the UTMUPS coordinates on this ellipsoid. Throw
* an error if any of the assumptions made in the MGRS class is not true.
* This check needs to be carried out if the ellipsoid parameters (or the
* UTM/UPS scales) are ever changed.
**********************************************************************/
static void Check();
};
} // namespace GeographicLib
#endif // GEOGRAPHICLIB_MGRS_HPP
Constants.hpp
Header for GeographicLib::Constants class.
GEOGRAPHICLIB_EXPORT
#define GEOGRAPHICLIB_EXPORT
Definition Constants.hpp:59
real
GeographicLib::Math::real real
Definition Geod3Solve.cpp:25
UTMUPS.hpp
Header for GeographicLib::UTMUPS class.
GeographicLib::MGRS::EquatorialRadius
static Math::real EquatorialRadius()
Definition MGRS.hpp:345
GeographicLib::MGRS::UTMUPS
friend class UTMUPS
Definition MGRS.hpp:99
GeographicLib::MGRS::Flattening
static Math::real Flattening()
Definition MGRS.hpp:353
GeographicLib::Math::real
double real
Definition Math.hpp:115
GeographicLib::UTMUPS::Flattening
static Math::real Flattening()
Definition UTMUPS.hpp:414
GeographicLib::UTMUPS::EquatorialRadius
static Math::real EquatorialRadius()
Definition UTMUPS.hpp:405
GeographicLib
Namespace for GeographicLib.
Definition Accumulator.cpp:12