GeographicLib  2.0
MGRS.hpp
Go to the documentation of this file.
1 /**
2  * \file MGRS.hpp
3  * \brief Header for GeographicLib::MGRS class
4  *
5  * Copyright (c) Charles Karney (2008-2022) <charles@karney.com> and licensed
6  * under the MIT/X11 License. For more information, see
7  * https://geographiclib.sourceforge.io/
8  **********************************************************************/
9 
10 #if !defined(GEOGRAPHICLIB_MGRS_HPP)
11 #define GEOGRAPHICLIB_MGRS_HPP 1
12 
14 #include <GeographicLib/UTMUPS.hpp>
15 
16 #if defined(_MSC_VER)
17 // Squelch warnings about dll vs string
18 # pragma warning (push)
19 # pragma warning (disable: 4251)
20 #endif
21 
22 namespace GeographicLib {
23 
24  /**
25  * \brief Convert between UTM/UPS and %MGRS
26  *
27  * MGRS is defined in Chapter 3 of
28  * - J. W. Hager, L. L. Fry, S. S. Jacks, D. R. Hill,
29  * <a href="https://web.archive.org/web/20161214054445/http://earth-info.nga.mil/GandG/publications/tm8358.1/pdf/TM8358_1.pdf">
30  * Datums, Ellipsoids, Grids, and Grid Reference Systems</a>,
31  * Defense Mapping Agency, Technical Manual TM8358.1 (1990).
32  * .
33  * This document has been updated by the two NGA documents
34  * - <a href="https://earth-info.nga.mil/php/download.php?file=coord-grids">
35  * Universal Grids and Grid Reference Systems</a>,
36  * NGA.STND.0037 (2014).
37  * - <a href="https://earth-info.nga.mil/php/download.php?file=coord-utmups">
38  * The Universal Grids and the Transverse Mercator and Polar Stereographic
39  * Map Projections</a>, NGA.SIG.0012 (2014).
40  *
41  * This implementation has the following properties:
42  * - The conversions are closed, i.e., output from Forward is legal input for
43  * Reverse and vice versa. Conversion in both directions preserve the
44  * UTM/UPS selection and the UTM zone.
45  * - Forward followed by Reverse and vice versa is approximately the
46  * identity. (This is affected in predictable ways by errors in
47  * determining the latitude band and by loss of precision in the MGRS
48  * coordinates.)
49  * - The trailing digits produced by Forward are consistent as the precision
50  * is varied. Specifically, the digits are obtained by operating on the
51  * easting with &lfloor;10<sup>6</sup> <i>x</i>&rfloor; and extracting the
52  * required digits from the resulting number (and similarly for the
53  * northing).
54  * - All MGRS coordinates truncate to legal 100 km blocks. All MGRS
55  * coordinates with a legal 100 km block prefix are legal (even though the
56  * latitude band letter may now belong to a neighboring band).
57  * - The range of UTM/UPS coordinates allowed for conversion to MGRS
58  * coordinates is the maximum consistent with staying within the letter
59  * ranges of the MGRS scheme.
60  * - All the transformations are implemented as static methods in the MGRS
61  * class.
62  *
63  * The <a href="http://www.nga.mil">NGA</a> software package
64  * <a href="https://earth-info.nga.mil/index.php?dir=wgs84&action=wgs84#tab_geotrans">geotrans</a>
65  * also provides conversions to and from MGRS. Version 3.0 (and earlier)
66  * suffers from some drawbacks:
67  * - Inconsistent rules are used to determine the whether a particular MGRS
68  * coordinate is legal. A more systematic approach is taken here.
69  * - The underlying projections are not very accurately implemented.
70  *
71  * Example of use:
72  * \include example-MGRS.cpp
73  **********************************************************************/
75  private:
76  typedef Math::real real;
77  static const char* const hemispheres_;
78  static const char* const utmcols_[3];
79  static const char* const utmrow_;
80  static const char* const upscols_[4];
81  static const char* const upsrows_[2];
82  static const char* const latband_;
83  static const char* const upsband_;
84  static const char* const digits_;
85 
86  static const int mineasting_[4];
87  static const int maxeasting_[4];
88  static const int minnorthing_[4];
89  static const int maxnorthing_[4];
90 #if GEOGRAPHICLIB_PRECISION == 4
91  // Work around an enum lossage introduced in boost 1.76
92  // https://github.com/boostorg/multiprecision/issues/324
93  // and fixed in
94  // https://github.com/boostorg/multiprecision/pull/333
95  static const int
96 #else
97  enum {
98 #endif
99  base_ = 10,
100  // Top-level tiles are 10^5 m = 100 km on a side
101  tilelevel_ = 5,
102  // Period of UTM row letters
103  utmrowperiod_ = 20,
104  // Row letters are shifted by 5 for even zones
105  utmevenrowshift_ = 5,
106  // Maximum precision is um
107  maxprec_ = 5 + 6,
108  // For generating digits at maxprec
109  mult_ = 1000000
110 #if GEOGRAPHICLIB_PRECISION == 4
111  ;
112 #else
113  };
114 #endif
115  static void CheckCoords(bool utmp, bool& northp, real& x, real& y);
116  static int UTMRow(int iband, int icol, int irow);
117 
118  friend class UTMUPS; // UTMUPS::StandardZone calls LatitudeBand
119  // Return latitude band number [-10, 10) for the given latitude (degrees).
120  // The bands are reckoned in include their southern edges.
121  static int LatitudeBand(real lat) {
122  using std::floor;
123  int ilat = int(floor(lat));
124  return (std::max)(-10, (std::min)(9, (ilat + 80)/8 - 10));
125  }
126  // Return approximate latitude band number [-10, 10) for the given northing
127  // (meters). With this rule, each 100km tile would have a unique band
128  // letter corresponding to the latitude at the center of the tile. This
129  // function isn't currently used.
130  static int ApproxLatitudeBand(real y) {
131  // northing at tile center in units of tile = 100km
132  using std::floor; using std::fabs; using std::fmin;
133  real ya = floor( fmin(real(88), fabs(y/tile_)) ) +
134  real(0.5);
135  // convert to lat (mult by 90/100) and then to band (divide by 8)
136  // the +1 fine tunes the boundary between bands 3 and 4
137  int b = int(floor( ((ya * 9 + 1) / 10) / 8 ));
138  // For the northern hemisphere we have
139  // band rows num
140  // N 0 0:8 9
141  // P 1 9:17 9
142  // Q 2 18:26 9
143  // R 3 27:34 8
144  // S 4 35:43 9
145  // T 5 44:52 9
146  // U 6 53:61 9
147  // V 7 62:70 9
148  // W 8 71:79 9
149  // X 9 80:94 15
150  return y >= 0 ? b : -(b + 1);
151  }
152  // UTMUPS accesses these enums
153 #if GEOGRAPHICLIB_PRECISION == 4
154  // Work around an enum lossage introduced in boost 1.76
155  // https://github.com/boostorg/multiprecision/issues/324
156  // and fixed in
157  // https://github.com/boostorg/multiprecision/pull/333
158  static const int
159 #else
160  enum {
161 #endif
162  tile_ = 100000, // Size MGRS blocks
163  minutmcol_ = 1,
164  maxutmcol_ = 9,
165  minutmSrow_ = 10,
166  maxutmSrow_ = 100, // Also used for UTM S false northing
167  minutmNrow_ = 0, // Also used for UTM N false northing
168  maxutmNrow_ = 95,
169  minupsSind_ = 8, // These 4 ind's apply to easting and northing
170  maxupsSind_ = 32,
171  minupsNind_ = 13,
172  maxupsNind_ = 27,
173  upseasting_ = 20, // Also used for UPS false northing
174  utmeasting_ = 5, // UTM false easting
175  // Difference between S hemisphere northing and N hemisphere northing
176  utmNshift_ = (maxutmSrow_ - minutmNrow_) * tile_
178  ;
179 #else
180  };
181 #endif
182  MGRS() = delete; // Disable constructor
183 
184  public:
185 
186  /**
187  * Convert UTM or UPS coordinate to an MGRS coordinate.
188  *
189  * @param[in] zone UTM zone (zero means UPS).
190  * @param[in] northp hemisphere (true means north, false means south).
191  * @param[in] x easting of point (meters).
192  * @param[in] y northing of point (meters).
193  * @param[in] prec precision relative to 100 km.
194  * @param[out] mgrs MGRS string.
195  * @exception GeographicErr if \e zone, \e x, or \e y is outside its
196  * allowed range.
197  * @exception GeographicErr if the memory for the MGRS string can't be
198  * allocated.
199  *
200  * \e prec specifies the precision of the MGRS string as follows:
201  * - \e prec = &minus;1 (min), only the grid zone is returned
202  * - \e prec = 0, 100 km
203  * - \e prec = 1, 10 km
204  * - \e prec = 2, 1 km
205  * - \e prec = 3, 100 m
206  * - \e prec = 4, 10 m
207  * - \e prec = 5, 1 m
208  * - \e prec = 6, 0.1 m
209  * - &hellip;
210  * - \e prec = 11 (max), 1 &mu;m
211  *
212  * UTM eastings are allowed to be in the range [100 km, 900 km], northings
213  * are allowed to be in in [0 km, 9500 km] for the northern hemisphere and
214  * in [1000 km, 10000 km] for the southern hemisphere. (However UTM
215  * northings can be continued across the equator. So the actual limits on
216  * the northings are [&minus;9000 km, 9500 km] for the "northern"
217  * hemisphere and [1000 km, 19500 km] for the "southern" hemisphere.)
218  *
219  * UPS eastings/northings are allowed to be in the range [1300 km, 2700 km]
220  * in the northern hemisphere and in [800 km, 3200 km] in the southern
221  * hemisphere.
222  *
223  * The ranges are 100 km more restrictive than for the conversion between
224  * geographic coordinates and UTM and UPS given by UTMUPS. These
225  * restrictions are dictated by the allowed letters in MGRS coordinates.
226  * The choice of 9500 km for the maximum northing for northern hemisphere
227  * and of 1000 km as the minimum northing for southern hemisphere provide
228  * at least 0.5 degree extension into standard UPS zones. The upper ends
229  * of the ranges for the UPS coordinates is dictated by requiring symmetry
230  * about the meridians 0E and 90E.
231  *
232  * All allowed UTM and UPS coordinates may now be converted to legal MGRS
233  * coordinates with the proviso that eastings and northings on the upper
234  * boundaries are silently reduced by about 4 nm (4 nanometers) to place
235  * them \e within the allowed range. (This includes reducing a southern
236  * hemisphere northing of 10000 km by 4 nm so that it is placed in latitude
237  * band M.) The UTM or UPS coordinates are truncated to requested
238  * precision to determine the MGRS coordinate. Thus in UTM zone 38n, the
239  * square area with easting in [444 km, 445 km) and northing in [3688 km,
240  * 3689 km) maps to MGRS coordinate 38SMB4488 (at \e prec = 2, 1 km),
241  * Khulani Sq., Baghdad.
242  *
243  * The UTM/UPS selection and the UTM zone is preserved in the conversion to
244  * MGRS coordinate. Thus for \e zone > 0, the MGRS coordinate begins with
245  * the zone number followed by one of [C--M] for the southern
246  * hemisphere and [N--X] for the northern hemisphere. For \e zone =
247  * 0, the MGRS coordinates begins with one of [AB] for the southern
248  * hemisphere and [XY] for the northern hemisphere.
249  *
250  * The conversion to the MGRS is exact for prec in [0, 5] except that a
251  * neighboring latitude band letter may be given if the point is within 5nm
252  * of a band boundary. For prec in [6, 11], the conversion is accurate to
253  * roundoff.
254  *
255  * If \e prec = &minus;1, then the "grid zone designation", e.g., 18T, is
256  * returned. This consists of the UTM zone number (absent for UPS) and the
257  * first letter of the MGRS string which labels the latitude band for UTM
258  * and the hemisphere for UPS.
259  *
260  * If \e x or \e y is NaN or if \e zone is UTMUPS::INVALID, the returned
261  * MGRS string is "INVALID".
262  *
263  * Return the result via a reference argument to avoid the overhead of
264  * allocating a potentially large number of small strings. If an error is
265  * thrown, then \e mgrs is unchanged.
266  **********************************************************************/
267  static void Forward(int zone, bool northp, real x, real y,
268  int prec, std::string& mgrs);
269 
270  /**
271  * Convert UTM or UPS coordinate to an MGRS coordinate when the latitude is
272  * known.
273  *
274  * @param[in] zone UTM zone (zero means UPS).
275  * @param[in] northp hemisphere (true means north, false means south).
276  * @param[in] x easting of point (meters).
277  * @param[in] y northing of point (meters).
278  * @param[in] lat latitude (degrees).
279  * @param[in] prec precision relative to 100 km.
280  * @param[out] mgrs MGRS string.
281  * @exception GeographicErr if \e zone, \e x, or \e y is outside its
282  * allowed range.
283  * @exception GeographicErr if \e lat is inconsistent with the given UTM
284  * coordinates.
285  * @exception std::bad_alloc if the memory for \e mgrs can't be allocated.
286  *
287  * The latitude is ignored for \e zone = 0 (UPS); otherwise the latitude is
288  * used to determine the latitude band and this is checked for consistency
289  * using the same tests as Reverse.
290  **********************************************************************/
291  static void Forward(int zone, bool northp, real x, real y, real lat,
292  int prec, std::string& mgrs);
293 
294  /**
295  * Convert a MGRS coordinate to UTM or UPS coordinates.
296  *
297  * @param[in] mgrs MGRS string.
298  * @param[out] zone UTM zone (zero means UPS).
299  * @param[out] northp hemisphere (true means north, false means south).
300  * @param[out] x easting of point (meters).
301  * @param[out] y northing of point (meters).
302  * @param[out] prec precision relative to 100 km.
303  * @param[in] centerp if true (default), return center of the MGRS square,
304  * else return SW (lower left) corner.
305  * @exception GeographicErr if \e mgrs is illegal.
306  *
307  * All conversions from MGRS to UTM/UPS are permitted provided the MGRS
308  * coordinate is a possible result of a conversion in the other direction.
309  * (The leading 0 may be dropped from an input MGRS coordinate for UTM
310  * zones 1--9.) In addition, MGRS coordinates with a neighboring
311  * latitude band letter are permitted provided that some portion of the
312  * 100 km block is within the given latitude band. Thus
313  * - 38VLS and 38WLS are allowed (latitude 64N intersects the square
314  * 38[VW]LS); but 38VMS is not permitted (all of 38WMS is north of 64N)
315  * - 38MPE and 38NPF are permitted (they straddle the equator); but 38NPE
316  * and 38MPF are not permitted (the equator does not intersect either
317  * block).
318  * - Similarly ZAB and YZB are permitted (they straddle the prime
319  * meridian); but YAB and ZZB are not (the prime meridian does not
320  * intersect either block).
321  *
322  * The UTM/UPS selection and the UTM zone is preserved in the conversion
323  * from MGRS coordinate. The conversion is exact for prec in [0, 5]. With
324  * \e centerp = true, the conversion from MGRS to geographic and back is
325  * stable. This is not assured if \e centerp = false.
326  *
327  * If a "grid zone designation" (for example, 18T or A) is given, then some
328  * suitable (but essentially arbitrary) point within that grid zone is
329  * returned. The main utility of the conversion is to allow \e zone and \e
330  * northp to be determined. In this case, the \e centerp parameter is
331  * ignored and \e prec is set to &minus;1.
332  *
333  * If the first 3 characters of \e mgrs are "INV", then \e x and \e y are
334  * set to NaN, \e zone is set to UTMUPS::INVALID, and \e prec is set to
335  * &minus;2.
336  *
337  * If an exception is thrown, then the arguments are unchanged.
338  **********************************************************************/
339  static void Reverse(const std::string& mgrs,
340  int& zone, bool& northp, real& x, real& y,
341  int& prec, bool centerp = true);
342 
343  /** \name Inspector functions
344  **********************************************************************/
345  ///@{
346  /**
347  * @return \e a the equatorial radius of the WGS84 ellipsoid (meters).
348  *
349  * (The WGS84 value is returned because the UTM and UPS projections are
350  * based on this ellipsoid.)
351  **********************************************************************/
353 
354  /**
355  * @return \e f the flattening of the WGS84 ellipsoid.
356  *
357  * (The WGS84 value is returned because the UTM and UPS projections are
358  * based on this ellipsoid.)
359  **********************************************************************/
360  static Math::real Flattening() { return UTMUPS::Flattening(); }
361  ///@}
362 
363  /**
364  * Perform some checks on the UTMUPS coordinates on this ellipsoid. Throw
365  * an error if any of the assumptions made in the MGRS class is not true.
366  * This check needs to be carried out if the ellipsoid parameters (or the
367  * UTM/UPS scales) are ever changed.
368  **********************************************************************/
369  static void Check();
370 
371  };
372 
373 } // namespace GeographicLib
374 
375 #if defined(_MSC_VER)
376 # pragma warning (pop)
377 #endif
378 
379 #endif // GEOGRAPHICLIB_MGRS_HPP
Header for GeographicLib::Constants class.
#define GEOGRAPHICLIB_EXPORT
Definition: Constants.hpp:67
GeographicLib::Math::real real
Definition: GeodSolve.cpp:31
#define GEOGRAPHICLIB_PRECISION
Definition: Math.hpp:35
Header for GeographicLib::UTMUPS class.
Convert between UTM/UPS and MGRS.
Definition: MGRS.hpp:74
static Math::real EquatorialRadius()
Definition: MGRS.hpp:352
static Math::real Flattening()
Definition: MGRS.hpp:360
Convert between geographic coordinates and UTM/UPS.
Definition: UTMUPS.hpp:75
static Math::real Flattening()
Definition: UTMUPS.hpp:414
static Math::real EquatorialRadius()
Definition: UTMUPS.hpp:405
Namespace for GeographicLib.
Definition: Accumulator.cpp:12