GeographicLib  2.1
MGRS.hpp
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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 / real(tile_))) ) + real(0.5);
134  // convert to lat (mult by 90/100) and then to band (divide by 8)
135  // the +1 fine tunes the boundary between bands 3 and 4
136  int b = int(floor( ((ya * 9 + 1) / 10) / 8 ));
137  // For the northern hemisphere we have
138  // band rows num
139  // N 0 0:8 9
140  // P 1 9:17 9
141  // Q 2 18:26 9
142  // R 3 27:34 8
143  // S 4 35:43 9
144  // T 5 44:52 9
145  // U 6 53:61 9
146  // V 7 62:70 9
147  // W 8 71:79 9
148  // X 9 80:94 15
149  return y >= 0 ? b : -(b + 1);
150  }
151  // UTMUPS accesses these enums
152 #if GEOGRAPHICLIB_PRECISION == 4
153  // Work around an enum lossage introduced in boost 1.76
154  // https://github.com/boostorg/multiprecision/issues/324
155  // and fixed in
156  // https://github.com/boostorg/multiprecision/pull/333
157  static const int
158 #else
159  enum {
160 #endif
161  tile_ = 100000, // Size MGRS blocks
162  minutmcol_ = 1,
163  maxutmcol_ = 9,
164  minutmSrow_ = 10,
165  maxutmSrow_ = 100, // Also used for UTM S false northing
166  minutmNrow_ = 0, // Also used for UTM N false northing
167  maxutmNrow_ = 95,
168  minupsSind_ = 8, // These 4 ind's apply to easting and northing
169  maxupsSind_ = 32,
170  minupsNind_ = 13,
171  maxupsNind_ = 27,
172  upseasting_ = 20, // Also used for UPS false northing
173  utmeasting_ = 5, // UTM false easting
174  // Difference between S hemisphere northing and N hemisphere northing
175  utmNshift_ = (maxutmSrow_ - minutmNrow_) * tile_
177  ;
178 #else
179  };
180 #endif
181  MGRS() = delete; // Disable constructor
182 
183  public:
184 
185  /**
186  * Convert UTM or UPS coordinate to an MGRS coordinate.
187  *
188  * @param[in] zone UTM zone (zero means UPS).
189  * @param[in] northp hemisphere (true means north, false means south).
190  * @param[in] x easting of point (meters).
191  * @param[in] y northing of point (meters).
192  * @param[in] prec precision relative to 100 km.
193  * @param[out] mgrs MGRS string.
194  * @exception GeographicErr if \e zone, \e x, or \e y is outside its
195  * allowed range.
196  * @exception GeographicErr if the memory for the MGRS string can't be
197  * allocated.
198  *
199  * \e prec specifies the precision of the MGRS string as follows:
200  * - \e prec = &minus;1 (min), only the grid zone is returned
201  * - \e prec = 0, 100 km
202  * - \e prec = 1, 10 km
203  * - \e prec = 2, 1 km
204  * - \e prec = 3, 100 m
205  * - \e prec = 4, 10 m
206  * - \e prec = 5, 1 m
207  * - \e prec = 6, 0.1 m
208  * - &hellip;
209  * - \e prec = 11 (max), 1 &mu;m
210  *
211  * UTM eastings are allowed to be in the range [100 km, 900 km], northings
212  * are allowed to be in in [0 km, 9500 km] for the northern hemisphere and
213  * in [1000 km, 10000 km] for the southern hemisphere. (However UTM
214  * northings can be continued across the equator. So the actual limits on
215  * the northings are [&minus;9000 km, 9500 km] for the "northern"
216  * hemisphere and [1000 km, 19500 km] for the "southern" hemisphere.)
217  *
218  * UPS eastings/northings are allowed to be in the range [1300 km, 2700 km]
219  * in the northern hemisphere and in [800 km, 3200 km] in the southern
220  * hemisphere.
221  *
222  * The ranges are 100 km more restrictive than for the conversion between
223  * geographic coordinates and UTM and UPS given by UTMUPS. These
224  * restrictions are dictated by the allowed letters in MGRS coordinates.
225  * The choice of 9500 km for the maximum northing for northern hemisphere
226  * and of 1000 km as the minimum northing for southern hemisphere provide
227  * at least 0.5 degree extension into standard UPS zones. The upper ends
228  * of the ranges for the UPS coordinates is dictated by requiring symmetry
229  * about the meridians 0E and 90E.
230  *
231  * All allowed UTM and UPS coordinates may now be converted to legal MGRS
232  * coordinates with the proviso that eastings and northings on the upper
233  * boundaries are silently reduced by about 4 nm (4 nanometers) to place
234  * them \e within the allowed range. (This includes reducing a southern
235  * hemisphere northing of 10000 km by 4 nm so that it is placed in latitude
236  * band M.) The UTM or UPS coordinates are truncated to requested
237  * precision to determine the MGRS coordinate. Thus in UTM zone 38n, the
238  * square area with easting in [444 km, 445 km) and northing in [3688 km,
239  * 3689 km) maps to MGRS coordinate 38SMB4488 (at \e prec = 2, 1 km),
240  * Khulani Sq., Baghdad.
241  *
242  * The UTM/UPS selection and the UTM zone is preserved in the conversion to
243  * MGRS coordinate. Thus for \e zone > 0, the MGRS coordinate begins with
244  * the zone number followed by one of [C--M] for the southern
245  * hemisphere and [N--X] for the northern hemisphere. For \e zone =
246  * 0, the MGRS coordinates begins with one of [AB] for the southern
247  * hemisphere and [XY] for the northern hemisphere.
248  *
249  * The conversion to the MGRS is exact for prec in [0, 5] except that a
250  * neighboring latitude band letter may be given if the point is within 5nm
251  * of a band boundary. For prec in [6, 11], the conversion is accurate to
252  * roundoff.
253  *
254  * If \e prec = &minus;1, then the "grid zone designation", e.g., 18T, is
255  * returned. This consists of the UTM zone number (absent for UPS) and the
256  * first letter of the MGRS string which labels the latitude band for UTM
257  * and the hemisphere for UPS.
258  *
259  * If \e x or \e y is NaN or if \e zone is UTMUPS::INVALID, the returned
260  * MGRS string is "INVALID".
261  *
262  * Return the result via a reference argument to avoid the overhead of
263  * allocating a potentially large number of small strings. If an error is
264  * thrown, then \e mgrs is unchanged.
265  **********************************************************************/
266  static void Forward(int zone, bool northp, real x, real y,
267  int prec, std::string& mgrs);
268 
269  /**
270  * Convert UTM or UPS coordinate to an MGRS coordinate when the latitude is
271  * known.
272  *
273  * @param[in] zone UTM zone (zero means UPS).
274  * @param[in] northp hemisphere (true means north, false means south).
275  * @param[in] x easting of point (meters).
276  * @param[in] y northing of point (meters).
277  * @param[in] lat latitude (degrees).
278  * @param[in] prec precision relative to 100 km.
279  * @param[out] mgrs MGRS string.
280  * @exception GeographicErr if \e zone, \e x, or \e y is outside its
281  * allowed range.
282  * @exception GeographicErr if \e lat is inconsistent with the given UTM
283  * coordinates.
284  * @exception std::bad_alloc if the memory for \e mgrs can't be allocated.
285  *
286  * The latitude is ignored for \e zone = 0 (UPS); otherwise the latitude is
287  * used to determine the latitude band and this is checked for consistency
288  * using the same tests as Reverse.
289  **********************************************************************/
290  static void Forward(int zone, bool northp, real x, real y, real lat,
291  int prec, std::string& mgrs);
292 
293  /**
294  * Convert a MGRS coordinate to UTM or UPS coordinates.
295  *
296  * @param[in] mgrs MGRS string.
297  * @param[out] zone UTM zone (zero means UPS).
298  * @param[out] northp hemisphere (true means north, false means south).
299  * @param[out] x easting of point (meters).
300  * @param[out] y northing of point (meters).
301  * @param[out] prec precision relative to 100 km.
302  * @param[in] centerp if true (default), return center of the MGRS square,
303  * else return SW (lower left) corner.
304  * @exception GeographicErr if \e mgrs is illegal.
305  *
306  * All conversions from MGRS to UTM/UPS are permitted provided the MGRS
307  * coordinate is a possible result of a conversion in the other direction.
308  * (The leading 0 may be dropped from an input MGRS coordinate for UTM
309  * zones 1--9.) In addition, MGRS coordinates with a neighboring
310  * latitude band letter are permitted provided that some portion of the
311  * 100 km block is within the given latitude band. Thus
312  * - 38VLS and 38WLS are allowed (latitude 64N intersects the square
313  * 38[VW]LS); but 38VMS is not permitted (all of 38WMS is north of 64N)
314  * - 38MPE and 38NPF are permitted (they straddle the equator); but 38NPE
315  * and 38MPF are not permitted (the equator does not intersect either
316  * block).
317  * - Similarly ZAB and YZB are permitted (they straddle the prime
318  * meridian); but YAB and ZZB are not (the prime meridian does not
319  * intersect either block).
320  *
321  * The UTM/UPS selection and the UTM zone is preserved in the conversion
322  * from MGRS coordinate. The conversion is exact for prec in [0, 5]. With
323  * \e centerp = true, the conversion from MGRS to geographic and back is
324  * stable. This is not assured if \e centerp = false.
325  *
326  * If a "grid zone designation" (for example, 18T or A) is given, then some
327  * suitable (but essentially arbitrary) point within that grid zone is
328  * returned. The main utility of the conversion is to allow \e zone and \e
329  * northp to be determined. In this case, the \e centerp parameter is
330  * ignored and \e prec is set to &minus;1.
331  *
332  * If the first 3 characters of \e mgrs are "INV", then \e x and \e y are
333  * set to NaN, \e zone is set to UTMUPS::INVALID, and \e prec is set to
334  * &minus;2.
335  *
336  * If an exception is thrown, then the arguments are unchanged.
337  **********************************************************************/
338  static void Reverse(const std::string& mgrs,
339  int& zone, bool& northp, real& x, real& y,
340  int& prec, bool centerp = true);
341 
342  /** \name Inspector functions
343  **********************************************************************/
344  ///@{
345  /**
346  * @return \e a the equatorial radius of the WGS84 ellipsoid (meters).
347  *
348  * (The WGS84 value is returned because the UTM and UPS projections are
349  * based on this ellipsoid.)
350  **********************************************************************/
352 
353  /**
354  * @return \e f the flattening of the WGS84 ellipsoid.
355  *
356  * (The WGS84 value is returned because the UTM and UPS projections are
357  * based on this ellipsoid.)
358  **********************************************************************/
359  static Math::real Flattening() { return UTMUPS::Flattening(); }
360  ///@}
361 
362  /**
363  * Perform some checks on the UTMUPS coordinates on this ellipsoid. Throw
364  * an error if any of the assumptions made in the MGRS class is not true.
365  * This check needs to be carried out if the ellipsoid parameters (or the
366  * UTM/UPS scales) are ever changed.
367  **********************************************************************/
368  static void Check();
369 
370  };
371 
372 } // namespace GeographicLib
373 
374 #if defined(_MSC_VER)
375 # pragma warning (pop)
376 #endif
377 
378 #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:351
static Math::real Flattening()
Definition: MGRS.hpp:359
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