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UTMUPS.hpp
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/**
* \file UTMUPS.hpp
* \brief Header for GeographicLib::UTMUPS class
*
* Copyright (c) Charles Karney (2008-2022) <karney@alum.mit.edu> and licensed
* under the MIT/X11 License. For more information, see
* https://geographiclib.sourceforge.io/
**********************************************************************/
#if !defined(GEOGRAPHICLIB_UTMUPS_HPP)
#define GEOGRAPHICLIB_UTMUPS_HPP 1
#include <GeographicLib/Constants.hpp>
namespace GeographicLib {
/**
* \brief Convert between geographic coordinates and UTM/UPS
*
* UTM and UPS are defined
* - J. W. Hager, J. F. Behensky, and B. W. Drew,
* <a href="https://web.archive.org/web/20161214054445/http://earth-info.nga.mil/GandG/publications/tm8358.2/TM8358_2.pdf">
* The Universal Grids: Universal Transverse Mercator (UTM) and Universal
* Polar Stereographic (UPS)</a>, Defense Mapping Agency, Technical Manual
* TM8358.2 (1989).
* .
* Section 2-3 defines UTM and section 3-2.4 defines UPS. This document also
* includes approximate algorithms for the computation of the underlying
* transverse Mercator and polar stereographic projections. Here we
* substitute much more accurate algorithms given by
* GeographicLib:TransverseMercator and GeographicLib:PolarStereographic.
* These are the algorithms recommended by the NGA document
* - <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).
*
* In this implementation, the conversions are closed, i.e., output from
* Forward is legal input for Reverse and vice versa. The error is about 5nm
* in each direction. However, the conversion from legal UTM/UPS coordinates
* to geographic coordinates and back might throw an error if the initial
* point is within 5nm of the edge of the allowed range for the UTM/UPS
* coordinates.
*
* The simplest way to guarantee the closed property is to define allowed
* ranges for the eastings and northings for UTM and UPS coordinates. The
* UTM boundaries are the same for all zones. (The only place the
* exceptional nature of the zone boundaries is evident is when converting to
* UTM/UPS coordinates requesting the standard zone.) The MGRS lettering
* scheme imposes natural limits on UTM/UPS coordinates which may be
* converted into MGRS coordinates. For the conversion to/from geographic
* coordinates these ranges have been extended by 100km in order to provide a
* generous overlap between UTM and UPS and between UTM zones.
*
* 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 UTM and UPS. Version 2.4.2 (and
* earlier) suffers from some drawbacks:
* - Inconsistent rules are used to determine the whether a particular UTM or
* UPS coordinate is legal. A more systematic approach is taken here.
* - The underlying projections are not very accurately implemented.
*
* The GeographicLib::UTMUPS::EncodeZone encodes the UTM zone and hemisphere
* to allow UTM/UPS coordinated to be displayed as, for example, "38N 444500
* 3688500". According to NGA.SIG.0012_2.0.0_UTMUPS the use of "N" to denote
* "north" in the context is not allowed (since a upper case letter in this
* context denotes the MGRS latitude band). Consequently, as of version
* 1.36, EncodeZone uses the lower case letters "n" and "s" to denote the
* hemisphere. In addition EncodeZone accepts an optional final argument \e
* abbrev, which, if false, results in the hemisphere being spelled out as in
* "38north".
*
* Example of use:
* \include example-UTMUPS.cpp
**********************************************************************/
class GEOGRAPHICLIB_EXPORT UTMUPS {
private:
typedef Math::real real;
static const int falseeasting_[4];
static const int falsenorthing_[4];
static const int mineasting_[4];
static const int maxeasting_[4];
static const int minnorthing_[4];
static const int maxnorthing_[4];
static const int epsg01N = 32601; // EPSG code for UTM 01N
static const int epsg60N = 32660; // EPSG code for UTM 60N
static const int epsgN = 32661; // EPSG code for UPS N
static const int epsg01S = 32701; // EPSG code for UTM 01S
static const int epsg60S = 32760; // EPSG code for UTM 60S
static const int epsgS = 32761; // EPSG code for UPS S
static real CentralMeridian(int zone)
{ return real(6 * zone - 183); }
// Throw an error if easting or northing are outside standard ranges. If
// throwp = false, return bool instead.
static bool CheckCoords(bool utmp, bool northp, real x, real y,
bool msgrlimits = false, bool throwp = true);
UTMUPS() = delete; // Disable constructor
public:
/**
* In this class we bring together the UTM and UPS coordinates systems.
* The UTM divides the earth between latitudes &minus;80&deg; and 84&deg;
* into 60 zones numbered 1 thru 60. Zone assign zone number 0 to the UPS
* regions, covering the two poles. Within UTMUPS, nonnegative zone
* numbers refer to one of the "physical" zones, 0 for UPS and [1, 60] for
* UTM. Negative "pseudo-zone" numbers are used to select one of the
* physical zones.
**********************************************************************/
enum zonespec {
/**
* The smallest pseudo-zone number.
**********************************************************************/
MINPSEUDOZONE = -4,
/**
* A marker for an undefined or invalid zone. Equivalent to NaN.
**********************************************************************/
INVALID = -4,
/**
* If a coordinate already include zone information (e.g., it is an MGRS
* coordinate), use that, otherwise apply the UTMUPS::STANDARD rules.
**********************************************************************/
MATCH = -3,
/**
* Apply the standard rules for UTM zone assigment extending the UTM zone
* to each pole to give a zone number in [1, 60]. For example, use UTM
* zone 38 for longitude in [42&deg;, 48&deg;). The rules include the
* Norway and Svalbard exceptions.
**********************************************************************/
UTM = -2,
/**
* Apply the standard rules for zone assignment to give a zone number in
* [0, 60]. If the latitude is not in [&minus;80&deg;, 84&deg;), then
* use UTMUPS::UPS = 0, otherwise apply the rules for UTMUPS::UTM. The
* tests on latitudes and longitudes are all closed on the lower end open
* on the upper. Thus for UTM zone 38, latitude is in [&minus;80&deg;,
* 84&deg;) and longitude is in [42&deg;, 48&deg;).
**********************************************************************/
STANDARD = -1,
/**
* The largest pseudo-zone number.
**********************************************************************/
MAXPSEUDOZONE = -1,
/**
* The smallest physical zone number.
**********************************************************************/
MINZONE = 0,
/**
* The zone number used for UPS
**********************************************************************/
UPS = 0,
/**
* The smallest UTM zone number.
**********************************************************************/
MINUTMZONE = 1,
/**
* The largest UTM zone number.
**********************************************************************/
MAXUTMZONE = 60,
/**
* The largest physical zone number.
**********************************************************************/
MAXZONE = 60,
};
/**
* The standard zone.
*
* @param[in] lat latitude (degrees).
* @param[in] lon longitude (degrees).
* @param[in] setzone zone override (optional). If omitted, use the
* standard rules for picking the zone. If \e setzone is given then use
* that zone if it is nonnegative, otherwise apply the rules given in
* UTMUPS::zonespec.
* @exception GeographicErr if \e setzone is outside the range
* [UTMUPS::MINPSEUDOZONE, UTMUPS::MAXZONE] = [&minus;4, 60].
*
* This is exact.
**********************************************************************/
static int StandardZone(real lat, real lon, int setzone = STANDARD);
/**
* Forward projection, from geographic to UTM/UPS.
*
* @param[in] lat latitude of point (degrees).
* @param[in] lon longitude of point (degrees).
* @param[out] zone the 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] gamma meridian convergence at point (degrees).
* @param[out] k scale of projection at point.
* @param[in] setzone zone override (optional).
* @param[in] mgrslimits if true enforce the stricter MGRS limits on the
* coordinates (default = false).
* @exception GeographicErr if \e lat is not in [&minus;90&deg;,
* 90&deg;].
* @exception GeographicErr if the resulting \e x or \e y is out of allowed
* range (see Reverse); in this case, these arguments are unchanged.
*
* If \e setzone is omitted, use the standard rules for picking the zone.
* If \e setzone is given then use that zone if it is nonnegative,
* otherwise apply the rules given in UTMUPS::zonespec. The accuracy of
* the conversion is about 5nm.
*
* The northing \e y jumps by UTMUPS::UTMShift() when crossing the equator
* in the southerly direction. Sometimes it is useful to remove this
* discontinuity in \e y by extending the "northern" hemisphere using
* UTMUPS::Transfer:
* \code
double lat = -1, lon = 123;
int zone;
bool northp;
double x, y, gamma, k;
GeographicLib::UTMUPS::Forward(lat, lon, zone, northp, x, y, gamma, k);
GeographicLib::UTMUPS::Transfer(zone, northp, x, y,
zone, true, x, y, zone);
northp = true;
\endcode
**********************************************************************/
static void Forward(real lat, real lon,
int& zone, bool& northp, real& x, real& y,
real& gamma, real& k,
int setzone = STANDARD, bool mgrslimits = false);
/**
* Reverse projection, from UTM/UPS to geographic.
*
* @param[in] zone the 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[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.
* @param[in] mgrslimits if true enforce the stricter MGRS limits on the
* coordinates (default = false).
* @exception GeographicErr if \e zone, \e x, or \e y is out of allowed
* range; this this case the arguments are unchanged.
*
* The accuracy of the conversion is about 5nm.
*
* UTM eastings are allowed to be in the range [0km, 1000km], northings are
* allowed to be in in [0km, 9600km] for the northern hemisphere and in
* [900km, 10000km] for the southern hemisphere. However UTM northings
* can be continued across the equator. So the actual limits on the
* northings are [-9100km, 9600km] for the "northern" hemisphere and
* [900km, 19600km] for the "southern" hemisphere.
*
* UPS eastings and northings are allowed to be in the range [1200km,
* 2800km] in the northern hemisphere and in [700km, 3300km] in the
* southern hemisphere.
*
* These ranges are 100km larger than allowed for the conversions to MGRS.
* (100km is the maximum extra padding consistent with eastings remaining
* nonnegative.) This allows generous overlaps between zones and UTM and
* UPS. If \e mgrslimits = true, then all the ranges are shrunk by 100km
* so that they agree with the stricter MGRS ranges. No checks are
* performed besides these (e.g., to limit the distance outside the
* standard zone boundaries).
**********************************************************************/
static void Reverse(int zone, bool northp, real x, real y,
real& lat, real& lon, real& gamma, real& k,
bool mgrslimits = false);
/**
* UTMUPS::Forward without returning convergence and scale.
**********************************************************************/
static void Forward(real lat, real lon,
int& zone, bool& northp, real& x, real& y,
int setzone = STANDARD, bool mgrslimits = false) {
real gamma, k;
Forward(lat, lon, zone, northp, x, y, gamma, k, setzone, mgrslimits);
}
/**
* UTMUPS::Reverse without returning convergence and scale.
**********************************************************************/
static void Reverse(int zone, bool northp, real x, real y,
real& lat, real& lon, bool mgrslimits = false) {
real gamma, k;
Reverse(zone, northp, x, y, lat, lon, gamma, k, mgrslimits);
}
/**
* Transfer UTM/UPS coordinated from one zone to another.
*
* @param[in] zonein the UTM zone for \e xin and \e yin (or zero for UPS).
* @param[in] northpin hemisphere for \e xin and \e yin (true means north,
* false means south).
* @param[in] xin easting of point (meters) in \e zonein.
* @param[in] yin northing of point (meters) in \e zonein.
* @param[in] zoneout the requested UTM zone for \e xout and \e yout (or
* zero for UPS).
* @param[in] northpout hemisphere for \e xout output and \e yout.
* @param[out] xout easting of point (meters) in \e zoneout.
* @param[out] yout northing of point (meters) in \e zoneout.
* @param[out] zone the actual UTM zone for \e xout and \e yout (or zero
* for UPS); this equals \e zoneout if \e zoneout &ge; 0.
* @exception GeographicErr if \e zonein is out of range (see below).
* @exception GeographicErr if \e zoneout is out of range (see below).
* @exception GeographicErr if \e xin or \e yin fall outside their allowed
* ranges (see UTMUPS::Reverse).
* @exception GeographicErr if \e xout or \e yout fall outside their
* allowed ranges (see UTMUPS::Reverse).
*
* \e zonein must be in the range [UTMUPS::MINZONE, UTMUPS::MAXZONE] = [0,
* 60] with \e zonein = UTMUPS::UPS, 0, indicating UPS. \e zonein may
* also be UTMUPS::INVALID.
*
* \e zoneout must be in the range [UTMUPS::MINPSEUDOZONE, UTMUPS::MAXZONE]
* = [-4, 60]. If \e zoneout &lt; UTMUPS::MINZONE then the rules give in
* the documentation of UTMUPS::zonespec are applied, and \e zone is set to
* the actual zone used for output.
*
* (\e xout, \e yout) can overlap with (\e xin, \e yin).
**********************************************************************/
static void Transfer(int zonein, bool northpin, real xin, real yin,
int zoneout, bool northpout, real& xout, real& yout,
int& zone);
/**
* Decode a UTM/UPS zone string.
*
* @param[in] zonestr string representation of zone and hemisphere.
* @param[out] zone the UTM zone (zero means UPS).
* @param[out] northp hemisphere (true means north, false means south).
* @exception GeographicErr if \e zonestr is malformed.
*
* For UTM, \e zonestr has the form of a zone number in the range
* [UTMUPS::MINUTMZONE, UTMUPS::MAXUTMZONE] = [1, 60] followed by a
* hemisphere letter, n or s (or "north" or "south" spelled out). For UPS,
* it consists just of the hemisphere letter (or the spelled out
* hemisphere). The returned value of \e zone is UTMUPS::UPS = 0 for UPS.
* Note well that "38s" indicates the southern hemisphere of zone 38 and
* not latitude band S, 32&deg; &le; \e lat &lt; 40&deg;. n, 01s, 2n, 38s,
* south, 3north are legal. 0n, 001s, +3n, 61n, 38P are illegal. INV is a
* special value for which the returned value of \e is UTMUPS::INVALID.
**********************************************************************/
static void DecodeZone(const std::string& zonestr,
int& zone, bool& northp);
/**
* Encode a UTM/UPS zone string.
*
* @param[in] zone the UTM zone (zero means UPS).
* @param[in] northp hemisphere (true means north, false means south).
* @param[in] abbrev if true (the default) use abbreviated (n/s) notation
* for hemisphere; otherwise spell out the hemisphere (north/south)
* @exception GeographicErr if \e zone is out of range (see below).
* @exception std::bad_alloc if memoy for the string can't be allocated.
* @return string representation of zone and hemisphere.
*
* \e zone must be in the range [UTMUPS::MINZONE, UTMUPS::MAXZONE] = [0,
* 60] with \e zone = UTMUPS::UPS, 0, indicating UPS (but the resulting
* string does not contain "0"). \e zone may also be UTMUPS::INVALID, in
* which case the returned string is "inv". This reverses
* UTMUPS::DecodeZone.
**********************************************************************/
static std::string EncodeZone(int zone, bool northp, bool abbrev = true);
/**
* Decode EPSG.
*
* @param[in] epsg the EPSG code.
* @param[out] zone the UTM zone (zero means UPS).
* @param[out] northp hemisphere (true means north, false means south).
*
* EPSG (European Petroleum Survery Group) codes are a way to refer to many
* different projections. DecodeEPSG decodes those referring to UTM or UPS
* projections for the WGS84 ellipsoid. If the code does not refer to one
* of these projections, \e zone is set to UTMUPS::INVALID. See
* https://www.spatialreference.org/ref/epsg/
**********************************************************************/
static void DecodeEPSG(int epsg, int& zone, bool& northp);
/**
* Encode zone as EPSG.
*
* @param[in] zone the UTM zone (zero means UPS).
* @param[in] northp hemisphere (true means north, false means south).
* @return EPSG code (or -1 if \e zone is not in the range
* [UTMUPS::MINZONE, UTMUPS::MAXZONE] = [0, 60])
*
* Convert \e zone and \e northp to the corresponding EPSG (European
* Petroleum Survery Group) codes
**********************************************************************/
static int EncodeEPSG(int zone, bool northp);
/**
* @return shift (meters) necessary to align north and south halves of a
* UTM zone (10<sup>7</sup>).
**********************************************************************/
static Math::real UTMShift();
/** \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 Constants::WGS84_a(); }
/**
* @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 Constants::WGS84_f(); }
///@}
};
} // namespace GeographicLib
#endif // GEOGRAPHICLIB_UTMUPS_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
GeographicLib::Constants::WGS84_f
static T WGS84_f()
Definition Constants.hpp:118
GeographicLib::Constants::WGS84_a
static T WGS84_a()
Definition Constants.hpp:112
GeographicLib::Math::real
double real
Definition Math.hpp:115
GeographicLib::UTMUPS::zonespec
zonespec
Definition UTMUPS.hpp:109
GeographicLib::UTMUPS::MINPSEUDOZONE
@ MINPSEUDOZONE
Definition UTMUPS.hpp:113
GeographicLib::UTMUPS::MAXZONE
@ MAXZONE
Definition UTMUPS.hpp:162
GeographicLib::UTMUPS::MINUTMZONE
@ MINUTMZONE
Definition UTMUPS.hpp:154
GeographicLib::UTMUPS::UPS
@ UPS
Definition UTMUPS.hpp:150
GeographicLib::UTMUPS::MATCH
@ MATCH
Definition UTMUPS.hpp:122
GeographicLib::UTMUPS::UTM
@ UTM
Definition UTMUPS.hpp:129
GeographicLib::UTMUPS::MAXPSEUDOZONE
@ MAXPSEUDOZONE
Definition UTMUPS.hpp:142
GeographicLib::UTMUPS::STANDARD
@ STANDARD
Definition UTMUPS.hpp:138
GeographicLib::UTMUPS::MAXUTMZONE
@ MAXUTMZONE
Definition UTMUPS.hpp:158
GeographicLib::UTMUPS::INVALID
@ INVALID
Definition UTMUPS.hpp:117
GeographicLib::UTMUPS::MINZONE
@ MINZONE
Definition UTMUPS.hpp:146
GeographicLib::UTMUPS::Flattening
static Math::real Flattening()
Definition UTMUPS.hpp:414
GeographicLib::UTMUPS::EquatorialRadius
static Math::real EquatorialRadius()
Definition UTMUPS.hpp:405
GeographicLib::UTMUPS::Forward
static void Forward(real lat, real lon, int &zone, bool &northp, real &x, real &y, real &gamma, real &k, int setzone=STANDARD, bool mgrslimits=false)
Definition UTMUPS.cpp:64
GeographicLib::UTMUPS::Forward
static void Forward(real lat, real lon, int &zone, bool &northp, real &x, real &y, int setzone=STANDARD, bool mgrslimits=false)
Definition UTMUPS.hpp:269
GeographicLib::UTMUPS::Reverse
static void Reverse(int zone, bool northp, real x, real y, real &lat, real &lon, real &gamma, real &k, bool mgrslimits=false)
Definition UTMUPS.cpp:118
GeographicLib::UTMUPS::Reverse
static void Reverse(int zone, bool northp, real x, real y, real &lat, real &lon, bool mgrslimits=false)
Definition UTMUPS.hpp:279
GeographicLib
Namespace for GeographicLib.
Definition Accumulator.cpp:12