Coverage for pygeodesy/utm.py: 97%
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2# -*- coding: utf-8 -*-
4u'''I{Veness}' Universal Transverse Mercator (UTM) projection.
6Classes L{Utm} and L{UTMError} and functions L{parseUTM5}, L{toUtm8} and
7L{utmZoneBand5}.
9Pure Python implementation of UTM / WGS-84 conversion functions using
10an ellipsoidal earth model, transcoded from JavaScript originals by
11I{(C) Chris Veness 2011-2016} published under the same MIT Licence**, see
12U{UTM<https://www.Movable-Type.co.UK/scripts/latlong-utm-mgrs.html>} and
13U{Module utm<https://www.Movable-Type.co.UK/scripts/geodesy/docs/module-utm.html>}.
15The U{UTM<https://WikiPedia.org/wiki/Universal_Transverse_Mercator_coordinate_system>}
16system is a 2-dimensional Cartesian coordinate system providing another way
17to identify locations on the surface of the earth. UTM is a set of 60
18transverse Mercator projections, normally based on the WGS-84 ellipsoid.
19Within each zone, coordinates are represented as B{C{easting}}s and B{C{northing}}s,
20measured in metres.
22This module includes some of I{Charles Karney}'s U{'Transverse Mercator with an
23accuracy of a few nanometers'<https://Arxiv.org/pdf/1002.1417v3.pdf>}, 2011
24(building on Krüger's U{'Konforme Abbildung des Erdellipsoids in der Ebene'
25<https://bib.GFZ-Potsdam.DE/pub/digi/krueger2.pdf>}, 1912) and C++ class
26U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/
27classGeographicLib_1_1TransverseMercator.html>}.
29Some other references are U{Universal Transverse Mercator coordinate system
30<https://WikiPedia.org/wiki/Universal_Transverse_Mercator_coordinate_system>},
31U{Transverse Mercator Projection<https://GeographicLib.SourceForge.io/tm.html>}
32and Henrik Seidel U{'Die Mathematik der Gauß-Krueger-Abbildung'
33<https://DE.WikiPedia.org/wiki/Gauß-Krüger-Koordinatensystem>}, 2006.
34'''
36from pygeodesy.basics import len2, map2, neg # splice
37from pygeodesy.constants import EPS, EPS0, _K0_UTM, _0_0, _0_0001
38from pygeodesy.datums import _ellipsoidal_datum, _WGS84
39from pygeodesy.dms import degDMS, parseDMS2
40from pygeodesy.errors import MGRSError, RangeError, _ValueError, \
41 _xkwds_get
42from pygeodesy.fmath import fdot3, hypot, hypot1
43from pygeodesy.interns import MISSING, NN, _by_, _COMMASPACE_, _N_, \
44 _NS_, _outside_, _range_, _S_, _scale0_, \
45 _SPACE_, _UTM_, _V_, _X_, _zone_, _UNDER
46from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS
47# from pygeodesy.named import _xnamed # from .utmupsBase
48from pygeodesy.namedTuples import EasNor2Tuple, UtmUps5Tuple, \
49 UtmUps8Tuple, UtmUpsLatLon5Tuple
50from pygeodesy.props import deprecated_method, property_doc_, \
51 Property_RO
52from pygeodesy.streprs import Fmt, unstr
53from pygeodesy.units import Band, Int, Lat, Lon, Meter, Zone
54from pygeodesy.utily import degrees90, degrees180, sincos2
55from pygeodesy.utmupsBase import _hemi, _LLEB, _parseUTMUPS5, _to4lldn, \
56 _to3zBhp, _to3zll, _UPS_LATS, _UPS_ZONE, \
57 _UTM_LAT_MAX, _UTM_ZONE_MAX, \
58 _UTM_LAT_MIN, _UTM_ZONE_MIN, \
59 _UTM_ZONE_OFF_MAX, UtmUpsBase, _xnamed
61from math import asinh, atan, atanh, atan2, cos, cosh, degrees, \
62 fabs, radians, sin, sinh, tan, tanh
63from operator import mul as _mul
65__all__ = _ALL_LAZY.utm
66__version__ = '23.03.19'
68_Bands = 'CDEFGHJKLMNPQRSTUVWXX' # UTM latitude bands C..X (no
69# I|O) 8° each, covering 80°S to 84°N and X repeated for 80-84°N
70_bandLat_ = 'bandLat'
71_FalseEasting = Meter( 500e3) # falsed offset (C{meter})
72_FalseNorthing = Meter(10000e3) # falsed offset (C{meter})
73_SvalbardXzone = {32: 9, 34: 21, 36: 33} # [zone] longitude
76class UTMError(_ValueError):
77 '''Universal Transverse Mercator (UTM parse or other L{Utm} issue.
78 '''
79 pass
82class _Kseries(object):
83 '''(INTERNAL) Alpha or Beta Krüger series.
85 Krüger series summations for B{C{eta}}, B{C{ksi}}, B{C{p}} and B{C{q}},
86 caching the C{cos}, C{cosh}, C{sin} and C{sinh} values for
87 the given B{C{eta}} and B{C{ksi}} angles (in C{radians}).
88 '''
89 def __init__(self, AB, x, y):
90 '''(INTERNAL) New Alpha or Beta Krüger series
92 @arg AB: Krüger Alpha or Beta series coefficients
93 (C{4-, 6- or 8-tuple}).
94 @arg x: Eta angle (C{radians}).
95 @arg y: Ksi angle (C{radians}).
96 '''
97 n, j2 = len2(range(2, len(AB) * 2 + 1, 2))
99 self._ab = AB
100 self._pq = map2(_mul, j2, AB)
101# assert len(self._ab) == len(self._pq) == n
103 x2 = map2(_mul, j2, (x,) * n)
104 self._chx = map2(cosh, x2)
105 self._shx = map2(sinh, x2)
106# assert len(x2) == len(self._chx) == len(self._shx) == n
108 y2 = map2(_mul, j2, (y,) * n)
109 self._cy = map2(cos, y2)
110 self._sy = map2(sin, y2)
111 # self._sy, self._cy = splice(sincos2(*y2)) # PYCHOK false
112# assert len(y2) == len(self._cy) == len(self._sy) == n
114 def xs(self, x0):
115 '''(INTERNAL) Eta summation (C{float}).
116 '''
117 return fdot3(self._ab, self._cy, self._shx, start=x0)
119 def ys(self, y0):
120 '''(INTERNAL) Ksi summation (C{float}).
121 '''
122 return fdot3(self._ab, self._sy, self._chx, start=y0)
124 def ps(self, p0):
125 '''(INTERNAL) P summation (C{float}).
126 '''
127 return fdot3(self._pq, self._cy, self._chx, start=p0)
129 def qs(self, q0):
130 '''(INTERNAL) Q summation (C{float}).
131 '''
132 return fdot3(self._pq, self._sy, self._shx, start=q0)
135def _cmlon(zone):
136 '''(INTERNAL) Central meridian longitude (C{degrees180}).
137 '''
138 return (zone * 6) - 183
141def _false2(e, n, h):
142 '''(INTERNAL) False easting and northing.
143 '''
144 # Karney, "Test data for the transverse Mercator projection (2009)"
145 # <https://GeographicLib.SourceForge.io/C++/doc/transversemercator.html>
146 # and <https://Zenodo.org/record/32470#.W4LEJS2ZON8>
147 e += _FalseEasting # make e relative to central meridian
148 if h == _S_:
149 n += _FalseNorthing # make n relative to equator
150 return e, n
153def _toBand(lat, *unused, **strict_Error): # see ups._toBand
154 '''(INTERNAL) Get the I{latitudinal} Band (row) letter.
155 '''
156 if _UTM_LAT_MIN <= lat < _UTM_LAT_MAX: # [-80, 84) like Veness
157 return _Bands[int(lat - _UTM_LAT_MIN) >> 3]
158 elif _xkwds_get(strict_Error, strict=True):
159 r = _range_(_UTM_LAT_MIN, _UTM_LAT_MAX, ropen=True)
160 t = _SPACE_(_outside_, _UTM_, _range_, r)
161 E = _xkwds_get(strict_Error, Error=RangeError)
162 raise E(lat=degDMS(lat), txt=t)
163 else:
164 return NN # None
167def _to3zBlat(zone, band, Error=UTMError): # in .mgrs
168 '''(INTERNAL) Check and return zone, Band and band latitude.
170 @arg zone: Zone number or string.
171 @arg band: Band letter.
172 @arg Error: Exception to raise (L{UTMError}).
174 @return: 3-Tuple (zone, Band, latitude).
175 '''
176 z, B, _ = _to3zBhp(zone, band, Error=Error)
177 if not (_UTM_ZONE_MIN <= z <= _UTM_ZONE_MAX or
178 (_UPS_ZONE == z and Error is MGRSError)):
179 raise Error(zone=zone)
181 b = None
182 if B:
183 if z == _UPS_ZONE: # polar
184 try:
185 b = Lat(_UPS_LATS[B], name=_bandLat_)
186 except KeyError:
187 raise Error(band=band or B, zone=z)
188 else: # UTM
189 b = _Bands.find(B)
190 if b < 0:
191 raise Error(band=band or B, zone=z)
192 b = Int((b << 3) - 80, name=_bandLat_)
193 B = Band(B)
194 elif Error is not UTMError:
195 raise Error(band=band, txt=MISSING)
197 return Zone(z), B, b
200def _to4zBll(lat, lon, cmoff=True, strict=True, Error=RangeError):
201 '''(INTERNAL) Return zone, Band and lat- and (central) longitude in degrees.
203 @arg lat: Latitude (C{degrees}).
204 @arg lon: Longitude (C{degrees}).
205 @kwarg cmoff: Offset B{C{lon}} from zone's central meridian.
206 @kwarg strict: Restrict B{C{lat}} to UTM ranges (C{bool}).
207 @kwarg Error: Error for out of UTM range B{C{lat}}s.
209 @return: 4-Tuple (zone, Band, lat, lon).
210 '''
211 z, lat, lon = _to3zll(lat, lon) # in .utmupsBase
213 x = lon - _cmlon(z) # z before Norway/Svalbard
214 if fabs(x) > _UTM_ZONE_OFF_MAX:
215 t = _SPACE_(_outside_, _UTM_, _zone_, str(z), _by_, degDMS(x, prec=6))
216 raise Error(lon=degDMS(lon), txt=t)
218 B = _toBand(lat, strict=strict, Error=Error)
219 if B == _X_: # and 0 <= lon < 42: z = int(lon + 183) // 6 + 1
220 x = _SvalbardXzone.get(z, None)
221 if x: # Svalbard/Spitsbergen archipelago
222 z += 1 if lon >= x else -1
223 elif B == _V_ and z == 31 and lon >= 3:
224 z += 1 # SouthWestern Norway
226 if cmoff: # lon off central meridian
227 lon -= _cmlon(z) # z after Norway/Svalbard
228 return Zone(z), (Band(B) if B else None), Lat(lat), Lon(lon)
231def _to7zBlldfn(latlon, lon, datum, falsed, name, zone, strict, Error, **cmoff):
232 '''(INTERNAL) Determine 7-tuple (zone, band, lat, lon, datum,
233 falsed, name) for methods L{toEtm8} and L{toUtm8}.
234 '''
235 f = falsed and _xkwds_get(cmoff, cmoff=True) # DEPRECATED
236 lat, lon, d, name = _to4lldn(latlon, lon, datum, name)
237 z, B, lat, lon = _to4zBll(lat, lon, cmoff=f, strict=strict)
238 if zone: # re-zone for ETM/UTM
239 r, _, _ = _to3zBhp(zone, B)
240 if r != z:
241 if not _UTM_ZONE_MIN <= r <= _UTM_ZONE_MAX:
242 raise Error(zone=zone)
243 if f: # re-offset from central meridian
244 lon += _cmlon(z) - _cmlon(r)
245 z = r
246 return z, B, lat, lon, d, f, name
249class Utm(UtmUpsBase):
250 '''Universal Transverse Mercator (UTM) coordinate.
251 '''
252# _band = NN # latitudinal band letter ('C'|..|'X', no 'I'|'O')
253 _Bands = _Bands # latitudinal Band letters (C{tuple})
254 _Error = UTMError # or etm.ETMError
255# _scale = None # grid scale factor (C{scalar}) or C{None}
256 _scale0 = _K0_UTM # central scale factor (C{scalar})
257 _zone = 0 # longitudinal zone (C{int} 1..60)
259 def __init__(self, zone=31, hemisphere=_N_, easting=166022, # PYCHOK expected
260 northing=0, band=NN, datum=_WGS84, falsed=True,
261 gamma=None, scale=None, name=NN, **convergence):
262 '''New L{Utm} UTM coordinate.
264 @kwarg zone: Longitudinal UTM zone (C{int}, 1..60) or zone with/-out
265 I{latitudinal} Band letter (C{str}, '1C'|..|'60X').
266 @kwarg hemisphere: Northern or southern hemisphere (C{str}, C{'N[orth]'}
267 or C{'S[outh]'}).
268 @kwarg easting: Easting, see B{C{falsed}} (C{meter}).
269 @kwarg northing: Northing, see B{C{falsed}} (C{meter}).
270 @kwarg band: Optional, I{latitudinal} band (C{str}, 'C'|..|'X', no 'I'|'O').
271 @kwarg datum: Optional, this coordinate's datum (L{Datum}, L{Ellipsoid},
272 L{Ellipsoid2} or L{a_f2Tuple}).
273 @kwarg falsed: If C{True}, both B{C{easting}} and B{C{northing}} are
274 falsed (C{bool}).
275 @kwarg gamma: Optional meridian convergence, bearing off grid North,
276 clockwise from true North (C{degrees}) or C{None}.
277 @kwarg scale: Optional grid scale factor (C{scalar}) or C{None}.
278 @kwarg name: Optional name (C{str}).
279 @kwarg convergence: DEPRECATED, use keyword argument C{B{gamma}=None}.
281 @raise TypeError: Invalid or near-spherical B{C{datum}}.
283 @raise UTMError: Invalid B{C{zone}}, B{C{hemishere}}, B{C{easting}},
284 B{C{northing}}, B{C{band}}, B{C{convergence}} or
285 B{C{scale}}.
287 @example:
289 >>> import pygeodesy
290 >>> u = pygeodesy.Utm(31, 'N', 448251, 5411932)
291 '''
292 if name:
293 self.name = name
295 self._zone, B, _ = _to3zBlat(zone, band)
297 h = str(hemisphere)[:1].upper()
298 if h not in _NS_:
299 raise self._Error(hemisphere=hemisphere)
301 e, n = easting, northing # Easting(easting), ...
302# if not falsed:
303# e, n = _false2(e, n, h)
304# # check easting/northing (with 40km overlap
305# # between zones) - is this worthwhile?
306# @raise RangeError: If B{C{easting}} or B{C{northing}} outside
307# the valid UTM range.
308# if 120e3 > e or e > 880e3:
309# raise RangeError(easting=easting)
310# if 0 > n or n > _FalseNorthing:
311# raise RangeError(northing=northing)
313 self._hemisphere = h
314 UtmUpsBase.__init__(self, e, n, band=B, datum=datum, falsed=falsed,
315 gamma=gamma, scale=scale, **convergence)
317 def __eq__(self, other):
318 return isinstance(other, Utm) and other.zone == self.zone \
319 and other.hemisphere == self.hemisphere \
320 and other.easting == self.easting \
321 and other.northing == self.northing \
322 and other.band == self.band \
323 and other.datum == self.datum
325 def __repr__(self):
326 return self.toRepr(B=True)
328 def __str__(self):
329 return self.toStr()
331 def _xcopy2(self, Xtm, name=NN):
332 '''(INTERNAL) Make copy as an B{C{Xtm}} instance.
334 @arg Xtm: Class to return the copy (C{Xtm=Etm}, C{Xtm=Utm} or
335 C{self.classof}).
336 '''
337 return Xtm(self.zone, self.hemisphere, self.easting, self.northing,
338 band=self.band, datum=self.datum, falsed=self.falsed,
339 gamma=self.gamma, scale=self.scale, name=name or self.name)
341 @property_doc_(''' the I{latitudinal} band.''')
342 def band(self):
343 '''Get the I{latitudinal} band (C{'C'|..|'X'}).
344 '''
345 if not self._band:
346 self._toLLEB()
347 return self._band
349 @band.setter # PYCHOK setter!
350 def band(self, band):
351 '''Set or reset the I{latitudinal} band letter (C{'C'|..|'X'})
352 or C{None} or C{""} to reset.
354 @raise TypeError: Invalid B{C{band}}.
356 @raise ValueError: Invalid B{C{band}}.
357 '''
358 self._band1(band)
360 @Property_RO
361 def _etm(self):
362 '''(INTERNAL) Cache for method L{toEtm}.
363 '''
364 return self._xcopy2(_MODS.etm.Etm)
366 @Property_RO
367 def falsed2(self):
368 '''Get the easting and northing falsing (L{EasNor2Tuple}C{(easting, northing)}).
369 '''
370 e = n = 0
371 if self.falsed:
372 e = _FalseEasting # relative to central meridian
373 if self.hemisphere == _S_: # relative to equator
374 n = _FalseNorthing
375 return EasNor2Tuple(e, n)
377 def parse(self, strUTM, name=NN):
378 '''Parse a string to a similar L{Utm} instance.
380 @arg strUTM: The UTM coordinate (C{str}),
381 see function L{parseUTM5}.
382 @kwarg name: Optional instance name (C{str}),
383 overriding this name.
385 @return: The similar instance (L{Utm}).
387 @raise UTMError: Invalid B{C{strUTM}}.
389 @see: Functions L{pygeodesy.parseUPS5} and L{pygeodesy.parseUTMUPS5}.
390 '''
391 return parseUTM5(strUTM, datum=self.datum, Utm=self.classof,
392 name=name or self.name)
394 @deprecated_method
395 def parseUTM(self, strUTM): # PYCHOK no cover
396 '''DEPRECATED, use method L{Utm.parse}.'''
397 return self.parse(strUTM)
399 @Property_RO
400 def pole(self):
401 '''Get the top center of (stereographic) projection, C{""} always.
402 '''
403 return NN # N/A for UTM
405 def toEtm(self):
406 '''Copy this UTM to an ETM coordinate.
408 @return: The ETM coordinate (L{Etm}).
409 '''
410 return self._etm
412 def toLatLon(self, LatLon=None, eps=EPS, unfalse=True, **LatLon_kwds):
413 '''Convert this UTM coordinate to an (ellipsoidal) geodetic point.
415 @kwarg LatLon: Optional, ellipsoidal class to return the geodetic
416 point (C{LatLon}) or C{None}.
417 @kwarg eps: Optional convergence limit, L{EPS} or above (C{float}).
418 @kwarg unfalse: Unfalse B{C{easting}} and B{C{northing}}
419 if falsed (C{bool}).
420 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
421 arguments, ignored if C{B{LatLon} is None}.
423 @return: This UTM as (B{C{LatLon}}) or if B{C{LatLon}} is
424 C{None}, as L{LatLonDatum5Tuple}C{(lat, lon, datum,
425 gamma, scale)}.
427 @raise TypeError: Invalid B{C{datum}} or B{C{LatLon}} is not ellipsoidal.
429 @raise UTMError: Invalid meridional radius or H-value.
431 @example:
433 >>> u = Utm(31, 'N', 448251.795, 5411932.678)
434 >>> from pygeodesy import ellipsoidalVincenty as eV
435 >>> ll = u.toLatLon(eV.LatLon) # 48°51′29.52″N, 002°17′40.20″E
436 '''
437 if eps < EPS:
438 eps = EPS # less doesn't converge
440 if self._latlon and self._latlon._toLLEB_args == (unfalse, eps):
441 return self._latlon5(LatLon)
442 else:
443 self._toLLEB(unfalse=unfalse, eps=eps)
444 return self._latlon5(LatLon, **LatLon_kwds)
446 def _toLLEB(self, unfalse=True, eps=EPS): # PYCHOK signature
447 '''(INTERNAL) Compute (ellipsoidal) lat- and longitude.
448 '''
449 x, y = self.eastingnorthing2(falsed=not unfalse)
451 E = self.datum.ellipsoid
452 # from Karney 2011 Eq 15-22, 36
453 A0 = self.scale0 * E.A
454 if A0 < EPS0:
455 raise self._Error(meridional=A0)
456 x = x / A0 # /= chokes PyChecker
457 y = y / A0
458 K = _Kseries(E.BetaKs, x, y) # Krüger series
459 x = neg(K.xs(-x)) # η' eta
460 y = neg(K.ys(-y)) # ξ' ksi
462 sy, cy = sincos2(y)
463 shx = sinh(x)
464 H = hypot(shx, cy)
465 if H < EPS0:
466 raise self._Error(H=H)
468 T = sy / H # τʹ == τ0
469 p = _0_0 # previous d
470 e = _0_0001 * eps
471 for T, i, d in E._es_tauf3(T, T): # max 5
472 # d may toggle on +/-1.12e-16 or +/-4.47e-16,
473 # see the references at C{Ellipsoid.es_tauf}
474 if fabs(d) < eps or fabs(d + p) < e:
475 break
476 p = d
477 else:
478 t = unstr(self.toLatLon, eps=eps, unfalse=unfalse)
479 raise self._Error(Fmt.no_convergence(d), txt=t)
481 a = atan(T) # phi, lat
482 b = atan2(shx, cy)
483 if unfalse and self.falsed:
484 b += radians(_cmlon(self.zone))
485 ll = _LLEB(degrees90(a), degrees180(b), datum=self.datum, name=self.name)
487 # gamma and scale: Karney 2011 Eq 26, 27 and 28
488 p = neg(K.ps(-1))
489 q = K.qs(0)
490 s = hypot(p, q) * E.a / A0
491 ll._gamma = degrees(atan(tan(y) * tanh(x)) + atan2(q, p))
492 ll._scale = (E.e2s(sin(a)) * H * hypot1(T) / s) if s else s # INF?
493 ll._iteration = i
494 self._latlon5args(ll, _toBand, unfalse, eps)
496 def toRepr(self, prec=0, fmt=Fmt.SQUARE, sep=_COMMASPACE_, B=False, cs=False, **unused): # PYCHOK expected
497 '''Return a string representation of this UTM coordinate.
499 Note that UTM coordinates are rounded, not truncated (unlike
500 MGRS grid references).
502 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
503 @kwarg fmt: Enclosing backets format (C{str}).
504 @kwarg sep: Optional separator between name:value pairs (C{str}).
505 @kwarg B: Optionally, include latitudinal band (C{bool}).
506 @kwarg cs: Optionally, include meridian convergence and grid
507 scale factor (C{bool} or non-zero C{int} to specify
508 the precison like B{C{prec}}).
510 @return: This UTM as a string C{"[Z:09[band], H:N|S, E:meter,
511 N:meter]"} plus C{", C:degrees, S:float"} if B{C{cs}} is
512 C{True} (C{str}).
513 '''
514 return self._toRepr(fmt, B, cs, prec, sep)
516 def toStr(self, prec=0, sep=_SPACE_, B=False, cs=False): # PYCHOK expected
517 '''Return a string representation of this UTM coordinate.
519 To distinguish from MGRS grid zone designators, a space is
520 left between the zone and the hemisphere.
522 Note that UTM coordinates are rounded, not truncated (unlike
523 MGRS grid references).
525 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
526 @kwarg sep: Optional separator to join (C{str}) or C{None}
527 to return an unjoined C{tuple} of C{str}s.
528 @kwarg B: Optionally, include latitudinal band (C{bool}).
529 @kwarg cs: Optionally, include meridian convergence and grid
530 scale factor (C{bool} or non-zero C{int} to specify
531 the precison like B{C{prec}}).
533 @return: This UTM as a string with C{zone[band], hemisphere,
534 easting, northing, [convergence, scale]} in
535 C{"00 N|S meter meter"} plus C{" degrees float"} if
536 B{C{cs}} is C{True} (C{str}).
538 @example:
540 >>> u = Utm(3, 'N', 448251, 5411932.0001)
541 >>> u.toStr(4) # 03 N 448251.0 5411932.0001
542 >>> u.toStr(sep=', ') # 03 N, 448251, 5411932
543 '''
545 return self._toStr(self.hemisphere, B, cs, prec, sep)
547 def toUps(self, pole=NN, eps=EPS, falsed=True, **unused):
548 '''Convert this UTM coordinate to a UPS coordinate.
550 @kwarg pole: Optional top/center of the UPS projection,
551 (C{str}, 'N[orth]'|'S[outh]').
552 @kwarg eps: Optional convergence limit, L{EPS} or above
553 (C{float}), see method L{Utm.toLatLon}.
554 @kwarg falsed: False both easting and northing (C{bool}).
556 @return: The UPS coordinate (L{Ups}).
557 '''
558 u = self._ups
559 if u is None or u.pole != (pole or u.pole) or falsed != bool(u.falsed):
560 ll = self.toLatLon(LatLon=_LLEB, eps=eps, unfalse=True)
561 ups = _MODS.ups
562 self._ups = u = ups.toUps8(ll, Ups=ups.Ups, falsed=falsed,
563 name=self.name, pole=pole)
564 return u
566 def toUtm(self, zone, eps=EPS, falsed=True, **unused):
567 '''Convert this UTM coordinate to a different zone.
569 @arg zone: New UTM zone (C{int}).
570 @kwarg eps: Optional convergence limit, L{EPS} or above
571 (C{float}), see method L{Utm.toLatLon}.
572 @kwarg falsed: False both easting and northing (C{bool}).
574 @return: The UTM coordinate (L{Utm}).
575 '''
576 if zone == self.zone and falsed == self.falsed:
577 return self.copy()
578 elif zone:
579 u = self._utm
580 if u is None or u.zone != zone or falsed != u.falsed:
581 ll = self.toLatLon(LatLon=_LLEB, eps=eps, unfalse=True)
582 self._utm = u = toUtm8(ll, Utm=self.classof, falsed=falsed,
583 name=self.name, zone=zone)
584 return u
585 raise self._Error(zone=zone)
587 @Property_RO
588 def zone(self):
589 '''Get the (longitudinal) zone (C{int}, 1..60).
590 '''
591 return self._zone
594def _parseUTM5(strUTM, datum, Xtm, falsed, Error=UTMError, name=NN): # imported by .etm
595 '''(INTERNAL) Parse a string representing a UTM coordinate,
596 consisting of C{"zone[band] hemisphere easting northing"},
597 see L{pygeodesy.parseETM5} and L{parseUTM5}.
598 '''
599 z, h, e, n, B = _parseUTMUPS5(strUTM, None, Error=Error)
600 if _UTM_ZONE_MIN > z or z > _UTM_ZONE_MAX or (B and B not in _Bands):
601 raise Error(strUTM=strUTM, zone=z, band=B)
603 if Xtm is None:
604 r = UtmUps5Tuple(z, h, e, n, B, Error=Error, name=name)
605 else:
606 r = Xtm(z, h, e, n, band=B, datum=datum, falsed=falsed)
607 if name:
608 r = _xnamed(r, name, force=True)
609 return r
612def parseUTM5(strUTM, datum=_WGS84, Utm=Utm, falsed=True, name=NN):
613 '''Parse a string representing a UTM coordinate, consisting
614 of C{"zone[band] hemisphere easting northing"}.
616 @arg strUTM: A UTM coordinate (C{str}).
617 @kwarg datum: Optional datum to use (L{Datum}, L{Ellipsoid},
618 L{Ellipsoid2} or L{a_f2Tuple}).
619 @kwarg Utm: Optional class to return the UTM coordinate
620 (L{Utm}) or C{None}.
621 @kwarg falsed: Both easting and northing are falsed (C{bool}).
622 @kwarg name: Optional B{C{Utm}} name (C{str}).
624 @return: The UTM coordinate (B{C{Utm}}) or if B{C{Utm}}
625 is C{None}, a L{UtmUps5Tuple}C{(zone, hemipole,
626 easting, northing, band)}. The C{hemipole} is
627 the C{'N'|'S'} hemisphere.
629 @raise UTMError: Invalid B{C{strUTM}}.
631 @raise TypeError: Invalid B{C{datum}}.
633 @example:
635 >>> u = parseUTM5('31 N 448251 5411932')
636 >>> u.toRepr() # [Z:31, H:N, E:448251, N:5411932]
637 >>> u = parseUTM5('31 N 448251.8 5411932.7')
638 >>> u.toStr() # 31 N 448252 5411933
639 '''
640 r = _parseUTM5(strUTM, datum, Utm, falsed, name=name)
641 return r
644def toUtm8(latlon, lon=None, datum=None, Utm=Utm, falsed=True,
645 name=NN, strict=True,
646 zone=None, **cmoff):
647 '''Convert a lat-/longitude point to a UTM coordinate.
649 @arg latlon: Latitude (C{degrees}) or an (ellipsoidal)
650 geodetic C{LatLon} point.
651 @kwarg lon: Optional longitude (C{degrees}) or C{None}.
652 @kwarg datum: Optional datum for this UTM coordinate,
653 overriding B{C{latlon}}'s datum (L{Datum},
654 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
655 @kwarg Utm: Optional class to return the UTM coordinate
656 (L{Utm}) or C{None}.
657 @kwarg falsed: False both easting and northing (C{bool}).
658 @kwarg name: Optional B{C{Utm}} name (C{str}).
659 @kwarg strict: Restrict B{C{lat}} to UTM ranges (C{bool}).
660 @kwarg zone: Optional UTM zone to enforce (C{int} or C{str}).
661 @kwarg cmoff: DEPRECATED, use B{C{falsed}}. Offset longitude
662 from the zone's central meridian (C{bool}).
664 @return: The UTM coordinate (B{C{Utm}}) or if B{C{Utm}} is
665 C{None} or not B{C{falsed}}, a L{UtmUps8Tuple}C{(zone,
666 hemipole, easting, northing, band, datum, gamma,
667 scale)}. The C{hemipole} is the C{'N'|'S'} hemisphere.
669 @raise RangeError: If B{C{lat}} outside the valid UTM bands or if
670 B{C{lat}} or B{C{lon}} outside the valid range
671 and L{pygeodesy.rangerrors} set to C{True}.
673 @raise TypeError: Invalid B{C{datum}} or B{C{latlon}} not ellipsoidal.
675 @raise UTMError: Invalid B{C{zone}}.
677 @raise ValueError: If B{C{lon}} value is missing or if
678 B{C{latlon}} is invalid.
680 @note: Implements Karney’s method, using 8-th order Krüger series,
681 giving results accurate to 5 nm (or better) for distances
682 up to 3900 km from the central meridian.
684 @example:
686 >>> p = LatLon(48.8582, 2.2945) # 31 N 448251.8 5411932.7
687 >>> u = toUtm(p) # 31 N 448252 5411933
688 >>> p = LatLon(13.4125, 103.8667) # 48 N 377302.4 1483034.8
689 >>> u = toUtm(p) # 48 N 377302 1483035
690 '''
691 z, B, lat, lon, d, f, name = _to7zBlldfn(latlon, lon, datum,
692 falsed, name, zone,
693 strict, UTMError, **cmoff)
694 d = _ellipsoidal_datum(d, name=name)
695 E = d.ellipsoid
697 a, b = radians(lat), radians(lon)
698 # easting, northing: Karney 2011 Eq 7-14, 29, 35
699 sb, cb = sincos2(b)
701 T = tan(a)
702 T12 = hypot1(T)
703 S = sinh(E.e * atanh(E.e * T / T12))
705 T_ = T * hypot1(S) - S * T12
706 H = hypot(T_, cb)
708 y = atan2(T_, cb) # ξ' ksi
709 x = asinh(sb / H) # η' eta
711 A0 = E.A * getattr(Utm, _UNDER(_scale0_), _K0_UTM) # Utm is class or None
713 K = _Kseries(E.AlphaKs, x, y) # Krüger series
714 y = K.ys(y) * A0 # ξ
715 x = K.xs(x) * A0 # η
717 # convergence: Karney 2011 Eq 23, 24
718 p_ = K.ps(1)
719 q_ = K.qs(0)
720 g = degrees(atan(T_ / hypot1(T_) * tan(b)) + atan2(q_, p_))
721 # scale: Karney 2011 Eq 25
722 k = E.e2s(sin(a)) * T12 / H * (A0 / E.a * hypot(p_, q_))
724 return _toXtm8(Utm, z, lat, x, y,
725 B, d, g, k, f, name, latlon, EPS)
728def _toXtm8(Xtm, z, lat, x, y, B, d, g, k, f, # PYCHOK 13+ args
729 name, latlon, eps, Error=UTMError):
730 '''(INTERNAL) Helper for methods L{toEtm8} and L{toUtm8}.
731 '''
732 h = _hemi(lat)
733 if f:
734 x, y = _false2(x, y, h)
735 if Xtm is None: # DEPRECATED
736 r = UtmUps8Tuple(z, h, x, y, B, d, g, k, Error=Error, name=name)
737 else:
738 r = _xnamed(Xtm(z, h, x, y, band=B, datum=d, falsed=f,
739 gamma=g, scale=k), name)
740 if isinstance(latlon, _LLEB) and d is latlon.datum: # see ups.toUtm8
741 r._latlon5args(latlon, _toBand, f, eps) # XXX weakref(latlon)?
742 latlon._gamma = g
743 latlon._scale = k
744 elif not r._band:
745 r._band = _toBand(lat)
746 return r
749def utmZoneBand5(lat, lon, cmoff=False, name=NN):
750 '''Return the UTM zone number, Band letter, hemisphere and
751 (clipped) lat- and longitude for a given location.
753 @arg lat: Latitude in degrees (C{scalar} or C{str}).
754 @arg lon: Longitude in degrees (C{scalar} or C{str}).
755 @kwarg cmoff: Offset longitude from the zone's central
756 meridian (C{bool}).
757 @kwarg name: Optional name (C{str}).
759 @return: A L{UtmUpsLatLon5Tuple}C{(zone, band, hemipole,
760 lat, lon)} where C{hemipole} is the C{'N'|'S'}
761 UTM hemisphere.
763 @raise RangeError: If B{C{lat}} outside the valid UTM bands or if
764 B{C{lat}} or B{C{lon}} outside the valid range
765 and L{pygeodesy.rangerrors} set to C{True}.
767 @raise ValueError: Invalid B{C{lat}} or B{C{lon}}.
768 '''
769 lat, lon = parseDMS2(lat, lon)
770 z, B, lat, lon = _to4zBll(lat, lon, cmoff=cmoff)
771 return UtmUpsLatLon5Tuple(z, B, _hemi(lat), lat, lon, name=name)
773# **) MIT License
774#
775# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
776#
777# Permission is hereby granted, free of charge, to any person obtaining a
778# copy of this software and associated documentation files (the "Software"),
779# to deal in the Software without restriction, including without limitation
780# the rights to use, copy, modify, merge, publish, distribute, sublicense,
781# and/or sell copies of the Software, and to permit persons to whom the
782# Software is furnished to do so, subject to the following conditions:
783#
784# The above copyright notice and this permission notice shall be included
785# in all copies or substantial portions of the Software.
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790# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
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792# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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