Coverage for pygeodesy/utm.py: 97%
265 statements
« prev ^ index » next coverage.py v7.2.2, created at 2024-05-15 16:36 -0400
« prev ^ index » next coverage.py v7.2.2, created at 2024-05-15 16:36 -0400
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, _operator
43# from pygeodesy.internals import _under # from .utmupsBase
44from pygeodesy.interns import MISSING, NN, _by_, _COMMASPACE_, _N_, \
45 _NS_, _outside_, _range_, _S_, _scale0_, \
46 _SPACE_, _UTM_, _V_, _X_, _zone_
47from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS
48# from pygeodesy.named import _xnamed # from .utmupsBase
49from pygeodesy.namedTuples import EasNor2Tuple, UtmUps5Tuple, \
50 UtmUps8Tuple, UtmUpsLatLon5Tuple
51from pygeodesy.props import deprecated_method, property_doc_, \
52 Property_RO
53from pygeodesy.streprs import Fmt, unstr
54from pygeodesy.units import Band, Int, Lat, Lon, Meter, Zone
55from pygeodesy.utily import atan1, degrees90, degrees180, sincos2
56from pygeodesy.utmupsBase import _hemi, _LLEB, _parseUTMUPS5, _to4lldn, \
57 _to3zBhp, _to3zll, _UPS_LATS, _UPS_ZONE, \
58 _UTM_LAT_MAX, _UTM_ZONE_MAX, _under, \
59 _UTM_LAT_MIN, _UTM_ZONE_MIN, _xnamed, \
60 _UTM_ZONE_OFF_MAX, UtmUpsBase
62from math import asinh, atanh, atan2, cos, cosh, degrees, fabs, \
63 radians, sin, sinh, tan, tanh
64# import operator as _operator # from .fmath
66__all__ = _ALL_LAZY.utm
67__version__ = '24.02.29'
69_Bands = 'CDEFGHJKLMNPQRSTUVWXX' # UTM latitude bands C..X (no
70# I|O) 8° each, covering 80°S to 84°N and X repeated for 80-84°N
71_bandLat_ = 'bandLat'
72_FalseEasting = Meter( 500e3) # falsed offset (C{meter})
73_FalseNorthing = Meter(10000e3) # falsed offset (C{meter})
74_SvalbardXzone = {32: 9, 34: 21, 36: 33} # [zone] longitude
77class UTMError(_ValueError):
78 '''Universal Transverse Mercator (UTM parse or other L{Utm} issue.
79 '''
80 pass
83class _Kseries(object):
84 '''(INTERNAL) Alpha or Beta Krüger series.
86 Krüger series summations for B{C{eta}}, B{C{ksi}}, B{C{p}} and B{C{q}},
87 caching the C{cos}, C{cosh}, C{sin} and C{sinh} values for
88 the given B{C{eta}} and B{C{ksi}} angles (in C{radians}).
89 '''
90 def __init__(self, AB, x, y):
91 '''(INTERNAL) New Alpha or Beta Krüger series
93 @arg AB: Krüger Alpha or Beta series coefficients
94 (C{4-, 6- or 8-tuple}).
95 @arg x: Eta angle (C{radians}).
96 @arg y: Ksi angle (C{radians}).
97 '''
98 n, j2 = len2(range(2, len(AB) * 2 + 1, 2))
99 _m2, _x = map2, _operator.mul
101 self._ab = AB
102 self._pq = _m2(_x, j2, AB)
103# assert len(self._ab) == len(self._pq) == n
105 x2 = _m2(_x, j2, (x,) * n)
106 self._chx = _m2(cosh, x2)
107 self._shx = _m2(sinh, x2)
108# assert len(x2) == len(self._chx) == len(self._shx) == n
110 y2 = _m2(_x, j2, (y,) * n)
111 self._cy = _m2(cos, y2)
112 self._sy = _m2(sin, y2)
113 # self._sy, self._cy = splice(sincos2(*y2)) # PYCHOK false
114# assert len(y2) == len(self._cy) == len(self._sy) == n
116 def xs(self, x0):
117 '''(INTERNAL) Eta summation (C{float}).
118 '''
119 return fdot3(self._ab, self._cy, self._shx, start=x0)
121 def ys(self, y0):
122 '''(INTERNAL) Ksi summation (C{float}).
123 '''
124 return fdot3(self._ab, self._sy, self._chx, start=y0)
126 def ps(self, p0):
127 '''(INTERNAL) P summation (C{float}).
128 '''
129 return fdot3(self._pq, self._cy, self._chx, start=p0)
131 def qs(self, q0):
132 '''(INTERNAL) Q summation (C{float}).
133 '''
134 return fdot3(self._pq, self._sy, self._shx, start=q0)
137def _cmlon(zone):
138 '''(INTERNAL) Central meridian longitude (C{degrees180}).
139 '''
140 return (zone * 6) - 183
143def _false2(e, n, h):
144 '''(INTERNAL) False easting and northing.
145 '''
146 # Karney, "Test data for the transverse Mercator projection (2009)"
147 # <https://GeographicLib.SourceForge.io/C++/doc/transversemercator.html>
148 # and <https://Zenodo.org/record/32470#.W4LEJS2ZON8>
149 e += _FalseEasting # make e relative to central meridian
150 if h == _S_:
151 n += _FalseNorthing # make n relative to equator
152 return e, n
155def _toBand(lat, *unused, **strict_Error): # see ups._toBand
156 '''(INTERNAL) Get the I{latitudinal} Band (row) letter.
157 '''
158 if _UTM_LAT_MIN <= lat < _UTM_LAT_MAX: # [-80, 84) like Veness
159 return _Bands[int(lat - _UTM_LAT_MIN) >> 3]
160 elif _xkwds_get(strict_Error, strict=True):
161 r = _range_(_UTM_LAT_MIN, _UTM_LAT_MAX, ropen=True)
162 t = _SPACE_(_outside_, _UTM_, _range_, r)
163 E = _xkwds_get(strict_Error, Error=RangeError)
164 raise E(lat=degDMS(lat), txt=t)
165 else:
166 return NN # None
169def _to3zBlat(zone, band, Error=UTMError): # in .mgrs
170 '''(INTERNAL) Check and return zone, Band and band latitude.
172 @arg zone: Zone number or string.
173 @arg band: Band letter.
174 @arg Error: Exception to raise (L{UTMError}).
176 @return: 3-Tuple (zone, Band, latitude).
177 '''
178 z, B, _ = _to3zBhp(zone, band, Error=Error)
179 if not (_UTM_ZONE_MIN <= z <= _UTM_ZONE_MAX or
180 (_UPS_ZONE == z and Error is MGRSError)):
181 raise Error(zone=zone)
183 b = None
184 if B:
185 if z == _UPS_ZONE: # polar
186 try:
187 b = Lat(_UPS_LATS[B], name=_bandLat_)
188 except KeyError:
189 raise Error(band=band or B, zone=z)
190 else: # UTM
191 b = _Bands.find(B)
192 if b < 0:
193 raise Error(band=band or B, zone=z)
194 b = Int((b << 3) - 80, name=_bandLat_)
195 B = Band(B)
196 elif Error is not UTMError:
197 raise Error(band=band, txt=MISSING)
199 return Zone(z), B, b
202def _to4zBll(lat, lon, cmoff=True, strict=True, Error=RangeError):
203 '''(INTERNAL) Return zone, Band and lat- and (central) longitude in degrees.
205 @arg lat: Latitude (C{degrees}).
206 @arg lon: Longitude (C{degrees}).
207 @kwarg cmoff: Offset B{C{lon}} from zone's central meridian.
208 @kwarg strict: Restrict B{C{lat}} to UTM ranges (C{bool}).
209 @kwarg Error: Error for out of UTM range B{C{lat}}s.
211 @return: 4-Tuple (zone, Band, lat, lon).
212 '''
213 z, lat, lon = _to3zll(lat, lon) # in .utmupsBase
215 x = lon - _cmlon(z) # z before Norway/Svalbard
216 if fabs(x) > _UTM_ZONE_OFF_MAX:
217 t = _SPACE_(_outside_, _UTM_, _zone_, str(z), _by_, degDMS(x, prec=6))
218 raise Error(lon=degDMS(lon), txt=t)
220 B = _toBand(lat, strict=strict, Error=Error)
221 if B == _X_: # and 0 <= lon < 42: z = int(lon + 183) // 6 + 1
222 x = _SvalbardXzone.get(z, None)
223 if x: # Svalbard/Spitsbergen archipelago
224 z += 1 if lon >= x else -1
225 elif B == _V_ and z == 31 and lon >= 3:
226 z += 1 # SouthWestern Norway
228 if cmoff: # lon off central meridian
229 lon -= _cmlon(z) # z after Norway/Svalbard
230 return Zone(z), (Band(B) if B else None), Lat(lat), Lon(lon)
233def _to7zBlldfn(latlon, lon, datum, falsed, name, zone, strict, Error, **cmoff):
234 '''(INTERNAL) Determine 7-tuple (zone, band, lat, lon, datum,
235 falsed, name) for methods L{toEtm8} and L{toUtm8}.
236 '''
237 f = falsed and _xkwds_get(cmoff, cmoff=True) # DEPRECATED
238 lat, lon, d, name = _to4lldn(latlon, lon, datum, name)
239 z, B, lat, lon = _to4zBll(lat, lon, cmoff=f, strict=strict)
240 if zone: # re-zone for ETM/UTM
241 r, _, _ = _to3zBhp(zone, B)
242 if r != z:
243 if not _UTM_ZONE_MIN <= r <= _UTM_ZONE_MAX:
244 raise Error(zone=zone)
245 if f: # re-offset from central meridian
246 lon += _cmlon(z) - _cmlon(r)
247 z = r
248 return z, B, lat, lon, d, f, name
251class Utm(UtmUpsBase):
252 '''Universal Transverse Mercator (UTM) coordinate.
253 '''
254# _band = NN # latitudinal band letter ('C'|..|'X', no 'I'|'O')
255 _Bands = _Bands # latitudinal Band letters (C{tuple})
256 _Error = UTMError # or etm.ETMError
257# _scale = None # grid scale factor (C{scalar}) or C{None}
258 _scale0 = _K0_UTM # central scale factor (C{scalar})
259 _zone = 0 # longitudinal zone (C{int} 1..60)
261 def __init__(self, zone=31, hemisphere=_N_, easting=166022, # PYCHOK expected
262 northing=0, band=NN, datum=_WGS84, falsed=True,
263 gamma=None, scale=None, name=NN, **convergence):
264 '''New L{Utm} UTM coordinate.
266 @kwarg zone: Longitudinal UTM zone (C{int}, 1..60) or zone with/-out
267 I{latitudinal} Band letter (C{str}, '1C'|..|'60X').
268 @kwarg hemisphere: Northern or southern hemisphere (C{str}, C{'N[orth]'}
269 or C{'S[outh]'}).
270 @kwarg easting: Easting, see B{C{falsed}} (C{meter}).
271 @kwarg northing: Northing, see B{C{falsed}} (C{meter}).
272 @kwarg band: Optional, I{latitudinal} band (C{str}, 'C'|..|'X', no 'I'|'O').
273 @kwarg datum: Optional, this coordinate's datum (L{Datum}, L{Ellipsoid},
274 L{Ellipsoid2} or L{a_f2Tuple}).
275 @kwarg falsed: If C{True}, both B{C{easting}} and B{C{northing}} are
276 falsed (C{bool}).
277 @kwarg gamma: Optional meridian convergence, bearing off grid North,
278 clockwise from true North (C{degrees}) or C{None}.
279 @kwarg scale: Optional grid scale factor (C{scalar}) or C{None}.
280 @kwarg name: Optional name (C{str}).
281 @kwarg convergence: DEPRECATED, use keyword argument C{B{gamma}=None}.
283 @raise TypeError: Invalid or near-spherical B{C{datum}}.
285 @raise UTMError: Invalid B{C{zone}}, B{C{hemishere}}, B{C{easting}},
286 B{C{northing}}, B{C{band}}, B{C{convergence}} or
287 B{C{scale}}.
288 '''
289 if name:
290 self.name = name
292 self._zone, B, _ = _to3zBlat(zone, band)
294 h = str(hemisphere)[:1].upper()
295 if h not in _NS_:
296 raise self._Error(hemisphere=hemisphere)
298 e, n = easting, northing # Easting(easting), ...
299# if not falsed:
300# e, n = _false2(e, n, h)
301# # check easting/northing (with 40km overlap
302# # between zones) - is this worthwhile?
303# @raise RangeError: If B{C{easting}} or B{C{northing}} outside
304# the valid UTM range.
305# if 120e3 > e or e > 880e3:
306# raise RangeError(easting=easting)
307# if 0 > n or n > _FalseNorthing:
308# raise RangeError(northing=northing)
310 self._hemisphere = h
311 UtmUpsBase.__init__(self, e, n, band=B, datum=datum, falsed=falsed,
312 gamma=gamma, scale=scale, **convergence)
314 def __eq__(self, other):
315 return isinstance(other, Utm) and other.zone == self.zone \
316 and other.hemisphere == self.hemisphere \
317 and other.easting == self.easting \
318 and other.northing == self.northing \
319 and other.band == self.band \
320 and other.datum == self.datum
322 def __repr__(self):
323 return self.toRepr(B=True)
325 def __str__(self):
326 return self.toStr()
328 def _xcopy2(self, Xtm, name=NN):
329 '''(INTERNAL) Make copy as an B{C{Xtm}} instance.
331 @arg Xtm: Class to return the copy (C{Xtm=Etm}, C{Xtm=Utm} or
332 C{self.classof}).
333 '''
334 return Xtm(self.zone, self.hemisphere, self.easting, self.northing,
335 band=self.band, datum=self.datum, falsed=self.falsed,
336 gamma=self.gamma, scale=self.scale, name=name or self.name)
338 @property_doc_(''' the I{latitudinal} band.''')
339 def band(self):
340 '''Get the I{latitudinal} band (C{'C'|..|'X'}).
341 '''
342 if not self._band:
343 self._toLLEB()
344 return self._band
346 @band.setter # PYCHOK setter!
347 def band(self, band):
348 '''Set or reset the I{latitudinal} band letter (C{'C'|..|'X'})
349 or C{None} or C{""} to reset.
351 @raise TypeError: Invalid B{C{band}}.
353 @raise ValueError: Invalid B{C{band}}.
354 '''
355 self._band1(band)
357 @Property_RO
358 def _etm(self):
359 '''(INTERNAL) Cache for method L{toEtm}.
360 '''
361 return self._xcopy2(_MODS.etm.Etm)
363 @Property_RO
364 def falsed2(self):
365 '''Get the easting and northing falsing (L{EasNor2Tuple}C{(easting, northing)}).
366 '''
367 e = n = 0
368 if self.falsed:
369 e = _FalseEasting # relative to central meridian
370 if self.hemisphere == _S_: # relative to equator
371 n = _FalseNorthing
372 return EasNor2Tuple(e, n)
374 def parse(self, strUTM, name=NN):
375 '''Parse a string to a similar L{Utm} instance.
377 @arg strUTM: The UTM coordinate (C{str}),
378 see function L{parseUTM5}.
379 @kwarg name: Optional instance name (C{str}),
380 overriding this name.
382 @return: The similar instance (L{Utm}).
384 @raise UTMError: Invalid B{C{strUTM}}.
386 @see: Functions L{pygeodesy.parseUPS5} and L{pygeodesy.parseUTMUPS5}.
387 '''
388 return parseUTM5(strUTM, datum=self.datum, Utm=self.classof,
389 name=name or self.name)
391 @deprecated_method
392 def parseUTM(self, strUTM): # PYCHOK no cover
393 '''DEPRECATED, use method L{Utm.parse}.'''
394 return self.parse(strUTM)
396 @Property_RO
397 def pole(self):
398 '''Get the top center of (stereographic) projection, C{""} always.
399 '''
400 return NN # N/A for UTM
402 def toEtm(self):
403 '''Copy this UTM to an ETM coordinate.
405 @return: The ETM coordinate (L{Etm}).
406 '''
407 return self._etm
409 def toLatLon(self, LatLon=None, eps=EPS, unfalse=True, **LatLon_kwds):
410 '''Convert this UTM coordinate to an (ellipsoidal) geodetic point.
412 @kwarg LatLon: Optional, ellipsoidal class to return the geodetic
413 point (C{LatLon}) or C{None}.
414 @kwarg eps: Optional convergence limit, L{EPS} or above (C{float}).
415 @kwarg unfalse: Unfalse B{C{easting}} and B{C{northing}}
416 if falsed (C{bool}).
417 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
418 arguments, ignored if C{B{LatLon} is None}.
420 @return: This UTM as (B{C{LatLon}}) or if B{C{LatLon}} is
421 C{None}, as L{LatLonDatum5Tuple}C{(lat, lon, datum,
422 gamma, scale)}.
424 @raise TypeError: Invalid B{C{datum}} or B{C{LatLon}} is not ellipsoidal.
426 @raise UTMError: Invalid meridional radius or H-value.
428 '''
429 if eps < EPS:
430 eps = EPS # less doesn't converge
432 if self._latlon and self._latlon._toLLEB_args == (unfalse, eps):
433 return self._latlon5(LatLon)
434 else:
435 self._toLLEB(unfalse=unfalse, eps=eps)
436 return self._latlon5(LatLon, **LatLon_kwds)
438 def _toLLEB(self, unfalse=True, eps=EPS): # PYCHOK signature
439 '''(INTERNAL) Compute (ellipsoidal) lat- and longitude.
440 '''
441 x, y = self.eastingnorthing2(falsed=not unfalse)
443 E = self.datum.ellipsoid
444 # from Karney 2011 Eq 15-22, 36
445 A0 = self.scale0 * E.A
446 if A0 < EPS0:
447 raise self._Error(meridional=A0)
448 x = x / A0 # /= chokes PyChecker
449 y = y / A0
450 K = _Kseries(E.BetaKs, x, y) # Krüger series
451 x = neg(K.xs(-x)) # η' eta
452 y = neg(K.ys(-y)) # ξ' ksi
454 sy, cy = sincos2(y)
455 shx = sinh(x)
456 H = hypot(shx, cy)
457 if H < EPS0:
458 raise self._Error(H=H)
460 T = sy / H # τʹ == τ0
461 p = _0_0 # previous d
462 e = _0_0001 * eps
463 for T, i, d in E._es_tauf3(T, T): # 4-5 trips
464 # d may toggle on +/-1.12e-16 or +/-4.47e-16,
465 # see the references at C{Ellipsoid.es_tauf}
466 if fabs(d) < eps or fabs(d + p) < e:
467 break
468 p = d
469 else:
470 t = unstr(self.toLatLon, eps=eps, unfalse=unfalse)
471 raise self._Error(Fmt.no_convergence(d, eps), txt=t)
473 a = atan1(T) # phi, lat
474 b = atan2(shx, cy)
475 if unfalse and self.falsed:
476 b += radians(_cmlon(self.zone))
477 ll = _LLEB(degrees90(a), degrees180(b), datum=self.datum, name=self.name)
479 # gamma and scale: Karney 2011 Eq 26, 27 and 28
480 p = neg(K.ps(-1))
481 q = K.qs(0)
482 s = hypot(p, q) * E.a / A0
483 ll._gamma = degrees(atan1(tan(y) * tanh(x)) + atan2(q, p))
484 ll._scale = (E.e2s(sin(a)) * hypot1(T) * H / s) if s else s # INF?
485 ll._iteration = i
486 self._latlon5args(ll, _toBand, unfalse, eps)
488 def toRepr(self, prec=0, fmt=Fmt.SQUARE, sep=_COMMASPACE_, B=False, cs=False, **unused): # PYCHOK expected
489 '''Return a string representation of this UTM coordinate.
491 Note that UTM coordinates are rounded, not truncated (unlike
492 MGRS grid references).
494 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
495 @kwarg fmt: Enclosing backets format (C{str}).
496 @kwarg sep: Optional separator between name:value pairs (C{str}).
497 @kwarg B: Optionally, include latitudinal band (C{bool}).
498 @kwarg cs: Optionally, include meridian convergence and grid
499 scale factor (C{bool} or non-zero C{int} to specify
500 the precison like B{C{prec}}).
502 @return: This UTM as a string C{"[Z:09[band], H:N|S, E:meter,
503 N:meter]"} plus C{", C:degrees, S:float"} if B{C{cs}} is
504 C{True} (C{str}).
505 '''
506 return self._toRepr(fmt, B, cs, prec, sep)
508 def toStr(self, prec=0, sep=_SPACE_, B=False, cs=False): # PYCHOK expected
509 '''Return a string representation of this UTM coordinate.
511 To distinguish from MGRS grid zone designators, a space is
512 left between the zone and the hemisphere.
514 Note that UTM coordinates are rounded, not truncated (unlike
515 MGRS grid references).
517 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
518 @kwarg sep: Optional separator to join (C{str}) or C{None}
519 to return an unjoined C{tuple} of C{str}s.
520 @kwarg B: Optionally, include latitudinal band (C{bool}).
521 @kwarg cs: Optionally, include meridian convergence and grid
522 scale factor (C{bool} or non-zero C{int} to specify
523 the precison like B{C{prec}}).
525 @return: This UTM as a string with C{zone[band], hemisphere,
526 easting, northing, [convergence, scale]} in
527 C{"00 N|S meter meter"} plus C{" degrees float"} if
528 B{C{cs}} is C{True} (C{str}).
529 '''
530 return self._toStr(self.hemisphere, B, cs, prec, sep)
532 def toUps(self, pole=NN, eps=EPS, falsed=True, **unused):
533 '''Convert this UTM coordinate to a UPS coordinate.
535 @kwarg pole: Optional top/center of the UPS projection,
536 (C{str}, 'N[orth]'|'S[outh]').
537 @kwarg eps: Optional convergence limit, L{EPS} or above
538 (C{float}), see method L{Utm.toLatLon}.
539 @kwarg falsed: False both easting and northing (C{bool}).
541 @return: The UPS coordinate (L{Ups}).
542 '''
543 u = self._ups
544 if u is None or u.pole != (pole or u.pole) or falsed != bool(u.falsed):
545 ll = self.toLatLon(LatLon=_LLEB, eps=eps, unfalse=True)
546 ups = _MODS.ups
547 self._ups = u = ups.toUps8(ll, Ups=ups.Ups, falsed=falsed,
548 name=self.name, pole=pole)
549 return u
551 def toUtm(self, zone, eps=EPS, falsed=True, **unused):
552 '''Convert this UTM coordinate to a different zone.
554 @arg zone: New UTM zone (C{int}).
555 @kwarg eps: Optional convergence limit, L{EPS} or above
556 (C{float}), see method L{Utm.toLatLon}.
557 @kwarg falsed: False both easting and northing (C{bool}).
559 @return: The UTM coordinate (L{Utm}).
560 '''
561 if zone == self.zone and falsed == self.falsed:
562 return self.copy()
563 elif zone:
564 u = self._utm
565 if u is None or u.zone != zone or falsed != u.falsed:
566 ll = self.toLatLon(LatLon=_LLEB, eps=eps, unfalse=True)
567 self._utm = u = toUtm8(ll, Utm=self.classof, falsed=falsed,
568 name=self.name, zone=zone)
569 return u
570 raise self._Error(zone=zone)
572 @Property_RO
573 def zone(self):
574 '''Get the (longitudinal) zone (C{int}, 1..60).
575 '''
576 return self._zone
579def _parseUTM5(strUTM, datum, Xtm, falsed, Error=UTMError, name=NN): # imported by .etm
580 '''(INTERNAL) Parse a string representing a UTM coordinate,
581 consisting of C{"zone[band] hemisphere easting northing"},
582 see L{pygeodesy.parseETM5} and L{parseUTM5}.
583 '''
584 z, h, e, n, B = _parseUTMUPS5(strUTM, None, Error=Error)
585 if _UTM_ZONE_MIN > z or z > _UTM_ZONE_MAX or (B and B not in _Bands):
586 raise Error(strUTM=strUTM, zone=z, band=B)
588 if Xtm is None:
589 r = UtmUps5Tuple(z, h, e, n, B, Error=Error, name=name)
590 else:
591 r = Xtm(z, h, e, n, band=B, datum=datum, falsed=falsed)
592 if name:
593 r = _xnamed(r, name, force=True)
594 return r
597def parseUTM5(strUTM, datum=_WGS84, Utm=Utm, falsed=True, name=NN):
598 '''Parse a string representing a UTM coordinate, consisting
599 of C{"zone[band] hemisphere easting northing"}.
601 @arg strUTM: A UTM coordinate (C{str}).
602 @kwarg datum: Optional datum to use (L{Datum}, L{Ellipsoid},
603 L{Ellipsoid2} or L{a_f2Tuple}).
604 @kwarg Utm: Optional class to return the UTM coordinate
605 (L{Utm}) or C{None}.
606 @kwarg falsed: Both easting and northing are falsed (C{bool}).
607 @kwarg name: Optional B{C{Utm}} name (C{str}).
609 @return: The UTM coordinate (B{C{Utm}}) or if B{C{Utm}}
610 is C{None}, a L{UtmUps5Tuple}C{(zone, hemipole,
611 easting, northing, band)}. The C{hemipole} is
612 the C{'N'|'S'} hemisphere.
614 @raise UTMError: Invalid B{C{strUTM}}.
616 @raise TypeError: Invalid B{C{datum}}.
617 '''
618 return _parseUTM5(strUTM, datum, Utm, falsed, name=name)
621def toUtm8(latlon, lon=None, datum=None, Utm=Utm, falsed=True,
622 name=NN, strict=True,
623 zone=None, **cmoff):
624 '''Convert a lat-/longitude point to a UTM coordinate.
626 @arg latlon: Latitude (C{degrees}) or an (ellipsoidal)
627 geodetic C{LatLon} point.
628 @kwarg lon: Optional longitude (C{degrees}) or C{None}.
629 @kwarg datum: Optional datum for this UTM coordinate,
630 overriding B{C{latlon}}'s datum (L{Datum},
631 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
632 @kwarg Utm: Optional class to return the UTM coordinate
633 (L{Utm}) or C{None}.
634 @kwarg falsed: False both easting and northing (C{bool}).
635 @kwarg name: Optional B{C{Utm}} name (C{str}).
636 @kwarg strict: Restrict B{C{lat}} to UTM ranges (C{bool}).
637 @kwarg zone: Optional UTM zone to enforce (C{int} or C{str}).
638 @kwarg cmoff: DEPRECATED, use B{C{falsed}}. Offset longitude
639 from the zone's central meridian (C{bool}).
641 @return: The UTM coordinate (B{C{Utm}}) or if B{C{Utm}} is
642 C{None} or not B{C{falsed}}, a L{UtmUps8Tuple}C{(zone,
643 hemipole, easting, northing, band, datum, gamma,
644 scale)}. The C{hemipole} is the C{'N'|'S'} hemisphere.
646 @raise RangeError: If B{C{lat}} outside the valid UTM bands or if
647 B{C{lat}} or B{C{lon}} outside the valid range
648 and L{pygeodesy.rangerrors} set to C{True}.
650 @raise TypeError: Invalid B{C{datum}} or B{C{latlon}} not ellipsoidal.
652 @raise UTMError: Invalid B{C{zone}}.
654 @raise ValueError: If B{C{lon}} value is missing or if
655 B{C{latlon}} is invalid.
657 @note: Implements Karney’s method, using 8-th order Krüger series,
658 giving results accurate to 5 nm (or better) for distances
659 up to 3,900 Km from the central meridian.
660 '''
661 z, B, lat, lon, d, f, name = _to7zBlldfn(latlon, lon, datum,
662 falsed, name, zone,
663 strict, UTMError, **cmoff)
664 d = _ellipsoidal_datum(d, name=name)
665 E = d.ellipsoid
667 a, b = radians(lat), radians(lon)
668 # easting, northing: Karney 2011 Eq 7-14, 29, 35
669 sb, cb = sincos2(b)
671 T = tan(a)
672 T12 = hypot1(T)
673 S = sinh(E.e * atanh(E.e * T / T12))
675 T_ = T * hypot1(S) - S * T12
676 H = hypot(T_, cb)
678 y = atan2(T_, cb) # ξ' ksi
679 x = asinh(sb / H) # η' eta
681 A0 = E.A * getattr(Utm, _under(_scale0_), _K0_UTM) # Utm is class or None
683 K = _Kseries(E.AlphaKs, x, y) # Krüger series
684 y = K.ys(y) * A0 # ξ
685 x = K.xs(x) * A0 # η
687 # convergence: Karney 2011 Eq 23, 24
688 p_ = K.ps(1)
689 q_ = K.qs(0)
690 g = degrees(atan2(T_ * tan(b), hypot1(T_)) + atan2(q_, p_))
691 # scale: Karney 2011 Eq 25
692 k = E.e2s(sin(a)) * T12 / H * (A0 / E.a * hypot(p_, q_))
694 return _toXtm8(Utm, z, lat, x, y,
695 B, d, g, k, f, name, latlon, EPS)
698def _toXtm8(Xtm, z, lat, x, y, B, d, g, k, f, # PYCHOK 13+ args
699 name, latlon, eps, Error=UTMError):
700 '''(INTERNAL) Helper for methods L{toEtm8} and L{toUtm8}.
701 '''
702 h = _hemi(lat)
703 if f:
704 x, y = _false2(x, y, h)
705 if Xtm is None: # DEPRECATED
706 r = UtmUps8Tuple(z, h, x, y, B, d, g, k, Error=Error, name=name)
707 else:
708 r = _xnamed(Xtm(z, h, x, y, band=B, datum=d, falsed=f,
709 gamma=g, scale=k), name)
710 if isinstance(latlon, _LLEB) and d is latlon.datum: # see ups.toUtm8
711 r._latlon5args(latlon, _toBand, f, eps) # XXX weakref(latlon)?
712 latlon._gamma = g
713 latlon._scale = k
714 elif not r._band:
715 r._band = _toBand(lat)
716 return r
719def utmZoneBand5(lat, lon, cmoff=False, name=NN):
720 '''Return the UTM zone number, Band letter, hemisphere and
721 (clipped) lat- and longitude for a given location.
723 @arg lat: Latitude in degrees (C{scalar} or C{str}).
724 @arg lon: Longitude in degrees (C{scalar} or C{str}).
725 @kwarg cmoff: Offset longitude from the zone's central
726 meridian (C{bool}).
727 @kwarg name: Optional name (C{str}).
729 @return: A L{UtmUpsLatLon5Tuple}C{(zone, band, hemipole,
730 lat, lon)} where C{hemipole} is the C{'N'|'S'}
731 UTM hemisphere.
733 @raise RangeError: If B{C{lat}} outside the valid UTM bands or if
734 B{C{lat}} or B{C{lon}} outside the valid range
735 and L{pygeodesy.rangerrors} set to C{True}.
737 @raise ValueError: Invalid B{C{lat}} or B{C{lon}}.
738 '''
739 lat, lon = parseDMS2(lat, lon)
740 z, B, lat, lon = _to4zBll(lat, lon, cmoff=cmoff)
741 return UtmUpsLatLon5Tuple(z, B, _hemi(lat), lat, lon, name=name)
743# **) MIT License
744#
745# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
746#
747# Permission is hereby granted, free of charge, to any person obtaining a
748# copy of this software and associated documentation files (the "Software"),
749# to deal in the Software without restriction, including without limitation
750# the rights to use, copy, modify, merge, publish, distribute, sublicense,
751# and/or sell copies of the Software, and to permit persons to whom the
752# Software is furnished to do so, subject to the following conditions:
753#
754# The above copyright notice and this permission notice shall be included
755# in all copies or substantial portions of the Software.
756#
757# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
758# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
759# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
760# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
761# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
762# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
763# OTHER DEALINGS IN THE SOFTWARE.