Coverage for pygeodesy/etm.py: 92%
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2# -*- coding: utf-8 -*-
4u'''A pure Python version of I{Karney}'s C{Exact Transverse Mercator} (ETM) projection.
6Classes L{Etm}, L{ETMError} and L{ExactTransverseMercator}, transcoded from I{Karney}'s
7C++ class U{TransverseMercatorExact<https://GeographicLib.SourceForge.io/C++/doc/
8classGeographicLib_1_1TransverseMercatorExact.html>}, abbreviated as C{TMExact} below.
10Class L{ExactTransverseMercator} provides C{Exact Transverse Mercator} projections while
11instances of class L{Etm} represent ETM C{(easting, northing)} locations. See also
12I{Karney}'s utility U{TransverseMercatorProj<https://GeographicLib.SourceForge.io/C++/doc/
13TransverseMercatorProj.1.html>} and use C{"python[3] -m pygeodesy.etm ..."} to compare
14the results.
16Following is a copy of I{Karney}'s U{TransverseMercatorExact.hpp
17<https://GeographicLib.SourceForge.io/C++/doc/TransverseMercatorExact_8hpp_source.html>}
18file C{Header}.
20Copyright (C) U{Charles Karney<mailto:Karney@Alum.MIT.edu>} (2008-2023) and licensed
21under the MIT/X11 License. For more information, see the U{GeographicLib<https://
22GeographicLib.SourceForge.io>} documentation.
24The method entails using the U{Thompson Transverse Mercator<https://WikiPedia.org/
25wiki/Transverse_Mercator_projection>} as an intermediate projection. The projections
26from the intermediate coordinates to C{phi, lam} and C{x, y} are given by elliptic
27functions. The inverse of these projections are found by Newton's method with a
28suitable starting guess.
30The relevant section of L.P. Lee's paper U{Conformal Projections Based On Jacobian
31Elliptic Functions<https://DOI.org/10.3138/X687-1574-4325-WM62>} in part V, pp
3267-101. The C++ implementation and notation closely follow Lee, with the following
33exceptions::
35 Lee here Description
37 x/a xi Northing (unit Earth)
39 y/a eta Easting (unit Earth)
41 s/a sigma xi + i * eta
43 y x Easting
45 x y Northing
47 k e Eccentricity
49 k^2 mu Elliptic function parameter
51 k'^2 mv Elliptic function complementary parameter
53 m k Scale
55 zeta zeta Complex longitude = Mercator = chi in paper
57 s sigma Complex GK = zeta in paper
59Minor alterations have been made in some of Lee's expressions in an attempt to
60control round-off. For example, C{atanh(sin(phi))} is replaced by C{asinh(tan(phi))}
61which maintains accuracy near C{phi = pi/2}. Such changes are noted in the code.
62'''
63# make sure int/int division yields float quotient, see .basics
64from __future__ import division as _; del _ # PYCHOK semicolon
66from pygeodesy.basics import map1, neg, neg_, _xinstanceof
67from pygeodesy.constants import EPS, EPS02, PI_2, PI_4, _K0_UTM, \
68 _1_EPS, _0_0, _0_1, _0_5, _1_0, _2_0, \
69 _3_0, _4_0, _90_0, isnear0, isnear90
70from pygeodesy.datums import _ellipsoidal_datum, _WGS84, _EWGS84
71# from pygeodesy.ellipsoids import _EWGS84 # from .datums
72from pygeodesy.elliptic import _ALL_LAZY, Elliptic
73# from pygeodesy.errors import _incompatible # from .named
74from pygeodesy.fmath import cbrt, hypot, hypot1, hypot2
75from pygeodesy.fsums import Fsum, fsum1f_
76from pygeodesy.interns import NN, _COMMASPACE_, _DASH_, _near_, _SPACE_, \
77 _spherical_, _usage
78from pygeodesy.karney import _copyBit, _diff182, _fix90, _norm2, _norm180, \
79 _tand, _unsigned2
80# from pygeodesy.lazily import _ALL_LAZY # from .elliptic
81from pygeodesy.named import callername, _incompatible, _NamedBase
82from pygeodesy.namedTuples import Forward4Tuple, Reverse4Tuple
83from pygeodesy.props import deprecated_method, deprecated_property_RO, \
84 Property_RO, property_RO, _update_all, \
85 property_doc_
86from pygeodesy.streprs import Fmt, pairs, unstr
87from pygeodesy.units import Degrees, Scalar_
88from pygeodesy.utily import atan1d, atan2d, _loneg, sincos2
89from pygeodesy.utm import _cmlon, _LLEB, _parseUTM5, _toBand, _toXtm8, \
90 _to7zBlldfn, Utm, UTMError
92from math import asinh, atan2, degrees, radians, sinh, sqrt
94__all__ = _ALL_LAZY.etm
95__version__ = '23.10.15'
97_OVERFLOW = _1_EPS**2 # about 2e+31
98_TAYTOL = pow(EPS, 0.6)
99_TAYTOL2 = _TAYTOL * _2_0
100_TOL_10 = EPS * _0_1
101_TRIPS = 21 # C++ 10
104def _overflow(x):
105 '''(INTERNAL) Like C{copysign0(OVERFLOW, B{x})}.
106 '''
107 return _copyBit(_OVERFLOW, x)
110class ETMError(UTMError):
111 '''Exact Transverse Mercator (ETM) parse, projection or other
112 L{Etm} issue or L{ExactTransverseMercator} conversion failure.
113 '''
114 pass
117class Etm(Utm):
118 '''Exact Transverse Mercator (ETM) coordinate, a sub-class of L{Utm},
119 a Universal Transverse Mercator (UTM) coordinate using the
120 L{ExactTransverseMercator} projection for highest accuracy.
122 @note: Conversion of (geodetic) lat- and longitudes to/from L{Etm}
123 coordinates is 3-4 times slower than to/from L{Utm}.
125 @see: Karney's U{Detailed Description<https://GeographicLib.SourceForge.io/
126 html/classGeographicLib_1_1TransverseMercatorExact.html#details>}.
127 '''
128 _Error = ETMError # see utm.UTMError
129 _exactTM = None
131 __init__ = Utm.__init__
132 '''New L{Etm} Exact Transverse Mercator coordinate, raising L{ETMError}s.
134 @see: L{Utm.__init__} for more information.
136 @example:
138 >>> import pygeodesy
139 >>> u = pygeodesy.Etm(31, 'N', 448251, 5411932)
140 '''
142 @property_doc_(''' the ETM projection (L{ExactTransverseMercator}).''')
143 def exactTM(self):
144 '''Get the ETM projection (L{ExactTransverseMercator}).
145 '''
146 if self._exactTM is None:
147 self.exactTM = self.datum.exactTM # ExactTransverseMercator(datum=self.datum)
148 return self._exactTM
150 @exactTM.setter # PYCHOK setter!
151 def exactTM(self, exactTM):
152 '''Set the ETM projection (L{ExactTransverseMercator}).
154 @raise ETMError: The B{C{exacTM}}'s datum incompatible
155 with this ETM coordinate's C{datum}.
156 '''
157 _xinstanceof(ExactTransverseMercator, exactTM=exactTM)
159 E = self.datum.ellipsoid
160 if E != exactTM.ellipsoid: # may be None
161 raise ETMError(repr(exactTM), txt=_incompatible(repr(E)))
162 self._exactTM = exactTM
163 self._scale0 = exactTM.k0
165 def parse(self, strETM, name=NN):
166 '''Parse a string to a similar L{Etm} instance.
168 @arg strETM: The ETM coordinate (C{str}),
169 see function L{parseETM5}.
170 @kwarg name: Optional instance name (C{str}),
171 overriding this name.
173 @return: The instance (L{Etm}).
175 @raise ETMError: Invalid B{C{strETM}}.
177 @see: Function L{pygeodesy.parseUPS5}, L{pygeodesy.parseUTM5}
178 and L{pygeodesy.parseUTMUPS5}.
179 '''
180 return parseETM5(strETM, datum=self.datum, Etm=self.classof,
181 name=name or self.name)
183 @deprecated_method
184 def parseETM(self, strETM): # PYCHOK no cover
185 '''DEPRECATED, use method L{Etm.parse}.
186 '''
187 return self.parse(strETM)
189 def toLatLon(self, LatLon=None, unfalse=True, **unused): # PYCHOK expected
190 '''Convert this ETM coordinate to an (ellipsoidal) geodetic point.
192 @kwarg LatLon: Optional, ellipsoidal class to return the geodetic
193 point (C{LatLon}) or C{None}.
194 @kwarg unfalse: Unfalse B{C{easting}} and B{C{northing}} if
195 C{falsed} (C{bool}).
197 @return: This ETM coordinate as (B{C{LatLon}}) or a
198 L{LatLonDatum5Tuple}C{(lat, lon, datum, gamma,
199 scale)} if B{C{LatLon}} is C{None}.
201 @raise ETMError: This ETM coordinate's C{exacTM} and this C{datum}
202 incompatible or no convergence transforming to
203 lat- and longitude.
205 @raise TypeError: Invalid or non-ellipsoidal B{C{LatLon}}.
207 @example:
209 >>> from pygeodesy import ellipsoidalVincenty as eV, Etm
210 >>> u = Etm(31, 'N', 448251.795, 5411932.678)
211 >>> ll = u.toLatLon(eV.LatLon) # 48°51′29.52″N, 002°17′40.20″E
212 '''
213 if not self._latlon or self._latlon._toLLEB_args != (unfalse, self.exactTM):
214 self._toLLEB(unfalse=unfalse)
215 return self._latlon5(LatLon)
217 def _toLLEB(self, unfalse=True, **unused): # PYCHOK signature
218 '''(INTERNAL) Compute (ellipsoidal) lat- and longitude.
219 '''
220 xTM, d = self.exactTM, self.datum
221 # double check that this and exactTM's ellipsoid match
222 if xTM._E != d.ellipsoid: # PYCHOK no cover
223 t = repr(d.ellipsoid)
224 raise ETMError(repr(xTM._E), txt=_incompatible(t))
226 e, n = self.eastingnorthing2(falsed=not unfalse)
227 lon0 = _cmlon(self.zone) if bool(unfalse) == self.falsed else None
228 lat, lon, g, k = xTM.reverse(e, n, lon0=lon0)
230 ll = _LLEB(lat, lon, datum=d, name=self.name) # utm._LLEB
231 ll._gamma = g
232 ll._scale = k
233 self._latlon5args(ll, _toBand, unfalse, xTM)
235 def toUtm(self): # PYCHOK signature
236 '''Copy this ETM to a UTM coordinate.
238 @return: The UTM coordinate (L{Utm}).
239 '''
240 return self._xcopy2(Utm)
243class ExactTransverseMercator(_NamedBase):
244 '''Pure Python version of Karney's C++ class U{TransverseMercatorExact
245 <https://GeographicLib.SourceForge.io/C++/doc/TransverseMercatorExact_8cpp_source.html>},
246 a numerically exact transverse Mercator projection, further referred to as C{TMExact}.
247 '''
248 _datum = _WGS84 # Datum
249 _E = _EWGS84 # Ellipsoid
250 _extendp = False # use extended domain
251# _iteration = None # ._sigmaInv2 and ._zetaInv2
252 _k0 = _K0_UTM # central scale factor
253 _lat0 = _0_0 # central parallel
254 _lon0 = _0_0 # central meridian
255 _mu = _EWGS84.e2 # 1st eccentricity squared
256 _mv = _EWGS84.e21 # 1 - ._mu
257 _raiser = False # throw Error
258 _sigmaC = None # most recent _sigmaInv04 case C{int}
259 _zetaC = None # most recent _zetaInv04 case C{int}
261 def __init__(self, datum=_WGS84, lon0=0, k0=_K0_UTM, extendp=False, name=NN, raiser=False):
262 '''New L{ExactTransverseMercator} projection.
264 @kwarg datum: The I{non-spherical} datum or ellipsoid (L{Datum},
265 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
266 @kwarg lon0: Central meridian, default (C{degrees180}).
267 @kwarg k0: Central scale factor (C{float}).
268 @kwarg extendp: Use the I{extended} domain (C{bool}), I{standard} otherwise.
269 @kwarg name: Optional name for the projection (C{str}).
270 @kwarg raiser: If C{True}, throw an L{ETMError} for convergence failures (C{bool}).
272 @raise ETMError: Near-spherical B{C{datum}} or C{ellipsoid} or invalid B{C{lon0}}
273 or B{C{k0}}.
275 @see: U{Constructor TransverseMercatorExact<https://GeographicLib.SourceForge.io/
276 html/classGeographicLib_1_1TransverseMercatorExact.html>} for more details,
277 especially on B{X{extendp}}.
279 @note: For all 255.5K U{TMcoords.dat<https://Zenodo.org/record/32470>} tests (with
280 C{0 <= lat <= 84} and C{0 <= lon}) the maximum error is C{5.2e-08 .forward}
281 (or 52 nano-meter) easting and northing and C{3.8e-13 .reverse} (or 0.38
282 pico-degrees) lat- and longitude (with Python 3.7.3+, 2.7.16+, PyPy6 3.5.3
283 and PyPy6 2.7.13, all in 64-bit on macOS 10.13.6 High Sierra C{x86_64} and
284 12.2 Monterey C{arm64} and C{"arm64_x86_64"}).
285 '''
286 if extendp:
287 self._extendp = True
288 if name:
289 self.name = name
290 if raiser:
291 self.raiser = True
293 TM = ExactTransverseMercator
294 if datum not in (TM._datum, TM._E, None):
295 self.datum = datum # invokes ._resets
296 if lon0 or lon0 != TM._lon0:
297 self.lon0 = lon0
298 if k0 is not TM._k0:
299 self.k0 = k0
301 @property_doc_(''' the datum (L{Datum}).''')
302 def datum(self):
303 '''Get the datum (L{Datum}) or C{None}.
304 '''
305 return self._datum
307 @datum.setter # PYCHOK setter!
308 def datum(self, datum):
309 '''Set the datum and ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
311 @raise ETMError: Near-spherical B{C{datum}} or C{ellipsoid}.
312 '''
313 d = _ellipsoidal_datum(datum, name=self.name) # raiser=_datum_)
314 self._resets(d)
315 self._datum = d
317 @Property_RO
318 def _e(self):
319 '''(INTERNAL) Get and cache C{_e}.
320 '''
321 return self._E.e
323 @Property_RO
324 def _1_e_90(self): # PYCHOK no cover
325 '''(INTERNAL) Get and cache C{(1 - _e) * 90}.
326 '''
327 return (_1_0 - self._e) * _90_0
329 @property_RO
330 def ellipsoid(self):
331 '''Get the ellipsoid (L{Ellipsoid}).
332 '''
333 return self._E
335 @Property_RO
336 def _e_PI_2(self):
337 '''(INTERNAL) Get and cache C{_e * PI / 2}.
338 '''
339 return self._e * PI_2
341 @Property_RO
342 def _e_PI_4_(self):
343 '''(INTERNAL) Get and cache C{-_e * PI / 4}.
344 '''
345 return -self._e * PI_4
347 @Property_RO
348 def _1_e_PI_2(self):
349 '''(INTERNAL) Get and cache C{(1 - _e) * PI / 2}.
350 '''
351 return (_1_0 - self._e) * PI_2
353 @Property_RO
354 def _1_2e_PI_2(self):
355 '''(INTERNAL) Get and cache C{(1 - 2 * _e) * PI / 2}.
356 '''
357 return (_1_0 - self._e * _2_0) * PI_2
359 @property_RO
360 def equatoradius(self):
361 '''Get the C{ellipsoid}'s equatorial radius, semi-axis (C{meter}).
362 '''
363 return self._E.a
365 a = equatoradius
367 @Property_RO
368 def _e_TAYTOL(self):
369 '''(INTERNAL) Get and cache C{e * TAYTOL}.
370 '''
371 return self._e * _TAYTOL
373 @Property_RO
374 def _Eu(self):
375 '''(INTERNAL) Get and cache C{Elliptic(_mu)}.
376 '''
377 return Elliptic(self._mu)
379 @Property_RO
380 def _Eu_cE(self):
381 '''(INTERNAL) Get and cache C{_Eu.cE}.
382 '''
383 return self._Eu.cE
385 def _Eu_2cE_(self, xi):
386 '''(INTERNAL) Return C{_Eu.cE * 2 - B{xi}}.
387 '''
388 return self._Eu_cE * _2_0 - xi
390 @Property_RO
391 def _Eu_cE_4(self):
392 '''(INTERNAL) Get and cache C{_Eu.cE / 4}.
393 '''
394 return self._Eu_cE / _4_0
396 @Property_RO
397 def _Eu_cK(self):
398 '''(INTERNAL) Get and cache C{_Eu.cK}.
399 '''
400 return self._Eu.cK
402 @Property_RO
403 def _Eu_cK_cE(self):
404 '''(INTERNAL) Get and cache C{_Eu.cK / _Eu.cE}.
405 '''
406 return self._Eu_cK / self._Eu_cE
408 @Property_RO
409 def _Eu_2cK_PI(self):
410 '''(INTERNAL) Get and cache C{_Eu.cK * 2 / PI}.
411 '''
412 return self._Eu_cK / PI_2
414 @Property_RO
415 def _Ev(self):
416 '''(INTERNAL) Get and cache C{Elliptic(_mv)}.
417 '''
418 return Elliptic(self._mv)
420 @Property_RO
421 def _Ev_cK(self):
422 '''(INTERNAL) Get and cache C{_Ev.cK}.
423 '''
424 return self._Ev.cK
426 @Property_RO
427 def _Ev_cKE(self):
428 '''(INTERNAL) Get and cache C{_Ev.cKE}.
429 '''
430 return self._Ev.cKE
432 @Property_RO
433 def _Ev_3cKE_4(self):
434 '''(INTERNAL) Get and cache C{_Ev.cKE * 3 / 4}.
435 '''
436 return self._Ev_cKE * 0.75 # _0_75
438 @Property_RO
439 def _Ev_5cKE_4(self):
440 '''(INTERNAL) Get and cache C{_Ev.cKE * 5 / 4}.
441 '''
442 return self._Ev_cKE * 1.25 # _1_25
444 @Property_RO
445 def extendp(self):
446 '''Get the domain (C{bool}), I{extended} or I{standard}.
447 '''
448 return self._extendp
450 @property_RO
451 def flattening(self):
452 '''Get the C{ellipsoid}'s flattening (C{scalar}).
453 '''
454 return self._E.f
456 f = flattening
458 def forward(self, lat, lon, lon0=None, name=NN): # MCCABE 13
459 '''Forward projection, from geographic to transverse Mercator.
461 @arg lat: Latitude of point (C{degrees}).
462 @arg lon: Longitude of point (C{degrees}).
463 @kwarg lon0: Central meridian (C{degrees180}), overriding
464 the default if not C{None}.
465 @kwarg name: Optional name (C{str}).
467 @return: L{Forward4Tuple}C{(easting, northing, gamma, scale)}.
469 @see: C{void TMExact::Forward(real lon0, real lat, real lon,
470 real &x, real &y,
471 real &gamma, real &k)}.
473 @raise ETMError: No convergence, thrown iff property
474 C{B{raiser}=True}.
475 '''
476 lat = _fix90(lat - self._lat0)
477 lon, _ = _diff182((self.lon0 if lon0 is None else lon0), lon)
478 if self.extendp:
479 backside = _lat = _lon = False
480 else: # enforce the parity
481 lat, _lat = _unsigned2(lat)
482 lon, _lon = _unsigned2(lon)
483 backside = lon > 90
484 if backside: # PYCHOK no cover
485 lon = _loneg(lon)
486 if lat == 0:
487 _lat = True
489 # u, v = coordinates for the Thompson TM, Lee 54
490 if lat == 90: # isnear90(lat)
491 u = self._Eu_cK
492 v = self._iteration = self._zetaC = 0
493 elif lat == 0 and lon == self._1_e_90: # PYCHOK no cover
494 u = self._iteration = self._zetaC = 0
495 v = self._Ev_cK
496 else: # tau = tan(phi), taup = sinh(psi)
497 tau, lam = _tand(lat), radians(lon)
498 u, v = self._zetaInv2(self._E.es_taupf(tau), lam)
500 sncndn6 = self._sncndn6(u, v)
501 y, x, _ = self._sigma3(v, *sncndn6)
502 g, k = (lon, self.k0) if isnear90(lat) else \
503 self._zetaScaled(sncndn6, ll=False)
505 if backside:
506 y, g = self._Eu_2cE_(y), _loneg(g)
507 y *= self._k0_a
508 x *= self._k0_a
509 if _lat:
510 y, g = neg_(y, g)
511 if _lon:
512 x, g = neg_(x, g)
513 return Forward4Tuple(x, y, g, k, iteration=self._iteration,
514 name=name or self.name)
516 def _Inv03(self, psi, dlam, _3_mv_e): # (xi, deta, _3_mv)
517 '''(INTERNAL) Partial C{_zetaInv04} or C{_sigmaInv04}, Case 2
518 '''
519 # atan2(dlam-psi, psi+dlam) + 45d gives arg(zeta - zeta0) in
520 # range [-135, 225). Subtracting 180 (multiplier is negative)
521 # makes range [-315, 45). Multiplying by 1/3 (for cube root)
522 # gives range [-105, 15). In particular the range [-90, 180]
523 # in zeta space maps to [-90, 0] in w space as required.
524 a = atan2(dlam - psi, psi + dlam) / _3_0 - PI_4
525 s, c = sincos2(a)
526 h = hypot(psi, dlam)
527 r = cbrt(h * _3_mv_e)
528 u = r * c
529 v = r * s + self._Ev_cK
530 # Error using this guess is about 0.068 * rad^(5/3)
531 return u, v, h
533 @property_RO
534 def iteration(self):
535 '''Get the most recent C{ExactTransverseMercator.forward}
536 or C{ExactTransverseMercator.reverse} iteration number
537 (C{int}) or C{None} if not available/applicable.
538 '''
539 return self._iteration
541 @property_doc_(''' the central scale factor (C{float}).''')
542 def k0(self):
543 '''Get the central scale factor (C{float}), aka I{C{scale0}}.
544 '''
545 return self._k0 # aka scale0
547 @k0.setter # PYCHOK setter!
548 def k0(self, k0):
549 '''Set the central scale factor (C{float}), aka I{C{scale0}}.
551 @raise ETMError: Invalid B{C{k0}}.
552 '''
553 k0 = Scalar_(k0=k0, Error=ETMError, low=_TOL_10, high=_1_0)
554 if self._k0 != k0:
555 ExactTransverseMercator._k0_a._update(self) # redo ._k0_a
556 self._k0 = k0
558 @Property_RO
559 def _k0_a(self):
560 '''(INTERNAL) Get and cache C{k0 * equatoradius}.
561 '''
562 return self.k0 * self.equatoradius
564 @property_doc_(''' the central meridian (C{degrees180}).''')
565 def lon0(self):
566 '''Get the central meridian (C{degrees180}).
567 '''
568 return self._lon0
570 @lon0.setter # PYCHOK setter!
571 def lon0(self, lon0):
572 '''Set the central meridian (C{degrees180}).
574 @raise ETMError: Invalid B{C{lon0}}.
575 '''
576 self._lon0 = _norm180(Degrees(lon0=lon0, Error=ETMError))
578 @deprecated_property_RO
579 def majoradius(self): # PYCHOK no cover
580 '''DEPRECATED, use property C{equatoradius}.'''
581 return self.equatoradius
583 @Property_RO
584 def _1_mu_2(self):
585 '''(INTERNAL) Get and cache C{_mu / 2 + 1}.
586 '''
587 return self._mu * _0_5 + _1_0
589 @Property_RO
590 def _3_mv(self):
591 '''(INTERNAL) Get and cache C{3 / _mv}.
592 '''
593 return _3_0 / self._mv
595 @Property_RO
596 def _3_mv_e(self):
597 '''(INTERNAL) Get and cache C{3 / (_mv * _e)}.
598 '''
599 return _3_0 / (self._mv * self._e)
601 def _Newton2(self, taup, lam, u, v, C, *psi): # or (xi, eta, u, v)
602 '''(INTERNAL) Invert C{_zetaInv2} or C{_sigmaInv2} using Newton's method.
604 @return: 2-Tuple C{(u, v)}.
606 @raise ETMError: No convergence.
607 '''
608 sca1, tol2 = _1_0, _TOL_10
609 if psi: # _zetaInv2
610 sca1 = sca1 / hypot1(taup) # /= chokes PyChecker
611 tol2 = tol2 / max(psi[0], _1_0)**2
613 _zeta3 = self._zeta3
614 _zetaDwd2 = self._zetaDwd2
615 else: # _sigmaInv2
616 _zeta3 = self._sigma3
617 _zetaDwd2 = self._sigmaDwd2
619 d2, r = tol2, self.raiser
620 _U_2 = Fsum(u).fsum2_
621 _V_2 = Fsum(v).fsum2_
622 # min iterations 2, max 6 or 7, mean 3.9 or 4.0
623 for i in range(1, _TRIPS): # GEOGRAPHICLIB_PANIC
624 sncndn6 = self._sncndn6(u, v)
625 du, dv = _zetaDwd2(*sncndn6)
626 T, L, _ = _zeta3(v, *sncndn6)
627 T = (taup - T) * sca1
628 L -= lam
629 u, dU = _U_2(T * du, L * dv)
630 v, dV = _V_2(T * dv, -L * du)
631 if d2 < tol2:
632 r = False
633 break
634 d2 = hypot2(dU, dV)
636 self._iteration = i
637 if r: # PYCHOK no cover
638 n = callername(up=2, underOK=True)
639 t = unstr(n, taup, lam, u, v, C=C)
640 raise ETMError(Fmt.no_convergence(d2, tol2), txt=t)
641 return u, v
643 @property_doc_(''' raise an L{ETMError} for convergence failures (C{bool}).''')
644 def raiser(self):
645 '''Get the error setting (C{bool}).
646 '''
647 return self._raiser
649 @raiser.setter # PYCHOK setter!
650 def raiser(self, raiser):
651 '''Set the error setting (C{bool}), if C{True} throw an L{ETMError}
652 for convergence failures.
653 '''
654 self._raiser = bool(raiser)
656 def reset(self, lat0, lon0):
657 '''Set the central parallel and meridian.
659 @arg lat0: Latitude of the central parallel (C{degrees90}).
660 @arg lon0: Longitude of the central parallel (C{degrees180}).
662 @return: 2-Tuple C{(lat0, lon0)} of the previous central
663 parallel and meridian.
665 @raise ETMError: Invalid B{C{lat0}} or B{C{lon0}}.
666 '''
667 t = self._lat0, self.lon0
668 self._lat0 = _fix90(Degrees(lat0=lat0, Error=ETMError))
669 self. lon0 = lon0
670 return t
672 def _resets(self, datum):
673 '''(INTERNAL) Set the ellipsoid and elliptic moduli.
675 @arg datum: Ellipsoidal datum (C{Datum}).
677 @raise ETMError: Near-spherical B{C{datum}} or C{ellipsoid}.
678 '''
679 E = datum.ellipsoid
680 mu = E.e2 # .eccentricity1st2
681 mv = E.e21 # _1_0 - mu
682 if isnear0(E.e) or isnear0(mu, eps0=EPS02) \
683 or isnear0(mv, eps0=EPS02): # or sqrt(mu) != E.e
684 raise ETMError(ellipsoid=E, txt=_near_(_spherical_))
686 if self._datum or self._E:
687 _i = ExactTransverseMercator.iteration._uname
688 _update_all(self, _i, '_sigmaC', '_zetaC') # _under
690 self._E = E
691 self._mu = mu
692 self._mv = mv
694 def reverse(self, x, y, lon0=None, name=NN):
695 '''Reverse projection, from Transverse Mercator to geographic.
697 @arg x: Easting of point (C{meters}).
698 @arg y: Northing of point (C{meters}).
699 @kwarg lon0: Central meridian (C{degrees180}), overriding
700 the default if not C{None}.
701 @kwarg name: Optional name (C{str}).
703 @return: L{Reverse4Tuple}C{(lat, lon, gamma, scale)}.
705 @see: C{void TMExact::Reverse(real lon0, real x, real y,
706 real &lat, real &lon,
707 real &gamma, real &k)}
709 @raise ETMError: No convergence, thrown iff property
710 C{B{raiser}=True}.
711 '''
712 # undoes the steps in .forward.
713 xi = y / self._k0_a
714 eta = x / self._k0_a
715 if self.extendp:
716 backside = _lat = _lon = False
717 else: # enforce the parity
718 eta, _lon = _unsigned2(eta)
719 xi, _lat = _unsigned2(xi)
720 backside = xi > self._Eu_cE
721 if backside: # PYCHOK no cover
722 xi = self._Eu_2cE_(xi)
724 # u, v = coordinates for the Thompson TM, Lee 54
725 if xi or eta != self._Ev_cKE:
726 u, v = self._sigmaInv2(xi, eta)
727 else: # PYCHOK no cover
728 u = self._iteration = self._sigmaC = 0
729 v = self._Ev_cK
731 if v or u != self._Eu_cK:
732 g, k, lat, lon = self._zetaScaled(self._sncndn6(u, v))
733 else: # PYCHOK no cover
734 g, k, lat, lon = _0_0, self.k0, _90_0, _0_0
736 if backside: # PYCHOK no cover
737 lon, g = _loneg(lon), _loneg(g)
738 if _lat:
739 lat, g = neg_(lat, g)
740 if _lon:
741 lon, g = neg_(lon, g)
742 lat += self._lat0
743 lon += self._lon0 if lon0 is None else _norm180(lon0)
744 return Reverse4Tuple(lat, _norm180(lon), g, k, # _norm180(lat)
745 iteration=self._iteration,
746 name=name or self.name)
748 def _scaled2(self, tau, d2, snu, cnu, dnu, snv, cnv, dnv):
749 '''(INTERNAL) C{scaled}.
751 @note: Argument B{C{d2}} is C{_mu * cnu**2 + _mv * cnv**2}
752 from C{._zeta3}.
754 @return: 2-Tuple C{(convergence, scale)}.
756 @see: C{void TMExact::Scale(real tau, real /*lam*/,
757 real snu, real cnu, real dnu,
758 real snv, real cnv, real dnv,
759 real &gamma, real &k)}.
760 '''
761 mu, mv = self._mu, self._mv
762 cnudnv = cnu * dnv
763 # Lee 55.12 -- negated for our sign convention. g gives
764 # the bearing (clockwise from true north) of grid north
765 g = atan2d(mv * cnv * snv * snu, cnudnv * dnu)
766 # Lee 55.13 with nu given by Lee 9.1 -- in sqrt change
767 # the numerator from (1 - snu^2 * dnv^2) to (_mv * snv^2
768 # + cnu^2 * dnv^2) to maintain accuracy near phi = 90
769 # and change the denomintor from (dnu^2 + dnv^2 - 1) to
770 # (_mu * cnu^2 + _mv * cnv^2) to maintain accuracy near
771 # phi = 0, lam = 90 * (1 - e). Similarly rewrite sqrt in
772 # 9.1 as _mv + _mu * c^2 instead of 1 - _mu * sin(phi)^2
773 if d2 > 0:
774 # originally: sec2 = 1 + tau**2 # sec(phi)^2
775 # d2 = (mu * cnu**2 + mv * cnv**2)
776 # q2 = (mv * snv**2 + cnudnv**2) / d2
777 # k = sqrt(mv + mu / sec2) * sqrt(sec2) * sqrt(q2)
778 # = sqrt(mv * sec2 + mu) * sqrt(q2)
779 # = sqrt(mv + mv * tau**2 + mu) * sqrt(q2)
780 k, q2 = _0_0, (mv * snv**2 + cnudnv**2)
781 if q2 > 0:
782 k2 = fsum1f_(mu, mv, mv * tau**2)
783 if k2 > 0:
784 k = sqrt(k2) * sqrt(q2 / d2) * self.k0
785 else:
786 k = _OVERFLOW
787 return g, k
789 def _sigma3(self, v, snu, cnu, dnu, snv, cnv, dnv):
790 '''(INTERNAL) C{sigma}.
792 @return: 3-Tuple C{(xi, eta, d2)}.
794 @see: C{void TMExact::sigma(real /*u*/, real snu, real cnu, real dnu,
795 real v, real snv, real cnv, real dnv,
796 real &xi, real &eta)}.
798 @raise ETMError: No convergence.
799 '''
800 mu = self._mu * cnu
801 mv = self._mv * cnv
802 # Lee 55.4 writing
803 # dnu^2 + dnv^2 - 1 = _mu * cnu^2 + _mv * cnv^2
804 d2 = cnu * mu + cnv * mv
805 mu *= snu * dnu
806 mv *= snv * dnv
807 if d2 > 0: # /= chokes PyChecker
808 mu = mu / d2
809 mv = mv / d2
810 else:
811 mu, mv = map1(_overflow, mu, mv)
812 xi = self._Eu.fE(snu, cnu, dnu) - mu
813 v -= self._Ev.fE(snv, cnv, dnv) - mv
814 return xi, v, d2
816 def _sigmaDwd2(self, snu, cnu, dnu, snv, cnv, dnv):
817 '''(INTERNAL) C{sigmaDwd}.
819 @return: 2-Tuple C{(du, dv)}.
821 @see: C{void TMExact::dwdsigma(real /*u*/, real snu, real cnu, real dnu,
822 real /*v*/, real snv, real cnv, real dnv,
823 real &du, real &dv)}.
824 '''
825 snuv = snu * snv
826 # Reciprocal of 55.9: dw / ds = dn(w)^2/_mv,
827 # expanding complex dn(w) using A+S 16.21.4
828 d = self._mv * (cnv**2 + self._mu * snuv**2)**2
829 r = cnv * dnu * dnv
830 i = cnu * snuv * self._mu
831 du = (r**2 - i**2) / d
832 dv = neg(r * i * _2_0 / d)
833 return du, dv
835 def _sigmaInv2(self, xi, eta):
836 '''(INTERNAL) Invert C{sigma} using Newton's method.
838 @return: 2-Tuple C{(u, v)}.
840 @see: C{void TMExact::sigmainv(real xi, real eta,
841 real &u, real &v)}.
843 @raise ETMError: No convergence.
844 '''
845 u, v, t, self._sigmaC = self._sigmaInv04(xi, eta)
846 if not t:
847 u, v = self._Newton2(xi, eta, u, v, self._sigmaC)
848 return u, v
850 def _sigmaInv04(self, xi, eta):
851 '''(INTERNAL) Starting point for C{sigmaInv}.
853 @return: 4-Tuple C{(u, v, trip, Case)}.
855 @see: C{bool TMExact::sigmainv0(real xi, real eta,
856 real &u, real &v)}.
857 '''
858 t = False
859 d = eta - self._Ev_cKE
860 if eta > self._Ev_5cKE_4 or (xi < d and xi < -self._Eu_cE_4):
861 # sigma as a simple pole at
862 # w = w0 = Eu.K() + i * Ev.K()
863 # and sigma is approximated by
864 # sigma = (Eu.E() + i * Ev.KE()) + 1 / (w - w0)
865 u, v = _norm2(xi - self._Eu_cE, -d)
866 u += self._Eu_cK
867 v += self._Ev_cK
868 C = 1
870 elif (eta > self._Ev_3cKE_4 and xi < self._Eu_cE_4) or d > 0:
871 # At w = w0 = i * Ev.K(), we have
872 # sigma = sigma0 = i * Ev.KE()
873 # sigma' = sigma'' = 0
874 # including the next term in the Taylor series gives:
875 # sigma = sigma0 - _mv / 3 * (w - w0)^3
876 # When inverting this, we map arg(w - w0) = [-pi/2, -pi/6]
877 # to arg(sigma - sigma0) = [-pi/2, pi/2] mapping arg =
878 # [-pi/2, -pi/6] to [-pi/2, pi/2]
879 u, v, h = self._Inv03(xi, d, self._3_mv)
880 t = h < _TAYTOL2
881 C = 2
883 else: # use w = sigma * Eu.K/Eu.E (correct in limit _e -> 0)
884 u = v = self._Eu_cK_cE
885 u *= xi
886 v *= eta
887 C = 3
889 return u, v, t, C
891 def _sncndn6(self, u, v):
892 '''(INTERNAL) Get 6-tuple C{(snu, cnu, dnu, snv, cnv, dnv)}.
893 '''
894 # snu, cnu, dnu = self._Eu.sncndn(u)
895 # snv, cnv, dnv = self._Ev.sncndn(v)
896 return self._Eu.sncndn(u) + self._Ev.sncndn(v)
898 def toStr(self, joined=_COMMASPACE_, **kwds): # PYCHOK signature
899 '''Return a C{str} representation.
901 @kwarg joined: Separator to join the attribute strings
902 (C{str} or C{None} or C{NN} for non-joined).
903 @kwarg kwds: Optional, overriding keyword arguments.
904 '''
905 d = dict(datum=self.datum.name, lon0=self.lon0,
906 k0=self.k0, extendp=self.extendp)
907 if self.name:
908 d.update(name=self.name)
909 t = pairs(d, **kwds)
910 return joined.join(t) if joined else t
912 def _zeta3(self, unused, snu, cnu, dnu, snv, cnv, dnv): # _sigma3 signature
913 '''(INTERNAL) C{zeta}.
915 @return: 3-Tuple C{(taup, lambda, d2)}.
917 @see: C{void TMExact::zeta(real /*u*/, real snu, real cnu, real dnu,
918 real /*v*/, real snv, real cnv, real dnv,
919 real &taup, real &lam)}
920 '''
921 e, cnu2, mv = self._e, cnu**2, self._mv
922 # Overflow value like atan(overflow) = pi/2
923 t1 = t2 = _overflow(snu)
924 # Lee 54.17 but write
925 # atanh(snu * dnv) = asinh(snu * dnv / sqrt(cnu^2 + _mv * snu^2 * snv^2))
926 # atanh(_e * snu / dnv) = asinh(_e * snu / sqrt(_mu * cnu^2 + _mv * cnv^2))
927 d1 = cnu2 + mv * (snu * snv)**2
928 if d1 > EPS02: # _EPSmin
929 t1 = snu * dnv / sqrt(d1)
930 else:
931 d1 = 0
932 d2 = self._mu * cnu2 + mv * cnv**2
933 if d2 > EPS02: # _EPSmin
934 t2 = sinh(e * asinh(e * snu / sqrt(d2)))
935 else:
936 d2 = 0
937 # psi = asinh(t1) - asinh(t2)
938 # taup = sinh(psi)
939 taup = t1 * hypot1(t2) - t2 * hypot1(t1)
940 lam = (atan2(dnu * snv, cnu * cnv) -
941 atan2(cnu * snv * e, dnu * cnv) * e) if d1 and d2 else _0_0
942 return taup, lam, d2
944 def _zetaDwd2(self, snu, cnu, dnu, snv, cnv, dnv):
945 '''(INTERNAL) C{zetaDwd}.
947 @return: 2-Tuple C{(du, dv)}.
949 @see: C{void TMExact::dwdzeta(real /*u*/, real snu, real cnu, real dnu,
950 real /*v*/, real snv, real cnv, real dnv,
951 real &du, real &dv)}.
952 '''
953 cnu2 = cnu**2 * self._mu
954 cnv2 = cnv**2
955 dnuv = dnu * dnv
956 dnuv2 = dnuv**2
957 snuv = snu * snv
958 snuv2 = snuv**2 * self._mu
959 # Lee 54.21 but write (see A+S 16.21.4)
960 # (1 - dnu^2 * snv^2) = (cnv^2 + _mu * snu^2 * snv^2)
961 d = self._mv * (cnv2 + snuv2)**2 # max(d, EPS02)?
962 du = cnu * dnuv * (cnv2 - snuv2) / d
963 dv = cnv * snuv * (cnu2 + dnuv2) / d
964 return du, neg(dv)
966 def _zetaInv2(self, taup, lam):
967 '''(INTERNAL) Invert C{zeta} using Newton's method.
969 @return: 2-Tuple C{(u, v)}.
971 @see: C{void TMExact::zetainv(real taup, real lam,
972 real &u, real &v)}.
974 @raise ETMError: No convergence.
975 '''
976 psi = asinh(taup)
977 u, v, t, self._zetaC = self._zetaInv04(psi, lam)
978 if not t:
979 u, v = self._Newton2(taup, lam, u, v, self._zetaC, psi)
980 return u, v
982 def _zetaInv04(self, psi, lam):
983 '''(INTERNAL) Starting point for C{zetaInv}.
985 @return: 4-Tuple C{(u, v, trip, Case)}.
987 @see: C{bool TMExact::zetainv0(real psi, real lam, # radians
988 real &u, real &v)}.
989 '''
990 if lam > self._1_2e_PI_2:
991 d = lam - self._1_e_PI_2
992 if psi < d and psi < self._e_PI_4_: # PYCHOK no cover
993 # N.B. this branch is normally *not* taken because psi < 0
994 # is converted psi > 0 by .forward. There's a log singularity
995 # at w = w0 = Eu.K() + i * Ev.K(), corresponding to the south
996 # pole, where we have, approximately
997 # psi = _e + i * pi/2 - _e * atanh(cos(i * (w - w0)/(1 + _mu/2)))
998 # Inverting this gives:
999 e = self._e # eccentricity
1000 s, c = sincos2((PI_2 - lam) / e)
1001 h, r = sinh(_1_0 - psi / e), self._1_mu_2
1002 u = self._Eu_cK - r * asinh(s / hypot(c, h))
1003 v = self._Ev_cK - r * atan2(c, h)
1004 return u, v, False, 1
1006 elif psi < self._e_PI_2:
1007 # At w = w0 = i * Ev.K(), we have
1008 # zeta = zeta0 = i * (1 - _e) * pi/2
1009 # zeta' = zeta'' = 0
1010 # including the next term in the Taylor series gives:
1011 # zeta = zeta0 - (_mv * _e) / 3 * (w - w0)^3
1012 # When inverting this, we map arg(w - w0) = [-90, 0]
1013 # to arg(zeta - zeta0) = [-90, 180]
1014 u, v, h = self._Inv03(psi, d, self._3_mv_e)
1015 return u, v, (h < self._e_TAYTOL), 2
1017 # Use spherical TM, Lee 12.6 -- writing C{atanh(sin(lam) /
1018 # cosh(psi)) = asinh(sin(lam) / hypot(cos(lam), sinh(psi)))}.
1019 # This takes care of the log singularity at C{zeta = Eu.K()},
1020 # corresponding to the north pole.
1021 s, c = sincos2(lam)
1022 h, r = sinh(psi), self._Eu_2cK_PI
1023 # But scale to put 90, 0 on the right place
1024 u = r * atan2(h, c)
1025 v = r * asinh(s / hypot(h, c))
1026 return u, v, False, 3
1028 def _zetaScaled(self, sncndn6, ll=True):
1029 '''(INTERNAL) Recompute (T, L) from (u, v) to improve accuracy of Scale.
1031 @arg sncndn6: 6-Tuple C{(snu, cnu, dnu, snv, cnv, dnv)}.
1033 @return: 2-Tuple C{(g, k)} if not C{B{ll}} else
1034 4-tuple C{(g, k, lat, lon)}.
1035 '''
1036 t, lam, d2 = self._zeta3(None, *sncndn6)
1037 tau = self._E.es_tauf(t)
1038 g_k = self._scaled2(tau, d2, *sncndn6)
1039 if ll:
1040 g_k += atan1d(tau), degrees(lam)
1041 return g_k # or (g, k, lat, lon)
1044def parseETM5(strUTM, datum=_WGS84, Etm=Etm, falsed=True, name=NN):
1045 '''Parse a string representing a UTM coordinate, consisting
1046 of C{"zone[band] hemisphere easting northing"}.
1048 @arg strUTM: A UTM coordinate (C{str}).
1049 @kwarg datum: Optional datum to use (L{Datum}, L{Ellipsoid},
1050 L{Ellipsoid2} or L{a_f2Tuple}).
1051 @kwarg Etm: Optional class to return the UTM coordinate
1052 (L{Etm}) or C{None}.
1053 @kwarg falsed: Both easting and northing are C{falsed} (C{bool}).
1054 @kwarg name: Optional B{C{Etm}} name (C{str}).
1056 @return: The UTM coordinate (B{C{Etm}}) or if B{C{Etm}} is
1057 C{None}, a L{UtmUps5Tuple}C{(zone, hemipole, easting,
1058 northing, band)}. The C{hemipole} is the hemisphere
1059 C{'N'|'S'}.
1061 @raise ETMError: Invalid B{C{strUTM}}.
1063 @raise TypeError: Invalid or near-spherical B{C{datum}}.
1065 @example:
1067 >>> u = parseETM5('31 N 448251 5411932')
1068 >>> u.toRepr() # [Z:31, H:N, E:448251, N:5411932]
1069 >>> u = parseETM5('31 N 448251.8 5411932.7')
1070 >>> u.toStr() # 31 N 448252 5411933
1071 '''
1072 r = _parseUTM5(strUTM, datum, Etm, falsed, Error=ETMError, name=name)
1073 return r
1076def toEtm8(latlon, lon=None, datum=None, Etm=Etm, falsed=True,
1077 name=NN, strict=True,
1078 zone=None, **cmoff):
1079 '''Convert a geodetic lat-/longitude to an ETM coordinate.
1081 @arg latlon: Latitude (C{degrees}) or an (ellipsoidal)
1082 geodetic C{LatLon} instance.
1083 @kwarg lon: Optional longitude (C{degrees}) or C{None}.
1084 @kwarg datum: Optional datum for the ETM coordinate,
1085 overriding B{C{latlon}}'s datum (L{Datum},
1086 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
1087 @kwarg Etm: Optional class to return the ETM coordinate
1088 (L{Etm}) or C{None}.
1089 @kwarg falsed: False both easting and northing (C{bool}).
1090 @kwarg name: Optional B{C{Utm}} name (C{str}).
1091 @kwarg strict: Restrict B{C{lat}} to UTM ranges (C{bool}).
1092 @kwarg zone: Optional UTM zone to enforce (C{int} or C{str}).
1093 @kwarg cmoff: DEPRECATED, use B{C{falsed}}. Offset longitude
1094 from the zone's central meridian (C{bool}).
1096 @return: The ETM coordinate as an B{C{Etm}} instance or a
1097 L{UtmUps8Tuple}C{(zone, hemipole, easting, northing,
1098 band, datum, gamma, scale)} if B{C{Etm}} is C{None}
1099 or not B{C{falsed}}. The C{hemipole} is the C{'N'|'S'}
1100 hemisphere.
1102 @raise ETMError: No convergence transforming to ETM easting
1103 and northing.
1105 @raise ETMError: Invalid B{C{zone}} or near-spherical or
1106 incompatible B{C{datum}} or C{ellipsoid}.
1108 @raise RangeError: If B{C{lat}} outside the valid UTM bands or
1109 if B{C{lat}} or B{C{lon}} outside the valid
1110 range and L{pygeodesy.rangerrors} set to C{True}.
1112 @raise TypeError: Invalid or near-spherical B{C{datum}} or
1113 B{C{latlon}} not ellipsoidal.
1115 @raise ValueError: The B{C{lon}} value is missing or B{C{latlon}}
1116 is invalid.
1117 '''
1118 z, B, lat, lon, d, f, name = _to7zBlldfn(latlon, lon, datum,
1119 falsed, name, zone,
1120 strict, ETMError, **cmoff)
1121 lon0 = _cmlon(z) if f else None
1122 x, y, g, k = d.exactTM.forward(lat, lon, lon0=lon0)
1124 return _toXtm8(Etm, z, lat, x, y, B, d, g, k, f,
1125 name, latlon, d.exactTM, Error=ETMError)
1128if __name__ == '__main__': # MCCABE 13
1130 from pygeodesy import fstr, KTransverseMercator, printf
1131 from sys import argv, exit as _exit
1133 # mimick some of I{Karney}'s utility C{TransverseMercatorProj}
1134 _f = _r = _s = _t = False
1135 _as = argv[1:]
1136 while _as and _as[0].startswith(_DASH_):
1137 _a = _as.pop(0)
1138 if len(_a) < 2:
1139 _exit('%s: option %r invalid' % (_usage(*argv), _a))
1140 elif '-forward'.startswith(_a):
1141 _f, _r = True, False
1142 elif '-reverse'.startswith(_a):
1143 _f, _r = False, True
1144 elif '-series'.startswith(_a):
1145 _s, _t = True, False
1146 elif _a == '-t':
1147 _s, _t = False, True
1148 elif '-help'.startswith(_a):
1149 _exit(_usage(argv[0], '[-s | -t]',
1150 '[-f[orward] <lat> <lon>',
1151 '| -r[everse] <easting> <northing>',
1152 '| <lat> <lon>]',
1153 '| -h[elp]'))
1154 else:
1155 _exit('%s: option %r not supported' % (_usage(*argv), _a))
1156 if len(_as) > 1:
1157 f2 = map1(float, *_as[:2])
1158 else:
1159 _exit('%s ...: incomplete' % (_usage(*argv),))
1161 if _s: # -series
1162 tm = KTransverseMercator()
1163 else:
1164 tm = ExactTransverseMercator(extendp=_t)
1166 if _f:
1167 t = tm.forward(*f2)
1168 elif _r:
1169 t = tm.reverse(*f2)
1170 else:
1171 t = tm.forward(*f2)
1172 printf('%s: %s', tm.classname, fstr(t, sep=_SPACE_))
1173 t = tm.reverse(t.easting, t.northing)
1174 printf('%s: %s', tm.classname, fstr(t, sep=_SPACE_))
1177# % python3 -m pygeodesy.etm 33.33 44.44
1178# ExactTransverseMercator: 4276926.114804 4727193.767015 28.375537 1.233325
1179# ExactTransverseMercator: 33.33 44.44 28.375537 1.233325
1181# % python3 -m pygeodesy.etm -s 33.33 44.44
1182# KTransverseMercator: 4276926.114804 4727193.767015 28.375537 1.233325
1183# KTransverseMercator: 33.33 44.44 28.375537 1.233325
1185# % echo 33.33 44.44 | .../bin/TransverseMercatorProj
1186# 4276926.114804 4727193.767015 28.375536563148 1.233325101778
1188# **) MIT License
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1190# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
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1197# Software is furnished to do so, subject to the following conditions:
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1199# The above copyright notice and this permission notice shall be included
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