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
74# from pygeodesy.fsums import Fsum # from .fmath
75from pygeodesy.fmath import cbrt, hypot, hypot1, hypot2, Fsum
76from pygeodesy.interns import _COMMASPACE_, _DASH_, _near_, _SPACE_, \
77 _spherical_
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__ = '24.05.24'
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 C++/doc/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.
135 '''
137 @property_doc_(''' the ETM projection (L{ExactTransverseMercator}).''')
138 def exactTM(self):
139 '''Get the ETM projection (L{ExactTransverseMercator}).
140 '''
141 if self._exactTM is None:
142 self.exactTM = self.datum.exactTM # ExactTransverseMercator(datum=self.datum)
143 return self._exactTM
145 @exactTM.setter # PYCHOK setter!
146 def exactTM(self, exactTM):
147 '''Set the ETM projection (L{ExactTransverseMercator}).
149 @raise ETMError: The B{C{exacTM}}'s datum incompatible
150 with this ETM coordinate's C{datum}.
151 '''
152 _xinstanceof(ExactTransverseMercator, exactTM=exactTM)
154 E = self.datum.ellipsoid
155 if E != exactTM.ellipsoid: # may be None
156 raise ETMError(repr(exactTM), txt=_incompatible(repr(E)))
157 self._exactTM = exactTM
158 self._scale0 = exactTM.k0
160 def parse(self, strETM, **name):
161 '''Parse a string to a similar L{Etm} instance.
163 @arg strETM: The ETM coordinate (C{str}), see function
164 L{parseETM5}.
165 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding
166 this name.
168 @return: The instance (L{Etm}).
170 @raise ETMError: Invalid B{C{strETM}}.
172 @see: Function L{pygeodesy.parseUPS5}, L{pygeodesy.parseUTM5}
173 and L{pygeodesy.parseUTMUPS5}.
174 '''
175 return parseETM5(strETM, datum=self.datum, Etm=self.classof,
176 name=self._name__(name))
178 @deprecated_method
179 def parseETM(self, strETM): # PYCHOK no cover
180 '''DEPRECATED, use method L{Etm.parse}.
181 '''
182 return self.parse(strETM)
184 def toLatLon(self, LatLon=None, unfalse=True, **unused): # PYCHOK expected
185 '''Convert this ETM coordinate to an (ellipsoidal) geodetic point.
187 @kwarg LatLon: Optional, ellipsoidal class to return the geodetic
188 point (C{LatLon}) or C{None}.
189 @kwarg unfalse: Unfalse B{C{easting}} and B{C{northing}} if
190 C{falsed} (C{bool}).
192 @return: This ETM coordinate as (B{C{LatLon}}) or a
193 L{LatLonDatum5Tuple}C{(lat, lon, datum, gamma,
194 scale)} if B{C{LatLon}} is C{None}.
196 @raise ETMError: This ETM coordinate's C{exacTM} and this C{datum}
197 incompatible or no convergence transforming to
198 lat- and longitude.
200 @raise TypeError: Invalid or non-ellipsoidal B{C{LatLon}}.
201 '''
202 if not self._latlon or self._latlon._toLLEB_args != (unfalse, self.exactTM):
203 self._toLLEB(unfalse=unfalse)
204 return self._latlon5(LatLon)
206 def _toLLEB(self, unfalse=True, **unused): # PYCHOK signature
207 '''(INTERNAL) Compute (ellipsoidal) lat- and longitude.
208 '''
209 xTM, d = self.exactTM, self.datum
210 # double check that this and exactTM's ellipsoid match
211 if xTM._E != d.ellipsoid: # PYCHOK no cover
212 t = repr(d.ellipsoid)
213 raise ETMError(repr(xTM._E), txt=_incompatible(t))
215 e, n = self.eastingnorthing2(falsed=not unfalse)
216 lon0 = _cmlon(self.zone) if bool(unfalse) == self.falsed else None
217 lat, lon, g, k = xTM.reverse(e, n, lon0=lon0)
219 ll = _LLEB(lat, lon, datum=d, name=self.name) # utm._LLEB
220 ll._gamma = g
221 ll._scale = k
222 self._latlon5args(ll, _toBand, unfalse, xTM)
224 def toUtm(self): # PYCHOK signature
225 '''Copy this ETM to a UTM coordinate.
227 @return: The UTM coordinate (L{Utm}).
228 '''
229 return self._xcopy2(Utm)
232class ExactTransverseMercator(_NamedBase):
233 '''Pure Python version of Karney's C++ class U{TransverseMercatorExact
234 <https://GeographicLib.SourceForge.io/C++/doc/TransverseMercatorExact_8cpp_source.html>},
235 a numerically exact transverse Mercator projection, further referred to as C{TMExact}.
236 '''
237 _datum = _WGS84 # Datum
238 _E = _EWGS84 # Ellipsoid
239 _extendp = False # use extended domain
240# _iteration = None # ._sigmaInv2 and ._zetaInv2
241 _k0 = _K0_UTM # central scale factor
242 _lat0 = _0_0 # central parallel
243 _lon0 = _0_0 # central meridian
244 _mu = _EWGS84.e2 # 1st eccentricity squared
245 _mv = _EWGS84.e21 # 1 - ._mu
246 _raiser = False # throw Error
247 _sigmaC = None # most recent _sigmaInv04 case C{int}
248 _zetaC = None # most recent _zetaInv04 case C{int}
250 def __init__(self, datum=_WGS84, lon0=0, k0=_K0_UTM, extendp=False, raiser=False, **name):
251 '''New L{ExactTransverseMercator} projection.
253 @kwarg datum: The I{non-spherical} datum or ellipsoid (L{Datum},
254 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
255 @kwarg lon0: Central meridian, default (C{degrees180}).
256 @kwarg k0: Central scale factor (C{float}).
257 @kwarg extendp: Use the I{extended} domain (C{bool}), I{standard} otherwise.
258 @kwarg raiser: If C{True}, throw an L{ETMError} for convergence failures (C{bool}).
259 @kwarg name: Optional C{B{name}=NN} for the projection (C{str}).
261 @raise ETMError: Near-spherical B{C{datum}} or C{ellipsoid} or invalid B{C{lon0}}
262 or B{C{k0}}.
264 @see: U{Constructor TransverseMercatorExact<https://GeographicLib.SourceForge.io/
265 C++/doc/classGeographicLib_1_1TransverseMercatorExact.html>} for more details,
266 especially on B{X{extendp}}.
268 @note: For all 255.5K U{TMcoords.dat<https://Zenodo.org/record/32470>} tests (with
269 C{0 <= lat <= 84} and C{0 <= lon}) the maximum error is C{5.2e-08 .forward}
270 (or 52 nano-meter) easting and northing and C{3.8e-13 .reverse} (or 0.38
271 pico-degrees) lat- and longitude (with Python 3.7.3+, 2.7.16+, PyPy6 3.5.3
272 and PyPy6 2.7.13, all in 64-bit on macOS 10.13.6 High Sierra C{x86_64} and
273 12.2 Monterey C{arm64} and C{"arm64_x86_64"}).
274 '''
275 if extendp:
276 self._extendp = True
277 if name:
278 self.name = name
279 if raiser:
280 self.raiser = True
282 TM = ExactTransverseMercator
283 if datum not in (TM._datum, TM._E, None):
284 self.datum = datum # invokes ._resets
285 if lon0 or lon0 != TM._lon0:
286 self.lon0 = lon0
287 if k0 is not TM._k0:
288 self.k0 = k0
290 @property_doc_(''' the datum (L{Datum}).''')
291 def datum(self):
292 '''Get the datum (L{Datum}) or C{None}.
293 '''
294 return self._datum
296 @datum.setter # PYCHOK setter!
297 def datum(self, datum):
298 '''Set the datum and ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
300 @raise ETMError: Near-spherical B{C{datum}} or C{ellipsoid}.
301 '''
302 d = _ellipsoidal_datum(datum, name=self.name) # raiser=_datum_)
303 self._resets(d)
304 self._datum = d
306 @Property_RO
307 def _e(self):
308 '''(INTERNAL) Get and cache C{_e}.
309 '''
310 return self._E.e
312 @Property_RO
313 def _1_e_90(self): # PYCHOK no cover
314 '''(INTERNAL) Get and cache C{(1 - _e) * 90}.
315 '''
316 return (_1_0 - self._e) * _90_0
318 @property_RO
319 def ellipsoid(self):
320 '''Get the ellipsoid (L{Ellipsoid}).
321 '''
322 return self._E
324 @Property_RO
325 def _e_PI_2(self):
326 '''(INTERNAL) Get and cache C{_e * PI / 2}.
327 '''
328 return self._e * PI_2
330 @Property_RO
331 def _e_PI_4_(self):
332 '''(INTERNAL) Get and cache C{-_e * PI / 4}.
333 '''
334 return -self._e * PI_4
336 @Property_RO
337 def _1_e_PI_2(self):
338 '''(INTERNAL) Get and cache C{(1 - _e) * PI / 2}.
339 '''
340 return (_1_0 - self._e) * PI_2
342 @Property_RO
343 def _1_2e_PI_2(self):
344 '''(INTERNAL) Get and cache C{(1 - 2 * _e) * PI / 2}.
345 '''
346 return (_1_0 - self._e * _2_0) * PI_2
348 @property_RO
349 def equatoradius(self):
350 '''Get the C{ellipsoid}'s equatorial radius, semi-axis (C{meter}).
351 '''
352 return self._E.a
354 a = equatoradius
356 @Property_RO
357 def _e_TAYTOL(self):
358 '''(INTERNAL) Get and cache C{e * TAYTOL}.
359 '''
360 return self._e * _TAYTOL
362 @Property_RO
363 def _Eu(self):
364 '''(INTERNAL) Get and cache C{Elliptic(_mu)}.
365 '''
366 return Elliptic(self._mu)
368 @Property_RO
369 def _Eu_cE(self):
370 '''(INTERNAL) Get and cache C{_Eu.cE}.
371 '''
372 return self._Eu.cE
374 def _Eu_2cE_(self, xi):
375 '''(INTERNAL) Return C{_Eu.cE * 2 - B{xi}}.
376 '''
377 return self._Eu_cE * _2_0 - xi
379 @Property_RO
380 def _Eu_cE_4(self):
381 '''(INTERNAL) Get and cache C{_Eu.cE / 4}.
382 '''
383 return self._Eu_cE / _4_0
385 @Property_RO
386 def _Eu_cK(self):
387 '''(INTERNAL) Get and cache C{_Eu.cK}.
388 '''
389 return self._Eu.cK
391 @Property_RO
392 def _Eu_cK_cE(self):
393 '''(INTERNAL) Get and cache C{_Eu.cK / _Eu.cE}.
394 '''
395 return self._Eu_cK / self._Eu_cE
397 @Property_RO
398 def _Eu_2cK_PI(self):
399 '''(INTERNAL) Get and cache C{_Eu.cK * 2 / PI}.
400 '''
401 return self._Eu_cK / PI_2
403 @Property_RO
404 def _Ev(self):
405 '''(INTERNAL) Get and cache C{Elliptic(_mv)}.
406 '''
407 return Elliptic(self._mv)
409 @Property_RO
410 def _Ev_cK(self):
411 '''(INTERNAL) Get and cache C{_Ev.cK}.
412 '''
413 return self._Ev.cK
415 @Property_RO
416 def _Ev_cKE(self):
417 '''(INTERNAL) Get and cache C{_Ev.cKE}.
418 '''
419 return self._Ev.cKE
421 @Property_RO
422 def _Ev_3cKE_4(self):
423 '''(INTERNAL) Get and cache C{_Ev.cKE * 3 / 4}.
424 '''
425 return self._Ev_cKE * 0.75 # _0_75
427 @Property_RO
428 def _Ev_5cKE_4(self):
429 '''(INTERNAL) Get and cache C{_Ev.cKE * 5 / 4}.
430 '''
431 return self._Ev_cKE * 1.25 # _1_25
433 @Property_RO
434 def extendp(self):
435 '''Get the domain (C{bool}), I{extended} or I{standard}.
436 '''
437 return self._extendp
439 @property_RO
440 def flattening(self):
441 '''Get the C{ellipsoid}'s flattening (C{scalar}).
442 '''
443 return self._E.f
445 f = flattening
447 def forward(self, lat, lon, lon0=None, **name): # MCCABE 13
448 '''Forward projection, from geographic to transverse Mercator.
450 @arg lat: Latitude of point (C{degrees}).
451 @arg lon: Longitude of point (C{degrees}).
452 @kwarg lon0: Central meridian (C{degrees180}), overriding
453 the default if not C{None}.
454 @kwarg name: Optional C{B{name}=NN} (C{str}).
456 @return: L{Forward4Tuple}C{(easting, northing, gamma, scale)}.
458 @see: C{void TMExact::Forward(real lon0, real lat, real lon,
459 real &x, real &y,
460 real &gamma, real &k)}.
462 @raise ETMError: No convergence, thrown iff property
463 C{B{raiser}=True}.
464 '''
465 lat = _fix90(lat - self._lat0)
466 lon, _ = _diff182((self.lon0 if lon0 is None else lon0), lon)
467 if self.extendp:
468 backside = _lat = _lon = False
469 else: # enforce the parity
470 lat, _lat = _unsigned2(lat)
471 lon, _lon = _unsigned2(lon)
472 backside = lon > 90
473 if backside: # PYCHOK no cover
474 lon = _loneg(lon)
475 if lat == 0:
476 _lat = True
478 # u, v = coordinates for the Thompson TM, Lee 54
479 if lat == 90: # isnear90(lat)
480 u = self._Eu_cK
481 v = self._iteration = self._zetaC = 0
482 elif lat == 0 and lon == self._1_e_90: # PYCHOK no cover
483 u = self._iteration = self._zetaC = 0
484 v = self._Ev_cK
485 else: # tau = tan(phi), taup = sinh(psi)
486 tau, lam = _tand(lat), radians(lon)
487 u, v = self._zetaInv2(self._E.es_taupf(tau), lam)
489 sncndn6 = self._sncndn6(u, v)
490 y, x, _ = self._sigma3(v, *sncndn6)
491 g, k = (lon, self.k0) if isnear90(lat) else \
492 self._zetaScaled(sncndn6, ll=False)
494 if backside:
495 y, g = self._Eu_2cE_(y), _loneg(g)
496 y *= self._k0_a
497 x *= self._k0_a
498 if _lat:
499 y, g = neg_(y, g)
500 if _lon:
501 x, g = neg_(x, g)
502 return Forward4Tuple(x, y, g, k, iteration=self._iteration,
503 name=self._name__(name))
505 def _Inv03(self, psi, dlam, _3_mv_e): # (xi, deta, _3_mv)
506 '''(INTERNAL) Partial C{_zetaInv04} or C{_sigmaInv04}, Case 2
507 '''
508 # atan2(dlam-psi, psi+dlam) + 45d gives arg(zeta - zeta0) in
509 # range [-135, 225). Subtracting 180 (multiplier is negative)
510 # makes range [-315, 45). Multiplying by 1/3 (for cube root)
511 # gives range [-105, 15). In particular the range [-90, 180]
512 # in zeta space maps to [-90, 0] in w space as required.
513 a = atan2(dlam - psi, psi + dlam) / _3_0 - PI_4
514 s, c = sincos2(a)
515 h = hypot(psi, dlam)
516 r = cbrt(h * _3_mv_e)
517 u = r * c
518 v = r * s + self._Ev_cK
519 # Error using this guess is about 0.068 * rad^(5/3)
520 return u, v, h
522 @property_RO
523 def iteration(self):
524 '''Get the most recent C{ExactTransverseMercator.forward}
525 or C{ExactTransverseMercator.reverse} iteration number
526 (C{int}) or C{None} if not available/applicable.
527 '''
528 return self._iteration
530 @property_doc_(''' the central scale factor (C{float}).''')
531 def k0(self):
532 '''Get the central scale factor (C{float}), aka I{C{scale0}}.
533 '''
534 return self._k0 # aka scale0
536 @k0.setter # PYCHOK setter!
537 def k0(self, k0):
538 '''Set the central scale factor (C{float}), aka I{C{scale0}}.
540 @raise ETMError: Invalid B{C{k0}}.
541 '''
542 k0 = Scalar_(k0=k0, Error=ETMError, low=_TOL_10, high=_1_0)
543 if self._k0 != k0:
544 ExactTransverseMercator._k0_a._update(self) # redo ._k0_a
545 self._k0 = k0
547 @Property_RO
548 def _k0_a(self):
549 '''(INTERNAL) Get and cache C{k0 * equatoradius}.
550 '''
551 return self.k0 * self.equatoradius
553 @property_doc_(''' the central meridian (C{degrees180}).''')
554 def lon0(self):
555 '''Get the central meridian (C{degrees180}).
556 '''
557 return self._lon0
559 @lon0.setter # PYCHOK setter!
560 def lon0(self, lon0):
561 '''Set the central meridian (C{degrees180}).
563 @raise ETMError: Invalid B{C{lon0}}.
564 '''
565 self._lon0 = _norm180(Degrees(lon0=lon0, Error=ETMError))
567 @deprecated_property_RO
568 def majoradius(self): # PYCHOK no cover
569 '''DEPRECATED, use property C{equatoradius}.'''
570 return self.equatoradius
572 @Property_RO
573 def _1_mu_2(self):
574 '''(INTERNAL) Get and cache C{_mu / 2 + 1}.
575 '''
576 return self._mu * _0_5 + _1_0
578 @Property_RO
579 def _3_mv(self):
580 '''(INTERNAL) Get and cache C{3 / _mv}.
581 '''
582 return _3_0 / self._mv
584 @Property_RO
585 def _3_mv_e(self):
586 '''(INTERNAL) Get and cache C{3 / (_mv * _e)}.
587 '''
588 return _3_0 / (self._mv * self._e)
590 def _Newton2(self, taup, lam, u, v, C, *psi): # or (xi, eta, u, v)
591 '''(INTERNAL) Invert C{_zetaInv2} or C{_sigmaInv2} using Newton's method.
593 @return: 2-Tuple C{(u, v)}.
595 @raise ETMError: No convergence.
596 '''
597 sca1, tol2 = _1_0, _TOL_10
598 if psi: # _zetaInv2
599 sca1 = sca1 / hypot1(taup) # /= chokes PyChecker
600 tol2 = tol2 / max(psi[0], _1_0)**2
602 _zeta3 = self._zeta3
603 _zetaDwd2 = self._zetaDwd2
604 else: # _sigmaInv2
605 _zeta3 = self._sigma3
606 _zetaDwd2 = self._sigmaDwd2
608 d2, r = tol2, self.raiser
609 _U_2 = Fsum(u).fsum2f_
610 _V_2 = Fsum(v).fsum2f_
611 # min iterations 2, max 6 or 7, mean 3.9 or 4.0
612 _hy2 = hypot2
613 for i in range(1, _TRIPS): # GEOGRAPHICLIB_PANIC
614 sncndn6 = self._sncndn6(u, v)
615 du, dv = _zetaDwd2(*sncndn6)
616 T, L, _ = _zeta3(v, *sncndn6)
617 T = (taup - T) * sca1
618 L -= lam
619 u, dU = _U_2(T * du, L * dv)
620 v, dV = _V_2(T * dv, -L * du)
621 if d2 < tol2:
622 r = False
623 break
624 d2 = _hy2(dU, dV)
626 self._iteration = i
627 if r: # PYCHOK no cover
628 n = callername(up=2, underOK=True)
629 t = unstr(n, taup, lam, u, v, C=C)
630 raise ETMError(Fmt.no_convergence(d2, tol2), txt=t)
631 return u, v
633 @property_doc_(''' raise an L{ETMError} for convergence failures (C{bool}).''')
634 def raiser(self):
635 '''Get the error setting (C{bool}).
636 '''
637 return self._raiser
639 @raiser.setter # PYCHOK setter!
640 def raiser(self, raiser):
641 '''Set the error setting (C{bool}), if C{True} throw an L{ETMError}
642 for convergence failures.
643 '''
644 self._raiser = bool(raiser)
646 def reset(self, lat0, lon0):
647 '''Set the central parallel and meridian.
649 @arg lat0: Latitude of the central parallel (C{degrees90}).
650 @arg lon0: Longitude of the central parallel (C{degrees180}).
652 @return: 2-Tuple C{(lat0, lon0)} of the previous central
653 parallel and meridian.
655 @raise ETMError: Invalid B{C{lat0}} or B{C{lon0}}.
656 '''
657 t = self._lat0, self.lon0
658 self._lat0 = _fix90(Degrees(lat0=lat0, Error=ETMError))
659 self. lon0 = lon0
660 return t
662 def _resets(self, datum):
663 '''(INTERNAL) Set the ellipsoid and elliptic moduli.
665 @arg datum: Ellipsoidal datum (C{Datum}).
667 @raise ETMError: Near-spherical B{C{datum}} or C{ellipsoid}.
668 '''
669 E = datum.ellipsoid
670 mu = E.e2 # .eccentricity1st2
671 mv = E.e21 # _1_0 - mu
672 if isnear0(E.e) or isnear0(mu, eps0=EPS02) \
673 or isnear0(mv, eps0=EPS02): # or sqrt(mu) != E.e
674 raise ETMError(ellipsoid=E, txt=_near_(_spherical_))
676 if self._datum or self._E:
677 _i = ExactTransverseMercator.iteration._uname
678 _update_all(self, _i, '_sigmaC', '_zetaC') # _under
680 self._E = E
681 self._mu = mu
682 self._mv = mv
684 def reverse(self, x, y, lon0=None, **name):
685 '''Reverse projection, from Transverse Mercator to geographic.
687 @arg x: Easting of point (C{meters}).
688 @arg y: Northing of point (C{meters}).
689 @kwarg lon0: Optional central meridian (C{degrees180}),
690 overriding the default (C{iff not None}).
691 @kwarg name: Optional C{B{name}=NN} (C{str}).
693 @return: L{Reverse4Tuple}C{(lat, lon, gamma, scale)}.
695 @see: C{void TMExact::Reverse(real lon0, real x, real y,
696 real &lat, real &lon,
697 real &gamma, real &k)}
699 @raise ETMError: No convergence, thrown iff property
700 C{B{raiser}=True}.
701 '''
702 # undoes the steps in .forward.
703 xi = y / self._k0_a
704 eta = x / self._k0_a
705 if self.extendp:
706 backside = _lat = _lon = False
707 else: # enforce the parity
708 eta, _lon = _unsigned2(eta)
709 xi, _lat = _unsigned2(xi)
710 backside = xi > self._Eu_cE
711 if backside: # PYCHOK no cover
712 xi = self._Eu_2cE_(xi)
714 # u, v = coordinates for the Thompson TM, Lee 54
715 if xi or eta != self._Ev_cKE:
716 u, v = self._sigmaInv2(xi, eta)
717 else: # PYCHOK no cover
718 u = self._iteration = self._sigmaC = 0
719 v = self._Ev_cK
721 if v or u != self._Eu_cK:
722 g, k, lat, lon = self._zetaScaled(self._sncndn6(u, v))
723 else: # PYCHOK no cover
724 g, k, lat, lon = _0_0, self.k0, _90_0, _0_0
726 if backside: # PYCHOK no cover
727 lon, g = _loneg(lon), _loneg(g)
728 if _lat:
729 lat, g = neg_(lat, g)
730 if _lon:
731 lon, g = neg_(lon, g)
732 lat += self._lat0
733 lon += self._lon0 if lon0 is None else _norm180(lon0)
734 return Reverse4Tuple(lat, _norm180(lon), g, k, # _fix90(lat)
735 iteration=self._iteration,
736 name=self._name__(name))
738 def _scaled2(self, tau, d2, snu, cnu, dnu, snv, cnv, dnv):
739 '''(INTERNAL) C{scaled}.
741 @note: Argument B{C{d2}} is C{_mu * cnu**2 + _mv * cnv**2}
742 from C{._zeta3}.
744 @return: 2-Tuple C{(convergence, scale)}.
746 @see: C{void TMExact::Scale(real tau, real /*lam*/,
747 real snu, real cnu, real dnu,
748 real snv, real cnv, real dnv,
749 real &gamma, real &k)}.
750 '''
751 mu, mv = self._mu, self._mv
752 cnudnv = cnu * dnv
753 # Lee 55.12 -- negated for our sign convention. g gives
754 # the bearing (clockwise from true north) of grid north
755 g = atan2d(mv * cnv * snv * snu, cnudnv * dnu)
756 # Lee 55.13 with nu given by Lee 9.1 -- in sqrt change
757 # the numerator from (1 - snu^2 * dnv^2) to (_mv * snv^2
758 # + cnu^2 * dnv^2) to maintain accuracy near phi = 90
759 # and change the denomintor from (dnu^2 + dnv^2 - 1) to
760 # (_mu * cnu^2 + _mv * cnv^2) to maintain accuracy near
761 # phi = 0, lam = 90 * (1 - e). Similarly rewrite sqrt in
762 # 9.1 as _mv + _mu * c^2 instead of 1 - _mu * sin(phi)^2
763 if d2 > 0:
764 # originally: sec2 = 1 + tau**2 # sec(phi)^2
765 # d2 = (mu * cnu**2 + mv * cnv**2)
766 # q2 = (mv * snv**2 + cnudnv**2) / d2
767 # k = sqrt(mv + mu / sec2) * sqrt(sec2) * sqrt(q2)
768 # = sqrt(mv * sec2 + mu) * sqrt(q2)
769 # = sqrt(mv + mv * tau**2 + mu) * sqrt(q2)
770 k, q2 = _0_0, (mv * snv**2 + cnudnv**2)
771 if q2 > 0:
772 k2 = (tau**2 + _1_0) * mv + mu
773 if k2 > 0:
774 k = sqrt(k2) * sqrt(q2 / d2) * self.k0
775 else:
776 k = _OVERFLOW
777 return g, k
779 def _sigma3(self, v, snu, cnu, dnu, snv, cnv, dnv):
780 '''(INTERNAL) C{sigma}.
782 @return: 3-Tuple C{(xi, eta, d2)}.
784 @see: C{void TMExact::sigma(real /*u*/, real snu, real cnu, real dnu,
785 real v, real snv, real cnv, real dnv,
786 real &xi, real &eta)}.
788 @raise ETMError: No convergence.
789 '''
790 mu = self._mu * cnu
791 mv = self._mv * cnv
792 # Lee 55.4 writing
793 # dnu^2 + dnv^2 - 1 = _mu * cnu^2 + _mv * cnv^2
794 d2 = cnu * mu + cnv * mv
795 mu *= snu * dnu
796 mv *= snv * dnv
797 if d2 > 0: # /= chokes PyChecker
798 mu = mu / d2
799 mv = mv / d2
800 else:
801 mu, mv = map1(_overflow, mu, mv)
802 xi = self._Eu.fE(snu, cnu, dnu) - mu
803 v -= self._Ev.fE(snv, cnv, dnv) - mv
804 return xi, v, d2
806 def _sigmaDwd2(self, snu, cnu, dnu, snv, cnv, dnv):
807 '''(INTERNAL) C{sigmaDwd}.
809 @return: 2-Tuple C{(du, dv)}.
811 @see: C{void TMExact::dwdsigma(real /*u*/, real snu, real cnu, real dnu,
812 real /*v*/, real snv, real cnv, real dnv,
813 real &du, real &dv)}.
814 '''
815 mu = self._mu
816 snuv = snu * snv
817 # Reciprocal of 55.9: dw / ds = dn(w)^2/_mv,
818 # expanding complex dn(w) using A+S 16.21.4
819 d = (cnv**2 + snuv**2 * mu)**2 * self._mv
820 r = cnv * dnu * dnv
821 i = cnu * snuv * mu
822 du = (r**2 - i**2) / d # (r + i) * (r - i) / d
823 dv = neg(r * i * _2_0 / d)
824 return du, dv
826 def _sigmaInv2(self, xi, eta):
827 '''(INTERNAL) Invert C{sigma} using Newton's method.
829 @return: 2-Tuple C{(u, v)}.
831 @see: C{void TMExact::sigmainv(real xi, real eta,
832 real &u, real &v)}.
834 @raise ETMError: No convergence.
835 '''
836 u, v, t, self._sigmaC = self._sigmaInv04(xi, eta)
837 if not t:
838 u, v = self._Newton2(xi, eta, u, v, self._sigmaC)
839 return u, v
841 def _sigmaInv04(self, xi, eta):
842 '''(INTERNAL) Starting point for C{sigmaInv}.
844 @return: 4-Tuple C{(u, v, trip, Case)}.
846 @see: C{bool TMExact::sigmainv0(real xi, real eta,
847 real &u, real &v)}.
848 '''
849 t = False
850 d = eta - self._Ev_cKE
851 if eta > self._Ev_5cKE_4 or (xi < d and xi < -self._Eu_cE_4):
852 # sigma as a simple pole at
853 # w = w0 = Eu.K() + i * Ev.K()
854 # and sigma is approximated by
855 # sigma = (Eu.E() + i * Ev.KE()) + 1 / (w - w0)
856 u, v = _norm2(xi - self._Eu_cE, -d)
857 u += self._Eu_cK
858 v += self._Ev_cK
859 C = 1
861 elif (eta > self._Ev_3cKE_4 and xi < self._Eu_cE_4) or d > 0:
862 # At w = w0 = i * Ev.K(), we have
863 # sigma = sigma0 = i * Ev.KE()
864 # sigma' = sigma'' = 0
865 # including the next term in the Taylor series gives:
866 # sigma = sigma0 - _mv / 3 * (w - w0)^3
867 # When inverting this, we map arg(w - w0) = [-pi/2, -pi/6]
868 # to arg(sigma - sigma0) = [-pi/2, pi/2] mapping arg =
869 # [-pi/2, -pi/6] to [-pi/2, pi/2]
870 u, v, h = self._Inv03(xi, d, self._3_mv)
871 t = h < _TAYTOL2
872 C = 2
874 else: # use w = sigma * Eu.K/Eu.E (correct in limit _e -> 0)
875 u = v = self._Eu_cK_cE
876 u *= xi
877 v *= eta
878 C = 3
880 return u, v, t, C
882 def _sncndn6(self, u, v):
883 '''(INTERNAL) Get 6-tuple C{(snu, cnu, dnu, snv, cnv, dnv)}.
884 '''
885 # snu, cnu, dnu = self._Eu.sncndn(u)
886 # snv, cnv, dnv = self._Ev.sncndn(v)
887 return self._Eu.sncndn(u) + self._Ev.sncndn(v)
889 def toStr(self, joined=_COMMASPACE_, **kwds): # PYCHOK signature
890 '''Return a C{str} representation.
892 @kwarg joined: Separator to join the attribute strings
893 (C{str} or C{None} or C{NN} for non-joined).
894 @kwarg kwds: Optional, overriding keyword arguments.
895 '''
896 d = dict(datum=self.datum.name, lon0=self.lon0,
897 k0=self.k0, extendp=self.extendp)
898 if self.name:
899 d.update(name=self.name)
900 t = pairs(d, **kwds)
901 return joined.join(t) if joined else t
903 def _zeta3(self, unused, snu, cnu, dnu, snv, cnv, dnv): # _sigma3 signature
904 '''(INTERNAL) C{zeta}.
906 @return: 3-Tuple C{(taup, lambda, d2)}.
908 @see: C{void TMExact::zeta(real /*u*/, real snu, real cnu, real dnu,
909 real /*v*/, real snv, real cnv, real dnv,
910 real &taup, real &lam)}
911 '''
912 e, cnu2, mv = self._e, cnu**2, self._mv
913 # Overflow value like atan(overflow) = pi/2
914 t1 = t2 = _overflow(snu)
915 # Lee 54.17 but write
916 # atanh(snu * dnv) = asinh(snu * dnv / sqrt(cnu^2 + _mv * snu^2 * snv^2))
917 # atanh(_e * snu / dnv) = asinh(_e * snu / sqrt(_mu * cnu^2 + _mv * cnv^2))
918 d1 = cnu2 + mv * (snu * snv)**2
919 if d1 > EPS02: # _EPSmin
920 t1 = snu * dnv / sqrt(d1)
921 else:
922 d1 = 0
923 d2 = self._mu * cnu2 + mv * cnv**2
924 if d2 > EPS02: # _EPSmin
925 t2 = sinh(e * asinh(e * snu / sqrt(d2)))
926 else:
927 d2 = 0
928 # psi = asinh(t1) - asinh(t2)
929 # taup = sinh(psi)
930 taup = t1 * hypot1(t2) - t2 * hypot1(t1)
931 lam = (atan2(dnu * snv, cnu * cnv) -
932 atan2(cnu * snv * e, dnu * cnv) * e) if d1 and d2 else _0_0
933 return taup, lam, d2
935 def _zetaDwd2(self, snu, cnu, dnu, snv, cnv, dnv):
936 '''(INTERNAL) C{zetaDwd}.
938 @return: 2-Tuple C{(du, dv)}.
940 @see: C{void TMExact::dwdzeta(real /*u*/, real snu, real cnu, real dnu,
941 real /*v*/, real snv, real cnv, real dnv,
942 real &du, real &dv)}.
943 '''
944 cnu2 = cnu**2 * self._mu
945 cnv2 = cnv**2
946 dnuv = dnu * dnv
947 dnuv2 = dnuv**2
948 snuv = snu * snv
949 snuv2 = snuv**2 * self._mu
950 # Lee 54.21 but write (see A+S 16.21.4)
951 # (1 - dnu^2 * snv^2) = (cnv^2 + _mu * snu^2 * snv^2)
952 d = self._mv * (cnv2 + snuv2)**2 # max(d, EPS02)?
953 du = cnu * dnuv * (cnv2 - snuv2) / d
954 dv = cnv * snuv * (cnu2 + dnuv2) / d
955 return du, neg(dv)
957 def _zetaInv2(self, taup, lam):
958 '''(INTERNAL) Invert C{zeta} using Newton's method.
960 @return: 2-Tuple C{(u, v)}.
962 @see: C{void TMExact::zetainv(real taup, real lam,
963 real &u, real &v)}.
965 @raise ETMError: No convergence.
966 '''
967 psi = asinh(taup)
968 u, v, t, self._zetaC = self._zetaInv04(psi, lam)
969 if not t:
970 u, v = self._Newton2(taup, lam, u, v, self._zetaC, psi)
971 return u, v
973 def _zetaInv04(self, psi, lam):
974 '''(INTERNAL) Starting point for C{zetaInv}.
976 @return: 4-Tuple C{(u, v, trip, Case)}.
978 @see: C{bool TMExact::zetainv0(real psi, real lam, # radians
979 real &u, real &v)}.
980 '''
981 if lam > self._1_2e_PI_2:
982 d = lam - self._1_e_PI_2
983 if psi < d and psi < self._e_PI_4_: # PYCHOK no cover
984 # N.B. this branch is normally *not* taken because psi < 0
985 # is converted psi > 0 by .forward. There's a log singularity
986 # at w = w0 = Eu.K() + i * Ev.K(), corresponding to the south
987 # pole, where we have, approximately
988 # psi = _e + i * pi/2 - _e * atanh(cos(i * (w - w0)/(1 + _mu/2)))
989 # Inverting this gives:
990 e = self._e # eccentricity
991 s, c = sincos2((PI_2 - lam) / e)
992 h, r = sinh(_1_0 - psi / e), self._1_mu_2
993 u = self._Eu_cK - r * asinh(s / hypot(c, h))
994 v = self._Ev_cK - r * atan2(c, h)
995 return u, v, False, 1
997 elif psi < self._e_PI_2:
998 # At w = w0 = i * Ev.K(), we have
999 # zeta = zeta0 = i * (1 - _e) * pi/2
1000 # zeta' = zeta'' = 0
1001 # including the next term in the Taylor series gives:
1002 # zeta = zeta0 - (_mv * _e) / 3 * (w - w0)^3
1003 # When inverting this, we map arg(w - w0) = [-90, 0]
1004 # to arg(zeta - zeta0) = [-90, 180]
1005 u, v, h = self._Inv03(psi, d, self._3_mv_e)
1006 return u, v, (h < self._e_TAYTOL), 2
1008 # Use spherical TM, Lee 12.6 -- writing C{atanh(sin(lam) /
1009 # cosh(psi)) = asinh(sin(lam) / hypot(cos(lam), sinh(psi)))}.
1010 # This takes care of the log singularity at C{zeta = Eu.K()},
1011 # corresponding to the north pole.
1012 s, c = sincos2(lam)
1013 h, r = sinh(psi), self._Eu_2cK_PI
1014 # But scale to put 90, 0 on the right place
1015 u = r * atan2(h, c)
1016 v = r * asinh(s / hypot(h, c))
1017 return u, v, False, 3
1019 def _zetaScaled(self, sncndn6, ll=True):
1020 '''(INTERNAL) Recompute (T, L) from (u, v) to improve accuracy of Scale.
1022 @arg sncndn6: 6-Tuple C{(snu, cnu, dnu, snv, cnv, dnv)}.
1024 @return: 2-Tuple C{(g, k)} if not C{B{ll}} else
1025 4-tuple C{(g, k, lat, lon)}.
1026 '''
1027 t, lam, d2 = self._zeta3(None, *sncndn6)
1028 tau = self._E.es_tauf(t)
1029 g_k = self._scaled2(tau, d2, *sncndn6)
1030 if ll:
1031 g_k += atan1d(tau), degrees(lam)
1032 return g_k # or (g, k, lat, lon)
1035def parseETM5(strUTM, datum=_WGS84, Etm=Etm, falsed=True, **name):
1036 '''Parse a string representing a UTM coordinate, consisting
1037 of C{"zone[band] hemisphere easting northing"}.
1039 @arg strUTM: A UTM coordinate (C{str}).
1040 @kwarg datum: Optional datum to use (L{Datum}, L{Ellipsoid},
1041 L{Ellipsoid2} or L{a_f2Tuple}).
1042 @kwarg Etm: Optional class to return the UTM coordinate
1043 (L{Etm}) or C{None}.
1044 @kwarg falsed: Both easting and northing are C{falsed} (C{bool}).
1045 @kwarg name: Optional B{C{Etm}} C{B{name}=NN} (C{str}).
1047 @return: The UTM coordinate (B{C{Etm}}) or if B{C{Etm}} is
1048 C{None}, a L{UtmUps5Tuple}C{(zone, hemipole, easting,
1049 northing, band)}. The C{hemipole} is the hemisphere
1050 C{'N'|'S'}.
1052 @raise ETMError: Invalid B{C{strUTM}}.
1054 @raise TypeError: Invalid or near-spherical B{C{datum}}.
1055 '''
1056 r = _parseUTM5(strUTM, datum, Etm, falsed, Error=ETMError, **name)
1057 return r
1060def toEtm8(latlon, lon=None, datum=None, Etm=Etm, falsed=True,
1061 strict=True, zone=None,
1062 **name_cmoff):
1063 '''Convert a geodetic lat-/longitude to an ETM coordinate.
1065 @arg latlon: Latitude (C{degrees}) or an (ellipsoidal)
1066 geodetic C{LatLon} instance.
1067 @kwarg lon: Optional longitude (C{degrees}), required
1068 if B{C{latlon}} is in C{degrees}.
1069 @kwarg datum: Optional datum for the ETM coordinate,
1070 overriding B{C{latlon}}'s datum (L{Datum},
1071 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
1072 @kwarg Etm: Optional class to return the ETM coordinate
1073 (L{Etm}) or C{None}.
1074 @kwarg falsed: False both easting and northing (C{bool}).
1075 @kwarg strict: Restrict B{C{lat}} to UTM ranges (C{bool}).
1076 @kwarg zone: Optional UTM zone to enforce (C{int} or C{str}).
1077 @kwarg name_cmoff: Optional B{C{Etm}} C{B{name}=NN} (C{str})
1078 and DEPRECATED C{B{cmoff}=True} to offset longitude
1079 from the zone's central meridian (C{bool}), instead
1080 use C{B{falsed}=True}.
1082 @return: The ETM coordinate as an B{C{Etm}} instance or a
1083 L{UtmUps8Tuple}C{(zone, hemipole, easting, northing,
1084 band, datum, gamma, scale)} if B{C{Etm}} is C{None}
1085 or not B{C{falsed}}. The C{hemipole} is the C{'N'|'S'}
1086 hemisphere.
1088 @raise ETMError: No convergence transforming to ETM easting
1089 and northing.
1091 @raise ETMError: Invalid B{C{zone}} or near-spherical or
1092 incompatible B{C{datum}} or C{ellipsoid}.
1094 @raise RangeError: If B{C{lat}} outside the valid UTM bands or
1095 if B{C{lat}} or B{C{lon}} outside the valid
1096 range and L{pygeodesy.rangerrors} set to C{True}.
1098 @raise TypeError: Invalid or near-spherical B{C{datum}} or
1099 B{C{latlon}} not ellipsoidal.
1101 @raise ValueError: The B{C{lon}} value is missing or B{C{latlon}}
1102 is invalid.
1103 '''
1104 z, B, lat, lon, d, f, n = _to7zBlldfn(latlon, lon, datum,
1105 falsed, zone, strict,
1106 ETMError, **name_cmoff)
1107 lon0 = _cmlon(z) if f else None
1108 x, y, g, k = d.exactTM.forward(lat, lon, lon0=lon0)
1110 return _toXtm8(Etm, z, lat, x, y, B, d, g, k, f,
1111 n, latlon, d.exactTM, Error=ETMError)
1114if __name__ == '__main__': # MCCABE 13
1116 from pygeodesy import fstr, KTransverseMercator, printf
1117 from pygeodesy.internals import _usage
1118 from sys import argv, exit as _exit
1120 # mimick some of I{Karney}'s utility C{TransverseMercatorProj}
1121 _f = _r = _s = _t = False
1122 _p = -6
1123 _as = argv[1:]
1124 while _as and _as[0].startswith(_DASH_):
1125 _a = _as.pop(0)
1126 if len(_a) < 2:
1127 _exit('%s: option %r invalid' % (_usage(*argv), _a))
1128 elif '-forward'.startswith(_a):
1129 _f, _r = True, False
1130 elif '-reverse'.startswith(_a):
1131 _f, _r = False, True
1132 elif '-precision'.startswith(_a):
1133 _p = int(_as.pop(0))
1134 elif '-series'.startswith(_a):
1135 _s, _t = True, False
1136 elif _a == '-t':
1137 _s, _t = False, True
1138 elif '-help'.startswith(_a):
1139 _exit(_usage(argv[0], '[-s | -t ]',
1140 '[-p[recision] <ndigits>',
1141 '[-f[orward] <lat> <lon>',
1142 '|-r[everse] <easting> <northing>',
1143 '|<lat> <lon>]',
1144 '|-h[elp]'))
1145 else:
1146 _exit('%s: option %r not supported' % (_usage(*argv), _a))
1147 if len(_as) > 1:
1148 f2 = map1(float, *_as[:2])
1149 else:
1150 _exit('%s ...: incomplete' % (_usage(*argv),))
1152 if _s: # -series
1153 tm = KTransverseMercator()
1154 else:
1155 tm = ExactTransverseMercator(extendp=_t)
1157 if _f:
1158 t = tm.forward(*f2)
1159 elif _r:
1160 t = tm.reverse(*f2)
1161 else:
1162 t = tm.forward(*f2)
1163 printf('%s: %s', tm.classname, fstr(t, prec=_p, sep=_SPACE_))
1164 t = tm.reverse(t.easting, t.northing)
1165 printf('%s: %s', tm.classname, fstr(t, prec=_p, sep=_SPACE_))
1168# % python3 -m pygeodesy.etm -p 12 33.33 44.44
1169# ExactTransverseMercator: 4276926.11480390653 4727193.767015309073 28.375536563148 1.233325101778
1170# ExactTransverseMercator: 33.33 44.44 28.375536563148 1.233325101778
1172# % python3 -m pygeodesy.etm -s -p 12 33.33 44.44
1173# KTransverseMercator: 4276926.114803904667 4727193.767015310004 28.375536563148 1.233325101778
1174# KTransverseMercator: 33.33 44.44 28.375536563148 1.233325101778
1176# % echo 33.33 44.44 | .../bin/TransverseMercatorProj
1177# 4276926.114804 4727193.767015 28.375536563148 1.233325101778
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