Coverage for pygeodesy/trf.py: 95%
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2# -*- coding: utf-8 -*-
4u'''I{Veness}' Terrestrial Reference Frames (TRF).
6Classes L{RefFrame}, registry L{RefFrames} and L{TRFError}.
8Transcoded from I{Chris Veness'} (C) 2006-2024 JavaScript originals U{latlon-ellipsoidal-referenceframe.js
9<https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js>} and
10U{latlon-ellipsoidal-referenceframe-txparams.js
11<https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe-txparams.js>}.
13Following is a copy of the comments in I{Veness}' U{latlon-ellipsoidal-referenceframe.js
14<https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js>}.
16Modern geodetic reference frames: a latitude/longitude point defines a geographic location on,
17above or below the earth’s surface, measured in degrees from the equator and the U{International
18Reference Meridian<https://WikiPedia.org/wiki/IERS_Reference_Meridian>} (IRM) and metres above
19the ellipsoid within a given I{Terrestrial Reference Frame} at a given I{epoch}.
21This is scratching the surface of complexities involved in high precision geodesy, but may
22be of interest and/or value to those with less demanding requirements. More information U{here
23<https://www.Movable-Type.co.UK/scripts/geodesy-library.html>} and U{here
24<https://www.Movable-Type.co.UK/scripts/geodesy-library.html#latlon-ellipsoidal-referenceframe>}.
26Note that I{ITRF solutions} do not directly use an ellipsoid, but are specified by Cartesian
27coordinates. The GRS80 ellipsoid is recommended for transformations to geographical coordinates.
29Note WGS84(G730/G873/G1150) are coincident with ITRF at 10-centimetre level, see also U{here
30<ftp://ITRF.ENSG.IGN.Fr/pub/itrf/WGS84.TXT>}. WGS84(G1674) and ITRF20014 / ITRF2008 I{"are likely
31to agree at the centimeter level"}, see also U{QPS/Qinsy<https://Confluence.QPS.NL/qinsy/
32en/how-to-deal-with-etrs89-datum-and-time-dependent-transformation-parameters-45353274.html>}.
34@var RefFrames.ETRF2000: RefFrame(name='ETRF2000', epoch=2005, datum=Datums.GRS80) .Xforms=(0, -14)
35@var RefFrames.ETRF2005: RefFrame(name='ETRF2005', epoch=2005, datum=Datums.GRS80) .Xforms=(0, -1)
36@var RefFrames.ETRF2008: RefFrame(name='ETRF2008', epoch=2008, datum=Datums.GRS80) .Xforms=(0, 0)
37@var RefFrames.ETRF2014: RefFrame(name='ETRF2014', epoch=2014, datum=Datums.GRS80) .Xforms=(0, -14)
38@var RefFrames.ETRF2020: RefFrame(name='ETRF2020', epoch=2020, datum=Datums.GRS80) .Xforms=(0, -14)
39@var RefFrames.ETRF88: RefFrame(name='ETRF88', epoch=1988, datum=Datums.GRS80) .Xforms=(0, 0)
40@var RefFrames.ETRF89: RefFrame(name='ETRF89', epoch=1989, datum=Datums.GRS80) .Xforms=(0, -1)
41@var RefFrames.ETRF90: RefFrame(name='ETRF90', epoch=1990, datum=Datums.GRS80) .Xforms=(0, -1)
42@var RefFrames.ETRF91: RefFrame(name='ETRF91', epoch=1991, datum=Datums.GRS80) .Xforms=(0, -1)
43@var RefFrames.ETRF92: RefFrame(name='ETRF92', epoch=1992, datum=Datums.GRS80) .Xforms=(0, -1)
44@var RefFrames.ETRF93: RefFrame(name='ETRF93', epoch=1993, datum=Datums.GRS80) .Xforms=(0, -1)
45@var RefFrames.ETRF94: RefFrame(name='ETRF94', epoch=1994, datum=Datums.GRS80) .Xforms=(0, -1)
46@var RefFrames.ETRF96: RefFrame(name='ETRF96', epoch=1996, datum=Datums.GRS80) .Xforms=(0, -1)
47@var RefFrames.ETRF97: RefFrame(name='ETRF97', epoch=1997, datum=Datums.GRS80) .Xforms=(0, -1)
48@var RefFrames.GDA2020: RefFrame(name='GDA2020', epoch=2020, datum=Datums.GRS80) .Xforms=(0, -4)
49@var RefFrames.GDA94: RefFrame(name='GDA94', epoch=1994, datum=Datums.GRS80) .Xforms=(0, -3)
50@var RefFrames.ITRF2000: RefFrame(name='ITRF2000', epoch=1997, datum=Datums.GRS80) .Xforms=(15, -5)
51@var RefFrames.ITRF2005: RefFrame(name='ITRF2005', epoch=2000, datum=Datums.GRS80) .Xforms=(8, -3)
52@var RefFrames.ITRF2008: RefFrame(name='ITRF2008', epoch=2005, datum=Datums.GRS80) .Xforms=(17, -2)
53@var RefFrames.ITRF2014: RefFrame(name='ITRF2014', epoch=2010, datum=Datums.GRS80) .Xforms=(16, -1)
54@var RefFrames.ITRF2020: RefFrame(name='ITRF2020', epoch=2015, datum=Datums.GRS80) .Xforms=(16, 0)
55@var RefFrames.ITRF88: RefFrame(name='ITRF88', epoch=1988, datum=Datums.GRS80) .Xforms=(3, -4)
56@var RefFrames.ITRF89: RefFrame(name='ITRF89', epoch=1989, datum=Datums.GRS80) .Xforms=(4, -4)
57@var RefFrames.ITRF90: RefFrame(name='ITRF90', epoch=1988, datum=Datums.GRS80) .Xforms=(6, -4)
58@var RefFrames.ITRF91: RefFrame(name='ITRF91', epoch=1988, datum=Datums.GRS80) .Xforms=(4, -4)
59@var RefFrames.ITRF92: RefFrame(name='ITRF92', epoch=1988, datum=Datums.GRS80) .Xforms=(4, -4)
60@var RefFrames.ITRF93: RefFrame(name='ITRF93', epoch=1988, datum=Datums.GRS80) .Xforms=(4, -4)
61@var RefFrames.ITRF94: RefFrame(name='ITRF94', epoch=1993, datum=Datums.GRS80) .Xforms=(4, -4)
62@var RefFrames.ITRF96: RefFrame(name='ITRF96', epoch=1997, datum=Datums.GRS80) .Xforms=(5, -5)
63@var RefFrames.ITRF97: RefFrame(name='ITRF97', epoch=1997, datum=Datums.GRS80) .Xforms=(5, -4)
64@var RefFrames.NAD83: RefFrame(name='NAD83', epoch=1997, datum=Datums.GRS80) .Xforms=(0, -6)
65@var RefFrames.NAD83cors96: RefFrame(name='NAD83cors96', epoch=1997, datum=Datums.GRS80) .Xforms=(1, 0)
66@var RefFrames.WGS84: RefFrame(name='WGS84', epoch=1984, datum=Datums.GRS80) .Xforms=(0, -1)
67@var RefFrames.WGS84g1150: RefFrame(name='WGS84g1150', epoch=2001, datum=Datums.GRS80) .Xforms=(1, 0)
68@var RefFrames.WGS84g1674: RefFrame(name='WGS84g1674', epoch=2005, datum=Datums.GRS80) .Xforms=(0, 0)
69@var RefFrames.WGS84g1762: RefFrame(name='WGS84g1762', epoch=2005, datum=Datums.GRS80) .Xforms=(0, 0)
70'''
72from pygeodesy.basics import map1, neg, isidentifier, isstr, _xinstanceof, _xscalar
73from pygeodesy.constants import _float as _F, _0_0s, _0_0, _0_001, _0_5, _1_0
74from pygeodesy.datums import Datums, _earth_datum, _equall, _GDA2020_, _Names7, \
75 _negastr, Transform, _WGS84, _EWGS84, _operator
76# from pygeodesy.ellipsoids import _EWGS84 # from .datums
77from pygeodesy.errors import TRFError, _xattr, _xellipsoidall, _xkwds, _xkwds_item2
78from pygeodesy.interns import MISSING, NN, _AT_, _COMMASPACE_, _conversion_, \
79 _datum_, _DOT_, _exists_, _invalid_, _MINUS_, \
80 _NAD83_, _no_, _PLUS_, _reframe_, _s_, _SPACE_, \
81 _STAR_, _to_, _vs_, _WGS84_, _x_, _intern as _i
82# from pygeodesy.lazily import _ALL_LAZY # from .units
83from pygeodesy.named import ADict, classname, _lazyNamedEnumItem as _lazy, _name2__, \
84 _Named, _NamedEnum, _NamedEnumItem, _NamedTuple, Fmt, unstr
85from pygeodesy.props import deprecated_method, property_doc_, Property_RO, property_RO
86# from pygeodesy.streprs import Fmt, unstr # from .named
87from pygeodesy.units import Epoch, Float, _ALL_LAZY
88# from pygeodesy.utily import sincos2d_
90from math import ceil as _ceil, fabs
91# import operator as _operator # from .datums
93__all__ = _ALL_LAZY.trf
94__version__ = '24.10.14'
96_EP0CH = Epoch(0, low=0)
97_Es = {_EP0CH: _EP0CH} # L{Epoch}s, deleted below
98_GRS80 = Datums.GRS80
99_inverse_ = 'inverse'
100_MAS = _MM = _PPB = Float # Units
101_MM2M = _0_001 # scale mm2m, ppB2ppM, mas2as
102_mDays = (0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 0)
103_366_0 = _F(sum(_mDays))
104_rates_ = 'rates' # PYCHOK used!
105_Rs = {} # L{TRFXform7Tuple}s de-dup, deleted below
106_xform_ = 'xform' # PYCHOK used!
107_Xs = {} # L{TRFXform7Tuple}s de-dup, deleted below
109_ETRF88_ = _i('ETRF88')
110_ETRF89_ = _i('ETRF89')
111_ETRF90_ = _i('ETRF90')
112_ETRF91_ = _i('ETRF91')
113_ETRF92_ = _i('ETRF92')
114_ETRF93_ = _i('ETRF93')
115_ETRF94_ = _i('ETRF94')
116_ETRF96_ = _i('ETRF96')
117_ETRF97_ = _i('ETRF97')
118_ETRF2000_ = _i('ETRF2000')
119_ETRF2005_ = _i('ETRF2005')
120_ETRF2008_ = _i('ETRF2008')
121_ETRF2014_ = _i('ETRF2014')
122_ETRF2020_ = _i('ETRF2020')
123_GDA94_ = _i('GDA94')
124_ITRF_ = _i('ITRF')
125_ITRF88_ = _i('ITRF88')
126_ITRF89_ = _i('ITRF89')
127_ITRF90_ = _i('ITRF90')
128_ITRF91_ = _i('ITRF91')
129_ITRF92_ = _i('ITRF92')
130_ITRF93_ = _i('ITRF93')
131_ITRF94_ = _i('ITRF94')
132_ITRF96_ = _i('ITRF96')
133_ITRF97_ = _i('ITRF97')
134_ITRF2000_ = _i('ITRF2000')
135_ITRF2005_ = _i('ITRF2005')
136_ITRF2008_ = _i('ITRF2008')
137_ITRF2014_ = _i('ITRF2014')
138_ITRF2020_ = _i('ITRF2020')
139_NAD83cors96_ = _i('NAD83cors96')
140_WGS84g1150_ = _i('WGS84g1150')
141_WGS84g1674_ = _i('WGS84g1674')
142_WGS84g1762_ = _i('WGS84g1762')
145def _E(epoch): # deleted below
146 '''(INTERNAL) De-dup L{Epochs}s.
147 '''
148 e = Epoch(_F(epoch))
149 return _Es.setdefault(e, e) # PYCHOK del
152def _P(ps, name, _Ps): # deleted below
153 '''(INTERNAL) De-dup L{TRFXform7Tuple}s.
154 '''
155 t = TRFXform7Tuple(map(_F, ps), name=name)
156 return _Ps.setdefault(t, t)
159class RefFrame(_NamedEnumItem):
160 '''Terrestrial Reference Frame (TRF) parameters.
161 '''
162 _datum = _GRS80 # Datums.GRS80 or .WGS84 (L{Datum})
163 _epoch = _EP0CH # epoch, fractional year (L{Epoch})
165 def __init__(self, epoch, datum=_GRS80, name=NN):
166 '''New L{RefFrame}.
168 @arg epoch: Epoch, a fractional calendar year (C{scalar} or C{str}).
169 @arg datum: Datum or ellipsoid (L{Datum}, {Ellipsoid}, L{Ellipsoid2}
170 or L{a_f2Tuple}).
171 @kwarg name: Unique, non-empty name (C{str}).
173 @raise NameError: A L{RefFrame} with that B{C{name}} already exists.
175 @raise TRFError: Invalid B{C{epoch}}.
177 @raise TypeError: Invalid B{C{datum}}.
178 '''
179 if datum in (_GRS80, None):
180 pass
181 elif datum in (_WGS84, _EWGS84):
182 self._datum = _WGS84
183 else:
184 _earth_datum(self, datum, raiser=_datum_)
185 self._epoch = _Epoch(epoch)
186 self._Xto = {} # dict of Xforms
187 if name:
188 self._register(RefFrames, _stref(name=name))
190 def __eq__(self, other):
191 return isinstance(other, RefFrame) and other.epoch == self.epoch \
192 and other.datum == self.datum \
193 and other.name == self.name
195 def __lt__(self, other): # for sorting
196 return isinstance(other, RefFrame) and (self.name < other.name
197 or self.epoch < other.epoch)
199 @deprecated_method # PYCHOK Python 3.5+
200 def __matmul__(self, point):
201 '''DEPRECATED on 2024.02.16, use method C{B{point}.toRefFrame}.'''
202 return _toRefFrame(point, self)
204 @property_RO
205 def datum(self):
206 '''Get this reference frame's datum (L{Datum}).
207 '''
208 return self._datum
210 @property_RO
211 def ellipsoid(self):
212 '''Get this reference frame's ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
213 '''
214 return self._datum.ellipsoid
216 @Property_RO
217 def epoch(self):
218 '''Get this reference frame's epoch (C{Epoch}).
219 '''
220 return self._epoch
222 def toRefFrame(self, point, reframe2, **epoch_epoch2_name):
223 '''Convert an ellipsoidal point from this reframe and from C{epoch} to
224 an other C{reframe2} and C{epoch2 or epoch}.
226 @arg point: The point to convert (C{LatLon} or C{Cartesian}).
227 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}).
228 @kwarg epoch_epoch2_name: Optional keyword arguments C{B{epoch}=None},
229 C{B{epoch2}=None} and C{B{name}=B{reframe2}.name}.
231 @return: A copy of the B{C{point}}, converted and renamed.
233 @raise TypeError: Invalid B{C{point}}.
235 @note: The C{B{point}.reframe} is overridden by this reframe and
236 C{B{point}.epoch} by C{B{epoch}} or this reframe.C{epoch}.
238 @see: Methods L{LatLon.toRefFrame<ellipsoidalBase.LatLonEllipsoidalBase.toRefFrame>}
239 and L{Cartesian.toRefFrame<ellipsoidalBase.CartesianEllipsoidalBase.toRefFrame>}
240 for more details.
241 '''
242 return _toRefFrame(point, reframe2, reframe=self, **_xkwds(epoch_epoch2_name,
243 name=_xattr(reframe2, name=self.name)))
245 def toStr(self, epoch=None, name=NN, **unused): # PYCHOK signature
246 '''Return this reference frame as a string.
248 @kwarg epoch: Override this reframe's epoch (C{scalar} or C{str}).
249 @kwarg name: Override name (C{str}) or C{None} to exclude the
250 reframe's name.
252 @return: This L{RefFrame}'s attributes (C{str}).
253 '''
254 D = self.datum
255 e = self.epoch if epoch is None else _Epoch(epoch)
256 t = (Fmt.EQUAL(name=repr(self._name__(name))),
257 Fmt.EQUAL(epoch=e),
258 Fmt.EQUAL(datum=_DOT_(classname(D) + _s_, D.name)))
259 return _COMMASPACE_.join(t[int(name is None):])
261 def Xform(self, reframe2):
262 '''Get the converter Xform I{from} this reference frame I{to} C{reframe2}.
264 @arg reframe2: Destination frame to convert I{to} (L{RefFrame} or C{str}).
266 @return: The L{TRFXform} instance or C{None} if not available.
268 @raise TypeError: Invalid B{C{reframe2}}.
269 '''
270 _xinstanceof(RefFrame, str, reframe2=reframe2)
271 n2 = reframe2 if isstr(reframe2) else reframe2.name
272 return self._Xto.get(n2, None)
274 def Xforms(self, inverse=False):
275 '''Return all Xforms converting I{from} or I{to} this reference frame or both.
277 @kwarg inverse: If C{True}, get all I{from} otherwise I{to} Xforms
278 I{un-inverted} (C{bool}) or if C{B{inverse}=2} (C{int})
279 get all I{to} Xforms I{inverted} plus all I{from}s.
281 @return: An L{ADict} of C{name=}L{TRFXform}s I{from} this reframe or if
282 C{B{inverse}=True} I{to} this reframe or both if C{B{inverse}=2}.
283 '''
284 return ADict(self._Xitems(inverse, RefFrames))
286 def _Xfrom(self, RFs, inverted):
287 '''(INTERNAL) Yield all 2-tuples C{(name, I{from} Xform)} converting I{to}
288 this reframe, inverted if C{inverted is True}.
289 '''
290 n2 = self.name
291 for n1, r in RFs.items():
292 X = r._Xto.get(n2, None)
293 if X:
294 yield n1, (X.inverse() if inverted else X)
296 def _Xitems(self, inverse, RFs): # in _eXhaustives, .Xforms
297 '''(INTERNAL) Yield all C{._Xfrom} and C{._Xto}'s as 2-tuple items.
298 '''
299 i = inverse == 2
300 if i or inverse:
301 for item in self._Xfrom(RFs, i):
302 yield item
303 if i or not inverse:
304 for item in self._Xto.items():
305 yield item
308class RefFrames(_NamedEnum):
309 '''(INTERNAL) L{RefFrame} registry, I{must} be a sub-class
310 to accommodate the L{_LazyNamedEnumItem} properties.
311 '''
312 def _Lazy(self, epoch, datum=_GRS80, name=NN):
313 '''(INTERNAL) Instantiate the L{RefFrame}.
314 '''
315 return RefFrame(epoch, datum, name=name)
317RefFrames = RefFrames(RefFrame) # PYCHOK singleton
318'''Some pre-defined L{RefFrame}s, all I{lazily} instantiated.'''
319# <https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js>
320RefFrames._assert(
321 ETRF88 = _lazy(_ETRF88_, _E(1988)), # epoch, datum?
322 ETRF89 = _lazy(_ETRF89_, _E(1989)), # epoch, datum?
323 ETRF90 = _lazy(_ETRF90_, _E(1990)), # epoch, datum?
324 ETRF91 = _lazy(_ETRF91_, _E(1991)), # epoch, datum?
325 ETRF92 = _lazy(_ETRF92_, _E(1992)), # epoch, datum?
326 ETRF93 = _lazy(_ETRF93_, _E(1993)), # epoch, datum?
327 ETRF94 = _lazy(_ETRF94_, _E(1994)), # epoch, datum?
328 ETRF96 = _lazy(_ETRF96_, _E(1996)), # epoch, datum?
329 ETRF97 = _lazy(_ETRF97_, _E(1997)), # epoch, datum?
330 ETRF2000 = _lazy(_ETRF2000_, _E(2005)),
331 ETRF2005 = _lazy(_ETRF2005_, _E(2005)), # epoch, datum?
332 ETRF2008 = _lazy(_ETRF2008_, _E(2008)), # epoch, datum?
333 ETRF2014 = _lazy(_ETRF2014_, _E(2014)), # epoch, datum?
334 ETRF2020 = _lazy(_ETRF2020_, _E(2020)), # epoch, datum?
335 GDA94 = _lazy(_GDA94_, _E(1994)), # Australia
336 GDA2020 = _lazy(_GDA2020_, _E(2020)), # Australia
337 ITRF88 = _lazy(_ITRF88_, _E(1988)),
338 ITRF89 = _lazy(_ITRF89_, _E(1989)),
339 ITRF90 = _lazy(_ITRF90_, _E(1988)),
340 ITRF91 = _lazy(_ITRF91_, _E(1988)),
341 ITRF92 = _lazy(_ITRF92_, _E(1988)),
342 ITRF93 = _lazy(_ITRF93_, _E(1988)),
343 ITRF94 = _lazy(_ITRF94_, _E(1993)),
344 ITRF96 = _lazy(_ITRF96_, _E(1997)),
345 ITRF97 = _lazy(_ITRF97_, _E(1997)),
346 ITRF2000 = _lazy(_ITRF2000_, _E(1997)), # aka ITRF00
347 ITRF2005 = _lazy(_ITRF2005_, _E(2000)),
348 ITRF2008 = _lazy(_ITRF2008_, _E(2005)), # aka ITRF08
349 ITRF2014 = _lazy(_ITRF2014_, _E(2010)),
350 ITRF2020 = _lazy(_ITRF2020_, _E(2015)),
351 NAD83 = _lazy(_NAD83_, _E(1997)),
352 NAD83cors96 = _lazy(_NAD83cors96_, _E(1997)),
353 WGS84 = _lazy(_WGS84_, _E(1984), _WGS84),
354 WGS84g1150 = _lazy(_WGS84g1150_, _E(2001), _WGS84),
355 WGS84g1674 = _lazy(_WGS84g1674_, _E(2005), _WGS84),
356 WGS84g1762 = _lazy(_WGS84g1762_, _E(2005), _WGS84)) # same epoch
359class TransformXform(Transform):
360 '''Helmert transformation, extended with an C{Xform} TRF converter.
362 @see: L{Transform<datums.Transform>} and L{Xform<TRFXform>}.
363 '''
364 _Xform = None
366 def __init__(self, name=NN, **tx_ty_tz_s_sx_sy_sz): # PYCHOK signature
367 '''New L{TransformXform}.
369 @kwarg name: Optional name (C{str}), I{not registered}.
371 @see: L{Transform<datums.Transform>} for details.
373 @note: This L{TransformXform}'s name starts with C{"-"} iff
374 I{inversed}.
375 '''
376 Transform.__init__(self, **tx_ty_tz_s_sx_sy_sz)
377 if name:
378 self.name = name # unregistered
380 def __eq__(self, other):
381 return isinstance(other, TransformXform) and _equall(other, self)
383 def __hash__(self):
384 return Transform.__hash__(self)
386 def inverse(self, **name):
387 '''Return the inverse of this transform.
389 @kwarg name: Optional, unique C{B{name}=NN} (C{str}).
391 @return: Inverse (L{TransformXform}), unregistered.
392 '''
393 r = Transform.inverse(self, **name)
394 X = self.Xform
395 if X: # unregistered
396 r._Xform = X.inverse()
397 return r
399 def rename(self, name=NN):
400 '''Change this transform's name.
402 @arg name: New name (C{str}), overriding this transform's Xform's name.
404 @return: The previous name (C{str}).
405 '''
406 X = self.Xform
407 n = name or (X.toStr() if X else NN)
408 return Transform.rename(self, n)
410 def toRefFrame(self, point, **name): # PYCHOK signature
411 '''Convert an ellipsoidal point using this transform and Xform.
413 @arg point: The point to convert (C{Cartesian} or C{LatLon}).
414 @kwarg name: Optional C{B{name}=NN} (C{str}).
416 @return: A copy of the B{C{point}}, converted I{directly} to
417 this transform's Xform's C{refName2} and C{epoch}.
419 @note: The B{C{point}}'s original C{reframe} and C{epoch} are
420 I{ignored}, its C{datum} and C{height} are preserved
421 but I{not} taken into account.
422 '''
423 _ = _xellipsoidall(point)
424 p = point.dup() if self.isunity else point.toTransform(self)
425 X = self.Xform
426 if X: # see _toRefFrame below
427 p._reframe = X.reframe2
428 p._epoch = X.epoch
429 p.rename(self._name__(name))
430 return p
432 def toTransform(self, epoch1, **epoch2_inverse):
433 '''Return this transform observed at B{C{epoch1}} as a Helmert
434 L{TransformXform}, optionally at B{C{epoch2 or epoch1}}.
436 @arg epoch1: Epoch to observe I{from} (C{scalar}).
437 @kwarg epoch2_inverse: Optional C{B{epoch2}=None} to observe
438 I{to} and C{B{inverse}=False}, see method
439 L{toTransform<TRFXform.toTransform>} from
440 L{TRFXform}.
442 @return: The Helmert transform (L{TransformXform}).
444 @raise TRFError: Invalid B{C{epoch1}}, B{C{epoch2}} or
445 missing Xform.
446 '''
447 X = self.Xform
448 if X is None:
449 raise TRFError(Xform=X, txt=MISSING)
450 return X.toTransform(epoch1, **epoch2_inverse)
452 def transform2(self, x, y, z, vx=0, vy=0, vz=0, inverse=False, factor=_MM2M,
453 **Vector_and_kwds):
454 '''Transform a (cartesian) position I{with} velocities, forward or inverse.
456 @arg x: X coordinate (C{meter}).
457 @arg y: Y coordinate (C{meter}).
458 @arg z: Z coordinate (C{meter}).
459 @kwarg vx: X velocity (C{meter-per-year}).
460 @kwarg vy: Y velocity (C{meter-per-year}).
461 @kwarg vz: Z velocity (C{meter-per-year}).
462 @kwarg inverse: If C{True}, apply the inverse transform (C{bool}).
463 @kwarg factor: Factor to scale this Xform's C{rates} (C{scalar}),
464 default from C{milli-meter-} to C{meter-per-year},
465 from C{milli-arc-} to C{arc-seconds-per-year} and
466 from C{ppB-} to C{ppM-per-year}.
467 @kwarg Vector_and_kwds: An optional, (3-D) C{B{Vector}=None} or cartesian
468 class and additional C{B{Vector}} keyword arguments to
469 return the transformed position and the I{velocities}.
471 @return: 2-Tuple C{(position, velocities)}, the tranformed C{position}
472 and C{velocities}, each a L{Vector3Tuple}C{(x, y, z)} unless
473 some B{C{Vector_and_kwds}} are specified.
475 @note: If this transform's Xform is missing, the returned C{velocities}
476 are the given ones, I{un-transformed}.
478 @raise TypeError: Non-scalar B{C{factor}}.
480 @see: Soler, T. & Snay, R.A. "Transforming Positions and Velocities ...", U{equations
481 (4) and (5)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>}
482 and HTDP functions C{VTRANF} and C{VTRANF_IERS} in file U{HTDP/hdtp.f
483 <https://Geodesy.NOAA.gov/TOOLS/Htdp/Htdp.shtml>}.
484 '''
485 p = self.transform(x, y, z, inverse=inverse, **Vector_and_kwds)
486 X = self.Xform
487 if X is not None:
488 r = X.rates * factor # equ (4) ...
489 # vx', vy', vz' = (.tx + x * .s + y * .rz - z * .ry,
490 # .ty - x * .rz + y * .s + z * .rx,
491 # .tz + x * .ry - y * .rx + z * .s)
492 # using counter-/clockwise .rx, .ry, and .rz
493 V = Transform(**dict(r.items())) # unregistered
494 _ = V._s_s1(0) # XXX r.s?
495 v = V.transform(p.x, p.y, p.z, inverse=inverse)
496 # + (vx, vy, vz) like HTDP
497 vx += v.x
498 vy += v.y
499 vz += v.z
500 v = p.dup(x=vx, y=vy, z=vz, name=NN(p.name, _vs_))
501 return p, v
503 def velocities(self, factor=_MM2M, **Vector_and_kwds):
504 '''Compute the X, Y and Z I{velocities} of this transform.
506 @kwarg factor: Factor to scale this Xform's C{rates} (C{scalar}),
507 default from C{milli-meter-} to C{meter-per-year},
508 from C{milli-arc-} to C{arc-seconds-per-year} and
509 from C{ppB-} to C{ppM-per-year}.
510 @kwarg Vector_and_kwds: An optional, (3-D) C{B{Vector}=None} or
511 cartesian class and additional C{B{Vector}} keyword
512 arguments to return the I{velocities}.
514 @return: A L{Vector3Tuple}C{(x, y, z)} unless some B{C{Vector_and_kwds}}
515 are specified or C{None} if this transform's Xform is missing.
517 @raise TypeError: Non-scalar B{C{factor}}.
519 @see: Altamimi, Z. "EUREF-TN-1-Jan-31-2024", U{Appendix A, equation (3)
520 <http://ETRS89.ENSG.IGN.FR/pub/EUREF-TN-1-Jan-31-2024.pdf>} and
521 method L{transform2<TransformXform.transform2>}.
522 '''
523 v = X = self.Xform
524 if X is not None:
525 r = X.rates * factor # equ (3) ...
526 V = self.dup(tx=r.sx, ty=r.sy, tz=r.sz, _Xform=None, # Xyy-dot
527 name=NN(self.name, _vs_)) # unregistered
528 _ = V._s_s1(0)
529 v = V.transform(r.tx, r.ty, r.tz, inverse=False, # Xyy
530 **Vector_and_kwds)
531 return v
533 @property_doc_(''' the Xform (L{TRFXform}).''')
534 def Xform(self):
535 '''Get this Helmert transform's Xform (L{TRFXform} or C{None}).
536 '''
537 return self._Xform
539 @Xform.setter # PYCHOK setter!
540 def Xform(self, Xform):
541 '''Set this Helmert transform's Xform (L{TRFXform}).
543 @raise TypeError: Invalid B{C{Xform}}.
544 '''
545 _xinstanceof(TRFXform, Xform=Xform)
546 self._Xform = Xform
549class TRFXform7Tuple(_NamedTuple):
550 '''7-Tuple C{(tx, ty, tz, s, sx, sy, sz)} of conversion parameters with
551 translations C{tx}, C{ty} and C{tz} in C{milli-meter}, scale C{s} in
552 C{ppB} and rotations C{sx}, C{sy} and C{sz} in C{milli-arc-seconds}.
553 For C{rates} all are C{units-per-year}.
555 @note: The parameters are also named as C{(Tx, Ty, Tz, D, Rx, Ry, Rz)}
556 or C{(T1, T2, T3, D, R1, R2, R3)}.
558 @see: Class L{TransformXform}'s matching keyword argument names.
559 '''
560 _Names_ = _Names7 # ('tx', 'ty', 'tz', _s_, 'sx', 'sy', 'sz') == TransformXform.__init__
561 _Units_ = (_MM, _MM, _MM, _PPB, _MAS, _MAS, _MAS)
563 def __add__(self, other):
564 return self._add_sub(other, True)
566 def __eq__(self, other):
567 return isinstance(other, TRFXform7Tuple) and _equall(other, self)
568 # PYCHOK and self.name == other.name
570 def __hash__(self):
571 return _NamedTuple.__hash__(self)
573 def __mul__(self, factor):
574 _xscalar(factor=factor)
575 return type(self)((x * factor for x in self), name=_STAR_) # .fsums._mul_op
577 def __neg__(self):
578 return self.inverse()
580 def __sub__(self, other):
581 return self._add_sub(other, False)
583 def _add_sub(self, other, p_):
584 '''(INTERNAL) Return C{this +/- other} L{TRFXform7Tuple}.
585 '''
586 _xinstanceof(TRFXform7Tuple, other=other)
587 op = _operator.add if p_ else _operator.sub
588 return type(self)(map(op, self, other), name=_PLUS_ if p_ else _MINUS_)
590 def inverse(self, name=NN):
591 '''Return the inverse of this transform.
593 @kwarg name: Optional name (C{str}).
595 @return: Inverse (L{TransformXform}).
596 '''
597 n = name or _negastr(self.name)
598 return type(self)(map(neg, self), name=n)
600 @Property_RO
601 def isunity(self):
602 '''Is this a C{unity, identity} transform (C{bool}).
603 '''
604 return not any(self)
607class TRFXform(_Named):
608 '''A Terrestrial Reference Frame (TRF) converter between two
609 reference frames observed at an C{epoch}.
610 '''
611 _epoch = _EP0CH
612 _epoch_d = _0_0
613 _indir_d = NN # refName
614 _inver_d = False
615 refName1 = \
616 refName2 = NN
617 rates = \
618 xform = None
620 def __init__(self, refName1, refName2, epoch=None, xform=None,
621 rates=None, name=NN):
622 '''New L{TRFXform} TRF converter.
624 @arg refName1: Source reframe (C{str}), converting I{from}.
625 @arg refName2: Destination reframe (C{str}), converting I{to}.
626 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str}).
627 @kwarg xform: I{Transform} parameters at B{C{epoch}} (L{TRFXform7Tuple}).
628 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), like B{C{xform}},
629 but in C{units-per-year}.
630 @kwarg name: Optional name (C{str}), overriding the default from method
631 L{toStr<TRFXform.toStr>}.
633 @raise TRFError: Invalid B{C{refName1}}, B{C{refName2}} or B{C{epoch}}.
635 @raise TypeError: Invalid B{C{xform}} or B{C{rates}}.
637 @see: Functions L{trfXform}, L{trfTransform0} and L{trfTransforms}.
638 '''
639 self.refName1 = _stref(refName1=refName1)
640 self.refName2 = _stref(refName2=refName2)
641 _xinstanceof(TRFXform7Tuple, xform=xform, rates=rates)
642 self.epoch = epoch
643 self.xform = xform
644 self.rates = rates
645 self.rename(name or self.toStr())
647 def __add__(self, other):
648 return self._add_sub(other, True)
650 def __eq__(self, other):
651 return isinstance(other, TRFXform) and other.epoch == self.epoch \
652 and other.xform == self.xform \
653 and other.rates == self.rates
655# def __hash__(self):
656# return hash((self.epoch, self.xform, self.rates))
658 def __lt__(self, other): # for sorting
659 return isinstance(other, TRFXform) and (self.refName1 < other.refName1
660 or self.refName2 < other.refName2
661 or self.epoch < other.epoch)
663 def __neg__(self):
664 return self.inverse()
666 def __repr__(self):
667 return self.toRepr()
669 def __str__(self):
670 return self.toStr()
672 def __sub__(self, other):
673 return self._add_sub(other, False)
675 def _add_sub(self, other, p_, *n1_n2_n): # in _indirects below
676 '''(INTERNAL) Summate C{this +/- other} Xform at C{this.epoch}.
678 @see: U{Appendix, Table 7, last column "Sum of the previous ..."
679 <https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf">}
680 '''
681 _xinstanceof(TRFXform, other=other)
682 X1 = self
683 e1 = X1.epoch
684 X2 = other.toEpoch(e1) # if other.epoch != e1 else other
686 n1, n2, n = n1_n2_n or _n1_n2_n3(X1, X2)
688 X = type(X1)(n1, n2, epoch=e1, xform=X1.xform._add_sub(X2.xform, p_),
689 rates=X1.rates._add_sub(X2.rates, p_),
690 name=_sumstr(X1.name, X2.name, p_))
691 X._epoch_d = X1.epoched + X2.epoched
692 X._indir_d = n # reframe?
693 X._inver_d = X1.inversed and X2.inversed
694 return X
696 def _at(self, epoch):
697 '''(INTERNAL) Return C{"self.nameB{@}epoch"}.
698 '''
699 n = self.name
700 if epoch != self.epoch:
701 _e = _AT_(NN, epoch)
702 if not n.endswith(_e):
703 n = NN(n, _e)
704 return n
706 @property_doc_(''' the epoch, fractional year (L{Epoch}).''')
707 def epoch(self):
708 '''Get the epoch (L{Epoch}).
709 '''
710 return self._epoch
712 @epoch.setter # PYCHOK setter!
713 def epoch(self, epoch):
714 '''Set the epoch (L{Epoch}, C{scalar} or C{str}).
716 @raise TRFError: Invalid B{C{epoch}}.
717 '''
718 e = _Epoch(epoch)
719 if self._epoch != e:
720 self.rename(self._at(e))
721 self._epoch = e
723 @property_RO
724 def epoched(self):
725 '''Get this Xform's aggregate I{epoch} deltas (C{float}).
726 '''
727 return self._epoch_d
729 @property_RO
730 def indirected(self):
731 '''Is this an I{indirected} Xform? (C{str} of space-separated
732 refNames) or C{NN}.
733 '''
734 return self._indir_d
736 def inverse(self, name=NN):
737 '''Return this Xform {inversed}, C{refName1} and C{-2} swapped.
739 @return: The inverse (L{TRFXform}).
740 '''
741 n = name or _negastr(self.name)
742 X = self.dup(refName1=self.refName2, xform=-self.xform,
743 refName2=self.refName1, rates=-self.rates,
744 name=n, _inver_d=not self.inversed)
745# X = type(self)(self.refName2, self.refName1, epoch= self.epoch,
746# xform=-self.xform,
747# rates=-self.rates, name=n)
748# if self.epoched:
749# X._epoch_d = self.epoched
750# if self.indirected:
751# X._indir_d = self.indirected
752# if not self.inversed:
753# X._inver_d = True
754 return X
756 @property_RO
757 def inversed(self):
758 '''Is this an I{inversed} Xform? (C{bool}).
759 '''
760 return self._inver_d
762 def _reframe(self, name, datum=_GRS80):
763 '''(INTERNAL) Get an un-/registered frame.
764 '''
765 r = RefFrames.get(name)
766 if r is None or r.datum != datum:
767 r = RefFrame(self.epoch, datum)
768 r.name = name # unregistered
769 return r
771 @property_RO
772 def reframe1(self):
773 '''Get the un-/registered I{from} frame (C{RefFrame}).
774 '''
775 return self._reframe(self.refName1)
777 @property_RO
778 def reframe2(self):
779 '''Get the un-/registered I{to} frame (C{RefFrame}).
780 '''
781 return self._reframe(self.refName2)
783 def rename(self, name=NN):
784 '''Change this Xform's name.
786 @arg name: New name (C{str}), overriding the base
787 name C{"refName1B{@}epochB{x}refName2"}.
789 @return: The old name (C{str}).
790 '''
791 return _Named.rename(self, name or self.toStr())
793 def toEpoch(self, epoch):
794 '''Convert this Xform to B{C{epoch}}, if needed.
796 @arg epoch: Epoch, fractional year (C{Epoch}, C{scalar}
797 or C{str}).
799 @return: This Xform or a copy converted to B{C{epoch}}.
801 @raise TRFError: Invalid B{C{epoch}}.
802 '''
803 e = _Epoch(epoch)
804 X, d = self, e - self.epoch
805 if d:
806 t = X.xform + X.rates * d
807 X = X.dup(epoch=e, xform=t, name=X._at(e))
808 X._epoch_d += fabs(d)
809 return X
811 def toHelmert(self, factor=_MM2M):
812 '''Return the Helmert transform from this Xform scaled accordingly.
814 @kwarg factor: Factor to scale this Xform's C{xform} (C{scalar}),
815 default from C{milli-meter-} to C{meter-}, from
816 C{milli-arc-} to C{arc-seconds} and from C{ppB}
817 to C{ppM}.
819 @return: The Helmert transform (L{TransformXform}).
820 '''
821 h = self.xform * factor
822 H = TransformXform(**dict(h.items()))
823 H.name = self.name # unregistered
824 H.Xform = self
825 return H
827 def toRefFrame(self, point, datum=_GRS80, **epoch_epoch2_name):
828 '''Convert an ellipsoidal point from this Xform's C{refName1} and
829 C{epoch} to this Xform's C{refName2} and C{epoch2 or epoch}.
831 @arg point: The point to convert (C{Cartesian} or C{LatLon}).
832 @kwarg datum: Optional datum to define a temporary L{RefFrame} from
833 this Xform's C{refName1} or C{refName2} (C{datum}).
834 @kwarg epoch_epoch2_name: Optional keyword arguments C{B{epoch}=None},
835 B{C{epoch2}=None} and C{B{name}=refName1}.
837 @return: A copy of the B{C{point}}, converted and renamed.
839 @see: Method L{RefFrame.toRefFrame} for more details.
840 '''
841 r1 = self._reframe(self.refName1, datum=datum)
842 r2 = self._reframe(self.refName2, datum=datum)
843 return _toRefFrame(point, r2, reframe=r1,
844 **_xkwds(epoch_epoch2_name, name=r1.name))
846 def toRepr(self, **unused): # PYCHOK signature
847 '''Return the represention of this Xform (C{str}).
848 '''
849 return unstr(self.classname, name=self.name, epoch=self.epoch)
851 def toStr(self, epoch=None, **unused): # PYCHOK signature
852 '''Return this Xform as C{"refName1B{@}epochB{x}refName2"} (C{str}).
854 @kwarg epoch: Epoch (C{Epoch}, C{scalar} or C{str}), overriding
855 this Xform's epoch.
856 '''
857 e = self.epoch if epoch is None else _Epoch(epoch)
858 return NN(_AT_(self.refName1, e), _x_, self.refName2)
860 def toTransform(self, epoch=None, epoch2=None, inverse=False):
861 '''Combine this Xform observed at B{C{epoch}} into a Helmert
862 L{TransformXform}, optionally at B{C{epoch2 or epoch}}.
864 @kwarg epoch: Epoch to observe I{from} (C{scalar}),
865 overriding this converter's epoch.
866 @kwarg epoch2: Optional epoch to observe I{to} (C{scalar}),
867 overriding B{C{epoch}}.
868 @kwarg inverse: Use the Xform's inverse (C{bool}).
870 @return: The Helmert transform (L{TransformXform}).
872 @raise TRFError: Invalid B{C{epoch}} or B{C{epoch2}}.
874 @see: Method L{toHelmert}.
875 '''
876 if epoch2 is None:
877 e = self.epoch if epoch is None else epoch
878 elif isinstance(epoch2, Epoch):
879 e = epoch2
880 else:
881 e = Epoch(epoch2=epoch2)
882 X = self.toEpoch(e)
883 if inverse:
884 X = X.inverse()
885 return X.toHelmert()
888def date2epoch(year, month, day):
889 '''Return the C{epoch} for a calendar day.
891 @arg year: Year of the date (C{scalar}).
892 @arg month: Month in the B{C{year}} (C{scalar}, 1..12).
893 @arg day: Day in the B{C{month}} (C{scalar}, 1..31).
895 @return: Epoch, the fractional year (C{float}).
897 @raise TRFError: Invalid B{C{year}}, B{C{month}} or B{C{day}}.
899 @note: Any B{C{year}} is considered a leap year, i.e. having
900 29 days in February.
901 '''
902 try:
903 y, m, d = map1(int, year, month, day)
904 if y > 0 and 1 <= m <= 12 and 1 <= d <= _mDays[m]:
905 e = y + float(sum(_mDays[:m]) + d) / _366_0
906 return Epoch(e, low=0)
908 raise ValueError() # _invalid_
909 except (TRFError, TypeError, ValueError) as x:
910 raise TRFError(year=year, month=month, day=day, cause=x)
913def _direct(n1, n2):
914 '''(INTERNAL) Get the C{n1} to C{n2} Xform or C{None}.
915 '''
916 r = RefFrames.get(n1)
917 return r._Xto.get(n2, None) if r else None
920def _Epoch(e, **kwds):
921 '''(INTERNAL) Get the C{Epoch(B{e})}.
922 '''
923 return e if isinstance(e, Epoch) and not kwds else Epoch(e, **kwds)
926def epoch2date(epoch):
927 '''Return the date for a reference frame C{epoch}.
929 @arg epoch: Fractional year (C{scalar}).
931 @return: 3-Tuple C{(year, month, day)}.
933 @raise TRFError: Invalid B{C{epoch}}.
935 @note: Any B{C{year}} is considered a leap year, i.e. having
936 29 days in February.
937 '''
938 e = Epoch(epoch, low=0)
939 y = int(e)
940 d = int(_ceil((e - y) * _366_0))
941 for m, n in enumerate(_mDays[1:]):
942 if d > n:
943 d -= n
944 else:
945 break
946 return y, (m + 1), max(1, d)
949def _eXhaustives(n1, n2):
950 '''(INTERNAL) Yield all I{coalesced} Xforms from C{n1} to {n2}
951 via I{any number of} intermediate reframe conversions.
952 '''
953 def _k2(item):
954 return -item[1].epoch # most recent first
956 R = dict(RefFrames)
957 r = R.pop(n1, None)
958 if r:
959 Xs = list(sorted(tuple(r._Xitems(2, R)), key=_k2))
960 while Xs:
961 n, X = Xs.pop(0)
962 if n == n2:
963 yield _n_pop(X)
964 else:
965 r = R.pop(n, None)
966 if r:
967 for n, x in r._Xitems(2, R):
968 Xs.append((n, X + x))
971def _indirects(n1, n2):
972 '''(INTERNAL) Yield all Xforms between C{n1} and C{n2} via
973 I{one} intermediate reframe C{n} conversion.
974 '''
975 def _X4(_Xto, n2):
976 _d = _direct
977 for n, X1 in _Xto.items():
978 X2 = _d(n, n2)
979 if X2:
980 yield X1, X2, n, True # X1 + X2
981 X2 = _d(n2, n)
982 if X2:
983 yield X1, X2, n, False # X1 - X2
985 r1 = RefFrames.get(n1)
986 if r1:
987 for X1, X2, n, p_ in _X4(r1._Xto, n2):
988 e1, e2 = X1.epoch, X2.epoch
989 if e1 < e2: # X1 to e2
990 X1 = X1.toEpoch(e2)
991# elif e1 > e2: # X2 to e1
992# X2 = X2.toEpoch(e1)
993 yield X1._add_sub(X2, p_, n1, n2, n)
996def _n1_n2_n3(X1, X2):
997 '''(INTERNAL) L{TRFXform._add_sub} helper.
998 '''
999 n = X1.indirected
1000 n = _SPACE_(n, X1.refName2) if n else X1.refName2
1001 return X1.refName1, X2.refName2, n
1004def _n_pop(X):
1005 '''(INTERNAL) Pop L{TRFXform.indirected}'s ends.
1006 '''
1007 p, n = None, X.indirected.split()
1008 if n and n[-1] == X.refName2:
1009 p = n.pop()
1010 if n and n[ 0] == X.refName1:
1011 p = n.pop(0)
1012 if p:
1013 X._indir_d = _SPACE_.join(n) if n else NN
1014 return X
1017def _reframe(**name_reframe):
1018 '''(INTERNAL) Get a C{reframe}.
1019 '''
1020 _, r = _xkwds_item2(name_reframe)
1021 if isstr(r) and r: # not NN
1022 r = RefFrames.get(r)
1023 if r and isinstance(r, RefFrame):
1024 return r
1025 raise TRFError(**name_reframe) # _invalid_
1028def _stref(**name_refname):
1029 '''(INTERNAL) Check a reference frame name.
1030 '''
1031 _, n = _xkwds_item2(name_refname)
1032 if isstr(n) and isidentifier(n):
1033 return str(n)
1034 raise TRFError(**name_refname) # _invalid_
1037def _sumstr(name1, name2, p_):
1038 '''(INTERNAL) "Sum" of C{name1 + ('+' if p_ else '-') + name2}.
1039 '''
1040 if name2:
1041 n = name2 if p_ else _negastr(name2)
1042 p = NN if n.startswith(_MINUS_) or \
1043 n.startswith(_PLUS_) else _PLUS_
1044 name1 = NN(name1, p, n)
1045 return name1
1048def _toRefFrame(point, reframe2, reframe=None, epoch=None,
1049 epoch2=None, **name_LatLon_kwds):
1050 '''(INTERNAL) Convert an ellipsoidal point to C{reframe2}
1051 and C{epoch2 or epoch or pont.epoch or reframe.epoch}.
1052 '''
1053 ll = _xellipsoidall(point)
1054 r1 = reframe or point.reframe
1055 if not r1:
1056 t = _SPACE_(_DOT_(repr(point), _reframe_), MISSING)
1057 raise TRFError(_no_(_conversion_), txt=t)
1059 _xinstanceof(RefFrame, reframe2=reframe2, reframe=r1)
1061 e1 = _Epoch(epoch or point.epoch or r1.epoch)
1062 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2)
1063 t0 = _toTransform0(r1.name, e1, reframe2.name, e2)
1064 if t0 is None:
1065 t = _SPACE_(RefFrame.__name__, _AT_(r1.name, e1),
1066 _to_, _AT_(reframe2.name, e2))
1067 raise TRFError(_no_(_conversion_), txt=t)
1069 name, LatLon_kwds = _name2__(name_LatLon_kwds)
1070 if t0: # is not ()
1071 if t0.isunity:
1072 p = point.dup()
1073 elif point.datum:
1074 p = point.toCartesian() if ll else point
1075 p = p.toDatum( r1.datum).toTransform(t0) \
1076 .toDatum(reframe2.datum).toDatum(point.datum)
1077 if ll:
1078 p = p.toLatLon(LatLon=point.classof, **LatLon_kwds)
1079 elif ll: # and LatLon_kwds
1080 p = point.toTransform(t0, **LatLon_kwds)
1081 else:
1082 p = point.toTransform(t0)
1083 p._reframe = reframe2 # see TRFXform.toRefFrame above
1084 p._epoch = _xattr(t0.Xform, epoch=e2)
1085 p.rename(reframe2._name__(name))
1086 else:
1087 p = point.dup(_reframe=reframe2, # ditto
1088 _epoch=e2, name=name) if name else point
1089 return p
1092def _toTransform0(n1, e1, n2, e2, **indirect_inverse):
1093 '''(INTERNAL) Return a L{TransformXform}, 0-tuple or C{None}.
1094 '''
1095 if n1 == n2 and e1 == e2:
1096 return () # unity?
1098 for X in _toTransforms(n1, e1, n2, e2, **indirect_inverse):
1099 return X # first OK?
1101 if (n1.startswith(_ITRF_) and n2.startswith(_WGS84_)) or \
1102 (n2.startswith(_ITRF_) and n1.startswith(_WGS84_)): # and e1 == e2?
1103 return () # unity?
1105 return None
1108def _toTransforms(n1, e1, n2, e2, indirect=True, inverse=True, exhaust=False): # MCCABE 16
1109 '''(INTERNAL) Yield all possible Helmert transforms, if any.
1110 '''
1111 class Ts(list): # L{TransformXform}s de-dup
1112 def __call__(self, Xs, e1=e1, e2=e2, **inverse):
1113 for X in Xs:
1114 if X:
1115 T = X.toTransform(e1, epoch2=e2, **inverse)
1116 if T not in self:
1117 self.append(T)
1118 yield T
1120# def __contains__(self, T):
1121# _xinstanceof(TransformXform, T=T)
1122# return any(t == T for t in self)
1124 def _k(X):
1125 return -X.epoch # most recent first
1127 _Ts = Ts()
1129 for T in _Ts((_direct(n1, n2),), inverse=False):
1130 yield T
1131 if inverse:
1132 for T in _Ts((_direct(n2, n1),), inverse=True):
1133 yield T
1135 if indirect:
1136 for T in _Ts(sorted(_indirects(n1, n2), key=_k), inverse=False):
1137 yield T
1138 if inverse:
1139 for T in _Ts(sorted(_indirects(n2, n1), key=_k), inverse=True):
1140 yield T
1142 if exhaust:
1143 for T in _Ts(_eXhaustives(n1, n2), inverse=False):
1144 yield T
1145 for T in _Ts(_eXhaustives(n2, n1), inverse=True):
1146 yield T
1149def trfTransform0(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True, exhaust=False):
1150 '''Get a Helmert transform to convert one C{reframe} observed at C{epoch}
1151 to an other C{reframe2} at observed at C{epoch2 or epoch}.
1153 @return: A L{TransformXform} instance, a C{0-tuple} for I{unity, identity} or
1154 C{None} if no conversion exists.
1156 @see: Function L{trfTransforms} for futher details.
1157 '''
1158 return _trfT0s(_toTransform0, reframe, reframe2, epoch, epoch2,
1159 indirect=indirect, inverse=inverse, exhaust=exhaust)
1162def trfTransforms(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True, exhaust=False):
1163 '''Yield all Helmert transform to convert one C{reframe} observed at C{epoch}
1164 to an other C{reframe2} at observed at C{epoch2 or epoch}.
1166 @arg reframe: The frame to convert I{from} (L{RefFrame} or C{str}).
1167 @arg reframe2: The frame to convert I{to} (L{RefFrame} or C{str}).
1168 @arg epoch: Epoch to observe I{from} (L{Epoch}, C{scalar} or C{str}),
1169 otherwise C{B{reframe}}'s C{epoch}.
1170 @kwarg epoch2: Optional epoch to observe I{to} (L{Epoch}, C{scalar} or C{str}),
1171 otherwise B{C{epoch}}.
1172 @kwarg indirect: If C{True}, include transforms via I{one} intermediate reframe,
1173 otherwise only I{direct} B{C{reframe}} to B{C{reframe2}}
1174 transforms (C{bool}).
1175 @kwarg inverse: If C{True}, include inverse, otherwise only forward transforms
1176 (C{bool}).
1177 @kwarg exhaust: If C{True}, exhaustively generate all transforms, forward and
1178 inverse and via any number of intermediate reframes (C{bool}).
1180 @return: A L{TransformXform} instance for each available conversion, without
1181 duplicates.
1183 @raise TRFError: Invalid B{C{reframe}}, B{C{reframe2}}, B{C{epoch}} or B{C{epoch2}}.
1185 @raise TypeError: Invalid B{C{reframe}} or B{C{reframe2}}.
1186 '''
1187 return _trfT0s(_toTransforms, reframe, reframe2, epoch, epoch2,
1188 indirect=indirect, inverse=inverse, exhaust=exhaust)
1191def _trfT0s(_toT0s, reframe, reframe2, epoch, epoch2, **indirect_inverse_exhaust):
1192 '''(INTERNAL) Handle C{trfTransforms0} and C{trfTransforms} calls.
1193 '''
1194 r1 = _reframe(reframe=reframe)
1195 e1 = r1.epoch if epoch is None else _Epoch(epoch)
1196 r2 = _reframe(reframe2=reframe2)
1197 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2)
1198 return _toT0s(r1.name, e1, r2.name, e2, **indirect_inverse_exhaust)
1201def trfXform(reframe1, reframe2, epoch=None, xform=None, rates=None, raiser=True):
1202 '''Define a new Terrestrial Reference Frame (TRF) converter or get an
1203 existing one.
1205 @arg reframe1: Source frame (L{RefFrame} or C{str}), converting I{from}.
1206 @arg reframe2: Destination frame (L{RefFrame} or C{str}), converting I{to}.
1207 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str})
1208 or C{None} for C{B{reframe2}}'s epoch.
1209 @kwarg xform: I{Transform} parameters (L{TRFXform7Tuple}).
1210 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), as B{C{xform}},
1211 but in C{units-per-year}.
1212 @kwarg raiser: If C{False}, do not raise an error if the converter
1213 exists, replace it (C{bool}).
1215 @return: The new TRF converter (L{TRFXform}) or if no B{C{epoch}},
1216 B{C{xform}} and B{C{rates}} are given, return the existing
1217 one (L{TRFXform}) or C{None} if not available.
1219 @raise TRFError: Invalid B{C{reframe1}}, B{C{reframe2}}, B{C{epoch}},
1220 B{C{xform}} or B{C{rates}} or the TRF converter
1221 already exists.
1222 '''
1223 try:
1224 r1 = _reframe(reframe1=reframe1)
1225 r2 = _reframe(reframe2=reframe2)
1226 if epoch is None:
1227 if xform is rates is None:
1228 return r1._Xto.get(r2.name, None)
1229 e = r2.epoch
1230 else:
1231 e = _Epoch(epoch)
1232 return _trfX(r1.name, r2.name, raiser=raiser, epoch=e,
1233 xform=xform, rates=rates)
1234 except (TypeError, ValueError) as x:
1235 t = unstr(trfXform, reframe1, reframe2, epoch=epoch)
1236 raise TRFError(t, cause=x)
1239def _trfX(n1, n2, raiser=True, **epoch_xform_rates):
1240 '''(INTERNAL) New, I{unique} L{TRFXform} converter.
1241 '''
1242 r1 = RefFrames.get(n1)
1243 if r1 is None:
1244 raise ValueError(_invalid_)
1245 r2 = RefFrames.get(n2)
1246 if r2 is None:
1247 raise ValueError(_invalid_)
1248 if raiser:
1249 if n2 in r1._Xto:
1250 raise ValueError(_exists_)
1251 if n1 in r2._Xto:
1252 raise ValueError(_SPACE_(_inverse_, _exists_))
1253 r1._Xto[n2] = X = TRFXform(n1, n2, **epoch_xform_rates)
1254 return X
1257# def velocities2neu(vx, vy, vz, lat=0, lon=0):
1258# '''Convert X, Y, and Z I{velocities} to North, East, Up.
1259#
1260# @arg vx: X velocity (C{meter-per-time}).
1261# @arg vx: Y velocity (C{meter-per-time}).
1262# @arg vx: Z velocity (C{meter-per-time}).
1263# @kwarg lat: Latitude (C{degrees}).
1264# @kwarg lon: Longitude (C{degrees}).
1265#
1266# @return: 3-Tuple C{(vnorth, veast, vup)} with the
1267# North, East and Up velocities, same units
1268# as B{C{vx}, B{C{vy}} and B{C{vx}}.
1269# '''
1270# sa, ca, sb, cb = sincos2d_(lat, lon)
1271# ve = cb * vy - sb * vx
1272# v = cb * vx + sb * vy
1273# vn = ca * vz - sa * v
1274# vu = sa * vz + ca * v
1275# return vn, ve, vu
1278# def velocities2xyz(vn, ve, vu, lat=0, lon=0):
1279# '''Convert North, East and Up I{velocities} to X, Y, Z.
1280#
1281# @arg vn: North velocity (C{meter-per-time}).
1282# @arg ve: East velocity (C{meter-per-time}).
1283# @arg vu: Up velocity (C{meter-per-time}).
1284# @kwarg lat: Latitude (C{degrees}).
1285# @kwarg lon: Longitude (C{degrees}).
1286#
1287# @return: 3-Tuple C{(vx, vy, vz)} with the X, Y
1288# and Z velocities, same units as B{C{vn},
1289# B{C{ve}} and B{C{vu}}.
1290# '''
1291# sa, ca, sb, cb = sincos2d_(lat, lon)
1292# vz = ca * vn + sa * vu
1293# v = ca * vu - sa * vn
1294# vx = cb * v - sb * ve
1295# vy = sb * v + cb * ve
1296# return vx, vy, vz
1299def _X(*ps): # deleted below
1300 return _P(ps, _xform_, _Xs) # PYCHOK del
1303def _R(*ps): # deleted below
1304 return _P(ps, _rates_, _Rs) # PYCHOK del
1307_P_0_0s = TRFXform7Tuple(_0_0s(len(_Names7)), name='unity')
1309# TRF conversions specified as an epoch and 2 sets of 7 parameters. Most from Altamimi, Z. U{"EUREF Technical
1310# Note 1: Relationship and Transformation between the International and the European Terrestrial Reference
1311# Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Appendix A, more at U{Quinsy QPS <https://
1312# confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ITRF_Transformation_Parameters.xlsx>}.
1313# See also U{Quinsy International Terrestrial Reference Frame 2014 (ITRF2014)<https://confluence.QPS.NL/qinsy/latest/
1314# en/international-terrestrial-reference-frame-2014-itrf2014-182618383.html>}.
1315_trfX(_ITRF2020_, _ITRF2014_, epoch=_E(2015), # <https://ITRF.IGN.Fr/docs/solutions/itrf2020/Transfo-ITRF2020_TRFs.txt>
1316 xform=_X( -1.4, -0.9, 1.4, -0.42, _0_0, _0_0, _0_0),
1317 rates=_R( _0_0, -0.1, 0.2, _0_0, _0_0, _0_0, _0_0))
1318_trfX(_ITRF2020_, _ITRF2008_, epoch=_E(2015),
1319 xform=_X( 0.2, 1.0, 3.3, -0.29, _0_0, _0_0, _0_0),
1320 rates=_R( _0_0, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0))
1321_trfX(_ITRF2020_, _ITRF2005_, epoch=_E(2015),
1322 xform=_X( 2.7, 0.1, -1.4, 0.65, _0_0, _0_0, _0_0),
1323 rates=_R( 0.3, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0))
1324_trfX(_ITRF2020_, _ITRF2000_, epoch=_E(2015),
1325 xform=_X( -0.2, 0.8, -34.2, 2.25, _0_0, _0_0, _0_0),
1326 rates=_R( 0.1, _0_0, -1.7, 0.11, _0_0, _0_0, _0_0))
1327_trfX(_ITRF2020_, _ITRF97_, epoch=_E(2015),
1328 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
1329 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1330_trfX(_ITRF2020_, _ITRF96_, epoch=_E(2015),
1331 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
1332 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1333_trfX(_ITRF2020_, _ITRF94_, epoch=_E(2015),
1334 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
1335 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1336_trfX(_ITRF2020_, _ITRF93_, epoch=_E(2015),
1337 xform=_X( -65.8, 1.9, -71.3, 4.47, -3.36, -4.33, 0.75),
1338 rates=_R( -2.8, -0.2, -2.3, 0.12, -0.11, -0.19, 0.07))
1339_trfX(_ITRF2020_, _ITRF92_, epoch=_E(2015),
1340 xform=_X( 14.5, -1.9, -85.9, 3.27, _0_0, _0_0, 0.36),
1341 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1342_trfX(_ITRF2020_, _ITRF91_, epoch=_E(2015),
1343 xform=_X( 26.5, 12.1, -91.9, 4.67, _0_0, _0_0, 0.36),
1344 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1345_trfX(_ITRF2020_, _ITRF90_, epoch=_E(2015),
1346 xform=_X( 24.5, 8.1, -107.9, 4.97, _0_0, _0_0, 0.36),
1347 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1348_trfX(_ITRF2020_, _ITRF89_, epoch=_E(2015),
1349 xform=_X( 29.5, 32.1, -145.9, 8.37, _0_0, _0_0, 0.36),
1350 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1351_trfX(_ITRF2020_, _ITRF88_, epoch=_E(2015),
1352 xform=_X( 24.5, -3.9, -169.9, 11.47, 0.1, _0_0, 0.36),
1353 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1355# see U{Transformation Parameters ITRF2014<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2014_ITRFs.txt>} and
1356# Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1357# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1.pdf>} Appendix A.
1358_trfX(_ITRF2014_, _ITRF2008_, epoch=(2010), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2014/tp_14-08.php>
1359 xform=_X( 1.6, 1.9, 2.4, -0.02, _0_0, _0_0, _0_0),
1360 rates=_R( _0_0, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0))
1361_trfX(_ITRF2014_, _ITRF2005_, epoch=_E(2010),
1362 xform=_X( 2.6, _1_0, -2.3, 0.92, _0_0, _0_0, _0_0),
1363 rates=_R( 0.3, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0))
1364_trfX(_ITRF2014_, _ITRF2000_, epoch=_E(2010),
1365 xform=_X( 0.7, 1.2, -26.1, 2.12, _0_0, _0_0, _0_0),
1366 rates=_R( 0.1, 0.1, -1.9, 0.11, _0_0, _0_0, _0_0))
1367_trfX(_ITRF2014_, _ITRF97_, epoch=_E(2010),
1368 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1369 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1370_trfX(_ITRF2014_, _ITRF96_, epoch=_E(2010),
1371 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1372 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1373_trfX(_ITRF2014_, _ITRF94_, epoch=_E(2010),
1374 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1375 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1376_trfX(_ITRF2014_, _ITRF93_, epoch=_E(2010),
1377 xform=_X( -50.4, 3.3, -60.2, 4.29, -2.81, -3.38, 0.4),
1378 rates=_R( -2.8, -0.1, -2.5, 0.12, -0.11, -0.19, 0.07))
1379_trfX(_ITRF2014_, _ITRF92_, epoch=_E(2010),
1380 xform=_X( 15.4, 1.5, -70.8, 3.09, _0_0, _0_0, 0.26),
1381 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1382_trfX(_ITRF2014_, _ITRF91_, epoch=_E(2010),
1383 xform=_X( 27.4, 15.5, -76.8, 4.49, _0_0, _0_0, 0.26),
1384 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1385_trfX(_ITRF2014_, _ITRF90_, epoch=_E(2010),
1386 xform=_X( 25.4, 11.5, -92.8, 4.79, _0_0, _0_0, 0.26),
1387 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1388_trfX(_ITRF2014_, _ITRF89_, epoch=_E(2010),
1389 xform=_X( 30.4, 35.5, -130.8, 8.19, _0_0, _0_0, 0.26),
1390 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1391_trfX(_ITRF2014_, _ITRF88_, epoch=_E(2010),
1392 xform=_X( 25.4, -0.5, -154.8, 11.29, 0.1, _0_0, 0.26),
1393 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1395# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1396# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 1st and 2nd column
1397_trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2005),
1398 xform=_X( -0.5, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1399 rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1400# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(1997),
1401# xform=_X( -2.9, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1402# rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1403# see U{Transformation Parameters ITRF2008<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2008_ITRFs.txt>}
1404# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2008/tp_08-05.php>
1405# xform=_X( -2.0, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1406# rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1407_trfX(_ITRF2008_, _ITRF2000_, epoch=_E(2000),
1408 xform=_X( -1.9, -1.7, -10.5, 1.34, _0_0, _0_0, _0_0),
1409 rates=_R( 0.1, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1410_trfX(_ITRF2008_, _ITRF97_, epoch=_E(2000),
1411 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1412 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1413_trfX(_ITRF2008_, _ITRF96_, epoch=_E(2000),
1414 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1415 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1416_trfX(_ITRF2008_, _ITRF94_, epoch=_E(2000),
1417 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1418 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1419_trfX(_ITRF2008_, _ITRF93_, epoch=_E(2000),
1420 xform=_X( -24.0, 2.4, -38.6, 3.41, -1.71, -1.48, -0.3),
1421 rates=_R( -2.8, -0.1, -2.4, 0.09, -0.11, -0.19, 0.07))
1422_trfX(_ITRF2008_, _ITRF92_, epoch=_E(2000),
1423 xform=_X( 12.8, 4.6, -41.2, 2.21, _0_0, _0_0, 0.06),
1424 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1425_trfX(_ITRF2008_, _ITRF91_, epoch=_E(2000),
1426 xform=_X( 24.8, 18.6, -47.2, 3.61, _0_0, _0_0, 0.06),
1427 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1428_trfX(_ITRF2008_, _ITRF90_, epoch=_E(2000),
1429 xform=_X( 22.8, 14.6, -63.2, 3.91, _0_0, _0_0, 0.06),
1430 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1431_trfX(_ITRF2008_, _ITRF89_, epoch=_E(2000),
1432 xform=_X( 27.8, 38.6, -101.2, 7.31, _0_0, _0_0, 0.06),
1433 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1434_trfX(_ITRF2008_, _ITRF88_, epoch=_E(2000),
1435 xform=_X( 22.8, 2.6, -125.2, 10.41, 0.1, _0_0, 0.06),
1436 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1438# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1439# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 3rd column
1440# _trfX(_ITRF2005_, _ITRF2000_, epoch=_E(1997),
1441# xform=_X( 0.7, -1.1, -0.4, 0.16, -0.2, 0.1 -1.8),
1442# rates=_R( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1443_trfX(_ITRF2005_, _ITRF2000_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2005/tp_05-00.php>
1444 xform=_X( 0.1, -0.8, -5.8, 0.4, _0_0, _0_0, _0_0),
1445 rates=_R( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1447_trfX(_ITRF2000_, _ITRF97_, epoch=_E(1997),
1448 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1449 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, -0.02)) # 0.02?
1450_trfX(_ITRF2000_, _ITRF96_, epoch=_E(1997),
1451 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1452 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1453_trfX(_ITRF2000_, _ITRF94_, epoch=_E(1997),
1454 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1455 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1456_trfX(_ITRF2000_, _ITRF93_, epoch=_E(1988),
1457 xform=_X( 12.7, 6.5, -20.9, 1.95, -0.39, 0.8, -1.14),
1458 rates=_R( -2.9, -0.2, -0.6, 0.01, -0.11, -0.19, 0.07))
1459_trfX(_ITRF2000_, _ITRF92_, epoch=_E(1988),
1460 xform=_X( 1.47, 1.35, -1.39, 0.75, _0_0, _0_0, -0.18),
1461 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1462_trfX(_ITRF2000_, _ITRF91_, epoch=_E(1988),
1463 xform=_X( 26.7, 27.5, -19.9, 2.15, _0_0, _0_0, -0.18),
1464 rates=_R( _0_0, -0.6, -1.4, 0.01, _0_0, _0_0, 0.02))
1465_trfX(_ITRF2000_, _ITRF90_, epoch=_E(1988),
1466 xform=_X( 2.47, 2.35, -3.59, 2.45, _0_0, _0_0, -0.18),
1467 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1468_trfX(_ITRF2000_, _ITRF89_, epoch=_E(1988),
1469 xform=_X( 2.97, 4.75, -7.39, 5.85, _0_0, _0_0, -0.18),
1470 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1471_trfX(_ITRF2000_, _ITRF88_, epoch=_E(1988),
1472 xform=_X( 2.47, 1.15, -9.79, 8.95, 0.1, _0_0, -0.18),
1473 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1475# Soler, T .& Snay R.A. U{"Transforming Positions and Velocities between the International Terrestrial
1476# Reference Frame of 2000 and North American Datum of 1983"<https://www.ResearchGate.net/publication/245291390>},
1477# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1478# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 5th and 6th column
1479_trfX(_ITRF97_, _ITRF96_, epoch=_E(1997),
1480 xform=_X( -2.07, -0.21, 9.95, -0.93496, 0.1267, -0.22355, -0.06065,),
1481 rates=_R( 0.69, -0.1, 1.86, -0.19201, 0.01347, -0.01514, 0.00027))
1482_trfX(_ITRF96_, _NAD83_, epoch=_E(1997),
1483 xform=_X( 991.0, -190.72, -512.9, _0_0, 25.79, 9.65, 11.66,),
1484 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.0532, -0.7423, -0.0316,))
1486# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1487# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 1.
1488# _trfX(_ITRF2020_, _ETRF2020_, epoch=_E(1989), # see Table 2 below
1489# xform=_P_0_0s,
1490# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753))
1491# _trfX(_ITRF2014_, _ETRF2014_, epoch=_E(1989), # see Table 3 below
1492# xform=_P_0_0s,
1493# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77))
1494_trfX(_ITRF2005_, _ETRF2005_, epoch=_E(1989),
1495 xform=_X( 56.0, 48.0, -37.0, _0_0, _0_0, _0_0, _0_0),
1496 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.054, 0.518, -0.781))
1497# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(1989), # see Table 4 below
1498# xform=_X( 54.0, 51.0, -48.0, _0_0, _0_0, _0_0, _0_0),
1499# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1500_trfX(_ITRF97_, _ETRF97_, epoch=_E(1989),
1501 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1502 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1503_trfX(_ITRF96_, _ETRF96_, epoch=_E(1989),
1504 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1505 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1506_trfX(_ITRF94_, _ETRF94_, epoch=_E(1989),
1507 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1508 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1509_trfX(_ITRF93_, _ETRF93_, epoch=_E(1989),
1510 xform=_X( 19.0, 53.0, -21.0, _0_0, _0_0, _0_0, _0_0),
1511 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.32, 0.78, -0.67))
1512_trfX(_ITRF92_, _ETRF92_, epoch=_E(1989),
1513 xform=_X( 38.0, 40.0, -37.0, 0.0, 0.0, 0.0, 0.0),
1514 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68))
1515_trfX(_ITRF91_, _ETRF91_, epoch=_E(1989),
1516 xform=_X( 21.0, 25.0, -37.0, _0_0, _0_0, _0_0, _0_0),
1517 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68))
1518_trfX(_ITRF90_, _ETRF90_, epoch=_E(1989),
1519 xform=_X( 19.0, 28.0, -23.0, _0_0, _0_0, _0_0, _0_0),
1520 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71))
1521_trfX(_ITRF89_, _ETRF89_, epoch=_E(1989),
1522 xform=_P_0_0s,
1523 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71))
1525# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1526# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 2.
1527_trfX(_ITRF2020_, _ETRF2020_, epoch=_E(2015),
1528 xform=_X( _0_0, _0_0, _0_0, _0_0, 2.236, 13.494, -19.578),
1529 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753))
1530_trfX(_ITRF2014_, _ETRF2020_, epoch=_E(2015),
1531 xform=_X( 1.4, 0.9, -1.4, 0.42, 2.236, 13.494, -19.578),
1532 rates=_R( _0_0, 0.1, -0.2, _0_0, 0.086, 0.519, -0.753))
1533_trfX(_ITRF2008_, _ETRF2020_, epoch=_E(2015),
1534 xform=_X( 3.0, 2.8, 0.5, 0.55, 2.236, 13.494, -19.578),
1535 rates=_R( _0_0, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753))
1536_trfX(_ITRF2005_, _ETRF2020_, epoch=_E(2015),
1537 xform=_X( 5.5, 1.9, -4.2, 1.49, 2.236, 13.494, -19.578),
1538 rates=_R( 0.3, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753))
1539_trfX(_ITRF2000_, _ETRF2020_, epoch=_E(2015),
1540 xform=_X( 2.6, 2.6, -37.0, 3.09, 2.236, 13.494, -19.578),
1541 rates=_R( 0.1, 0.2, -2.1, 0.11, 0.086, 0.519, -0.753))
1542_trfX(_ITRF97_, _ETRF2020_, epoch=_E(2015),
1543 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1544 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1545_trfX(_ITRF96_, _ETRF2020_, epoch=_E(2015),
1546 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1547 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1548_trfX(_ITRF94_, _ETRF2020_, epoch=_E(2015),
1549 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1550 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1551_trfX(_ITRF93_, _ETRF2020_, epoch=_E(2015),
1552 xform=_X( -63.0, 3.7, -74.1, 5.31, -1.124, 9.164, -18.828),
1553 rates=_R( -2.8, _0_0, -2.7, 0.12, -0.024, 0.329, -0.683))
1554_trfX(_ITRF92_, _ETRF2020_, epoch=_E(2015),
1555 xform=_X( 17.3, -0.1, -88.7, 4.11, 2.236, 13.494, -19.218),
1556 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1557_trfX(_ITRF91_, _ETRF2020_, epoch=_E(2015),
1558 xform=_X( 29.3, 13.9, -94.7, 5.51, 2.236, 13.494, -19.218),
1559 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1560_trfX(_ITRF90_, _ETRF2020_, epoch=_E(2015),
1561 xform=_X( 27.3, 9.9, -110.7, 5.81, 2.236, 13.494, -19.218),
1562 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1563_trfX(_ITRF89_, _ETRF2020_, epoch=_E(2015),
1564 xform=_X( 32.3, 33.9, -148.7, 9.21, 2.236, 13.494, -19.218),
1565 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1566_trfX(_ITRF88_, _ETRF2020_, epoch=_E(2015),
1567 xform=_X( 27.3, -2.1, -172.7, 12.31, 2.336, 13.494, -19.218),
1568 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1570# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1571# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 3.
1572_trfX(_ITRF2020_, _ETRF2014_, epoch=_E(2015),
1573 xform=_X( -1.4, -0.9, 1.4, 0.42, 2.21, 13.806, -20.02),
1574 rates=_R( _0_0, -0.1, 0.2, _0_0, 0.085, 0.531, -0.77))
1575_trfX(_ITRF2014_, _ETRF2014_, epoch=_E(2015),
1576 xform=_X( _0_0, _0_0, _0_0, _0_0, 2.21, 13.806, -20.02),
1577 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77))
1578_trfX(_ITRF2008_, _ETRF2014_, epoch=_E(2015),
1579 xform=_X( -1.6, -1.9, -1.9, -0.13, 2.21, 13.806, -20.02),
1580 rates=_R( _0_0, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77))
1581_trfX(_ITRF2005_, _ETRF2014_, epoch=_E(2015),
1582 xform=_X( -4.1, -1.0, 2.8, -1.07, 2.21, 13.806, -20.02),
1583 rates=_R( -0.3, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77))
1584_trfX(_ITRF2000_, _ETRF2014_, epoch=_E(2015),
1585 xform=_X( -1.2, -1.7, 35.6, -2.67, 2.21, 13.806, -20.02),
1586 rates=_R( -0.1, -0.1, 1.9, -0.11, 0.085, 0.531, -0.77))
1587_trfX(_ITRF97_, _ETRF2014_, epoch=_E(2015),
1588 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1589 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1590_trfX(_ITRF96_, _ETRF2014_, epoch=_E(2015),
1591 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1592 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1593_trfX(_ITRF94_, _ETRF2014_, epoch=_E(2015),
1594 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1595 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1596_trfX(_ITRF93_, _ETRF2014_, epoch=_E(2015),
1597 xform=_X( 64.4, -2.8, 72.7, -4.89, 5.570, 18.136, -20.77),
1598 rates=_R( 2.8, 0.1, 2.5, -0.12, 0.195, 0.721, -0.84))
1599_trfX(_ITRF92_, _ETRF2014_, epoch=_E(2015),
1600 xform=_X( -15.9, 1.0, 87.3, -3.69, 2.21, 13.806, -20.38),
1601 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1602_trfX(_ITRF91_, _ETRF2014_, epoch=_E(2015),
1603 xform=_X( -27.9, -13.0, 93.3, -5.09, 2.21, 13.806, -20.38),
1604 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1605_trfX(_ITRF90_, _ETRF2014_, epoch=_E(2015),
1606 xform=_X( -25.9, -9.0, 109.3, -5.39, 2.21, 13.806, -20.38),
1607 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1608_trfX(_ITRF89_, _ETRF2014_, epoch=_E(2015),
1609 xform=_X( -30.9, -33.0, 147.3, -8.79, 2.21, 13.806, -20.38),
1610 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1611_trfX(_ITRF88_, _ETRF2014_, epoch=_E(2015),
1612 xform=_X( -25.9, 3.0, 171.3, -11.89, 2.11, 13.806, -20.38),
1613 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1615# see U{Altamimi, Z. "EUREF Technical Note 1: Relationship and Transformation between the International and
1616# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 4,
1617# U{Boucher, C. & Altamimi, Z. "Memo: Specifications for reference frame fixing in the analysis of a EUREF GPS
1618# campaign" (2011) <https://ETRS89.ENSG.IGN.Fr/memo-V8.pdf>} and U{Altamimi, Z. "Key results of ITRF2014 and
1619# implication to ETRS89 realization", EUREF2016<https://www.EUREF.EU/symposia/2016SanSebastian/01-02-Altamimi.pdf>}.
1620_trfX(_ITRF2020_, _ETRF2000_, epoch=_E(2015),
1621 xform=_X( 53.8, 51.8, -82.2, 2.25, 2.106, 12.74, -20.592),
1622 rates=_R( 0.1, _0_0, -1.7, 0.11, 0.081, 0.49, -0.792))
1623# _trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2000),
1624# xform=_X( 53.7, 51.2, -55.1, 1.02, 0.891, 5.39, -8.712),
1625# rates=_R( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792))
1626_trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2015),
1627 xform=_X( 55.2, 52.7, -83.6, 2.67, 2.106, 12.74, -20.592),
1628 rates=_R( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792))
1629# _trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2000),
1630# xform=_X( 52.1, 49.3, -58.5, 1.34, 0.891, 5.39, -8.712),
1631# rates=_R( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1632_trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2015),
1633 xform=_X( 53.6, 50.8, -85.5, 2.54, 2.106, 12.74, -20.592),
1634 rates=_R( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1635# _trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2000),
1636# xform=_X( 54.1, 50.2, -53.8, 0.4, 0.891, 5.39, -8.712),
1637# rates=_R( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1638_trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2015),
1639 xform=_X( 51.1, 51.7, -80.8, 1.6, 2.106, 12.74, -20.592),
1640 rates=_R( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1641# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2000),
1642# xform=_X( 54.0, 51.0, -48.0, _0_0, 0.891, 5.39, -8.712),
1643# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1644_trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2015),
1645 xform=_X( 54.0, 51.0, -48.0, _0_0, 2.106, 12.74, -20.592),
1646 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1647_trfX(_ITRF97_, _ETRF2000_, epoch=_E(2015),
1648 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1649 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1650_trfX(_ITRF96_, _ETRF2000_, epoch=_E(2015),
1651 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1652 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1653_trfX(_ITRF94_, _ETRF2000_, epoch=_E(2015),
1654 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1655 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1656_trfX(_ITRF93_, _ETRF2000_, epoch=_E(2015),
1657 xform=_X( 119.6, 49.9, -10.9, -2.22, 5.466, 17.07, -21.342),
1658 rates=_R( 2.9, 0.2, 0.6, -0.01, 0.191, 0.68, -0.862))
1659_trfX(_ITRF92_, _ETRF2000_, epoch=_E(2015),
1660 xform=_X( 39.3, 53.7, 3.7, -1.02, 2.106, 12.74, -20.952),
1661 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1662_trfX(_ITRF91_, _ETRF2000_, epoch=_E(2015),
1663 xform=_X( 27.3, 39.7, 9.7, -2.42, 2.106, 12.74, -20.952),
1664 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1665_trfX(_ITRF90_, _ETRF2000_, epoch=_E(2015),
1666 xform=_X( 29.3, 43.7, 25.7, -2.72, 2.106, 12.74, -20.952),
1667 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1668_trfX(_ITRF89_, _ETRF2000_, epoch=_E(2015),
1669 xform=_X( 24.3, 19.7, 63.7, -6.12, 2.106, 12.74, -20.952),
1670 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1671_trfX(_ITRF88_, _ETRF2000_, epoch=_E(2015),
1672 xform=_X( 29.3, 55.7, 87.7, -9.22, 2.006, 12.74, -20.952),
1673 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1675# GDA2020 "Geocentric Datum of Australia 2020 Technical Manual", v1.5, 2020-12-09, Table 3.3 and 3.4
1676# <https://www.ICSM.gov.AU/sites/default/files/2020-12/GDA2020%20Technical%20Manual%20V1.5_4.pdf>
1677# (the GDA2020 xforms are different but the rates are the same as GDA94, further below)
1678_trfX(_ITRF2014_, _GDA2020_, epoch=_E(2020),
1679 xform=_P_0_0s,
1680 rates=_R( _0_0, _0_0, _0_0, _0_0, 1.50379, 1.18346, 1.20716))
1681_trfX(_ITRF2008_, _GDA2020_, epoch=_E(2020),
1682 xform=_X( 13.79, 4.55, 15.22, 2.5, 0.2808, 0.2677, -0.4638),
1683 rates=_R( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))
1684_trfX(_ITRF2005_, _GDA2020_, epoch=_E(2020),
1685 xform=_X( 40.32, -33.85, -16.72, 4.286, -1.2893, -0.8492, -0.3342),
1686 rates=_R( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))
1687_trfX(_ITRF2000_, _GDA2020_, epoch=_E(2020),
1688 xform=_X(-105.52, 51.58, 231.68, 3.55, 4.2175, 6.3941, 0.8617),
1689 rates=_R( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))
1691# see Table 2 in U{Dawson, J. & Woods, A. "ITRF to GDA94 coordinate transformations", Journal of Applied
1692# Geodesy 4 (2010), 189-199<https://www.ResearchGate.net/publication/258401581_ITRF_to_GDA94_coordinate_transformations>}
1693# (note, sign of rotations for GDA94 reversed as "Australia assumes rotation to be of coordinate axes",
1694# rather than the more conventional "position around the coordinate axes")
1695_trfX(_ITRF2008_, _GDA94_, epoch=_E(1994),
1696 xform=_X( -84.68, -19.42, 32.01, 9.71, -0.4254, 2.2578, 2.4015),
1697 rates=_R( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))
1698_trfX(_ITRF2005_, _GDA94_, epoch=_E(1994),
1699 xform=_X( -79.73, -6.86, 38.03, 6.636, 0.0351, -2.1211, -2.1411),
1700 rates=_R( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))
1701_trfX(_ITRF2000_, _GDA94_, epoch=_E(1994),
1702 xform=_X( -45.91, -29.85, -20.37, 7.07, -1.6705, 0.4594, 1.9356),
1703 rates=_R( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))
1705# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
1706# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 and Pearson, C. & Snay, R. U{"Introducing
1707# HTDP 3.1 to transform coordinates across time and spatial reference frames"<https://Geodesy.NOAA.gov/
1708# TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 7th column
1709_trfX(_ITRF2008_, _NAD83_, epoch=_E(1997),
1710 xform=_X( 993.43, -1903.31, -526.55, 1.71504, -25.91467, -9.42645, -11.59935),
1711 rates=_R( 0.79, -0.6, -1.34, -0.10201, -0.06667, 0.75744, 0.05133))
1712# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
1713# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83
1714_trfX(_ITRF2005_, _NAD83_, epoch=_E(1997),
1715 xform=_X( 996.3, -1902.4, -521.9, 0.775, -25.915, -9.426, -11.599),
1716 rates=_R( 0.5, -0.6, -1.3, -0.10201, -0.06667, 0.75744, 0.05133))
1717# see U{Solar, T. & Snay, R.A. "Transforming Positions and Velocities between the International Terrestrial Reference
1718# Frame of 2000 and North American Datum of 1983" (2004)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>}
1719_trfX(_ITRF2000_, _NAD83_, epoch=_E(1997), # note NAD83(CORS96)
1720 xform=_X( 995.6, -1901.3, -521.5, 0.615, -25.915, -9.426, -11.599),
1721 rates=_R( 0.7, -0.7, _0_5, -0.182, -0.06667, 0.75744, 0.05133))
1722_trfX(_ITRF90_, _NAD83_, epoch=_E(1997),
1723 xform=_X( 973.0, -1919.2, -482.9, -0.9, -25.79, -9.65, -11.66),
1724 rates=_R( _0_0, _0_0, _0_0, _0_0, -0.053, 0.742, 0.032))
1725_trfX(_ITRF90_, _WGS84_, epoch=_E(1984), # coverage
1726 xform=_X( 60.0, -517.0, -223.0, -11.0, 18.3, -0.3, 7.0),
1727 rates=_P_0_0s)
1729# equivalents U{"Transformations Between NAD83 and WGS84"<https://www.NGS.NOAA.gov/CORS/Articles/WGS84NAD83.pdf>}
1730trfXform(_NAD83cors96_, _NAD83_, epoch=_E(1997), xform=_P_0_0s, rates=_P_0_0s)
1731trfXform(_WGS84g1150_, _ITRF2000_, epoch=_E(2004), xform=_P_0_0s, rates=_P_0_0s)
1733del _E, _Es, _i, _P, _P_0_0s, _R, _Rs, _X, _Xs
1735if __name__ == '__main__':
1737 def _main():
1738 from pygeodesy.basics import _args_kwds_names
1739 from pygeodesy.interns import _COLONSPACE_,_COMMA_, _NL_, _NLATvar_, _vs_
1740 from pygeodesy import printf
1741 from time import localtime
1743 D = date2epoch.__name__
1744 E = epoch2date.__name__
1745 y = localtime()[0]
1746 for m in range(1, 13):
1747 for d in (1, 15, _mDays[m] - 1, _mDays[m]):
1748 f = '%s(%d,%3d,%3d)' % (D, y, m, d)
1749 e = date2epoch(y, m, d)
1750 t = epoch2date(e)
1751 x = NN if t == (y, m, d) else _STAR_
1752 e = '%.3f' % (e,)
1753 e = '%s, %s(%s)' % (e, E, e)
1754 t = '%d,%3d,%3d' % t
1755 printf('# %s = %s = %s %s', f, e, t, x)
1757 # __doc__ of this file, force all into registery
1758 def _RFs():
1759 yield NN
1760 for t in RefFrames.toRepr(all=True).split(_NL_):
1761 t = t.strip(_COMMA_)
1762 n = t.split(_COLONSPACE_)[0].split(_DOT_)[1]
1763 r = RefFrames.get(n)
1764 x = len(r.Xforms()), -len(r.Xforms(inverse=True))
1765 yield '%s .Xforms=%s' % (t, x)
1767 printf(_NLATvar_.join(sorted(_RFs())), nt=1)
1769 X, t = (), 0 # all form
1770 for r in RefFrames.values():
1771 X += tuple(r._Xto.values())
1772 for X in sorted(X):
1773 t += 1
1774 printf('#%4d %-24s xform=%r', t, X.name, X.xform)
1775 printf('#%29s rates=%r', _SPACE_, X.rates)
1777 t = _args_kwds_names(Transform.__init__)
1778 for n in TRFXform7Tuple._Names_:
1779 if n not in t:
1780 raise AssertionError(_SPACE_(n, _vs_, t))
1782 _main()
1783# del _main
1785# **) MIT License
1786#
1787# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
1788#
1789# Permission is hereby granted, free of charge, to any person obtaining a
1790# copy of this software and associated documentation files (the "Software"),
1791# to deal in the Software without restriction, including without limitation
1792# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1793# and/or sell copies of the Software, and to permit persons to whom the
1794# Software is furnished to do so, subject to the following conditions:
1795#
1796# The above copyright notice and this permission notice shall be included
1797# in all copies or substantial portions of the Software.
1798#
1799# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1800# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1801# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1802# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1803# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1804# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1805# OTHER DEALINGS IN THE SOFTWARE.
1807# % python -m pygeodesy.trf
1808#
1809# date2epoch(2024, 1, 1) = 2024.003, epoch2date(2024.003) = 2024, 1, 1
1810# date2epoch(2024, 1, 15) = 2024.041, epoch2date(2024.041) = 2024, 1, 15
1811# date2epoch(2024, 1, 30) = 2024.082, epoch2date(2024.082) = 2024, 1, 30
1812# date2epoch(2024, 1, 31) = 2024.085, epoch2date(2024.085) = 2024, 1, 31
1813# date2epoch(2024, 2, 1) = 2024.087, epoch2date(2024.087) = 2024, 2, 2 *
1814# date2epoch(2024, 2, 15) = 2024.126, epoch2date(2024.126) = 2024, 2, 16 *
1815# date2epoch(2024, 2, 28) = 2024.161, epoch2date(2024.161) = 2024, 2, 28
1816# date2epoch(2024, 2, 29) = 2024.164, epoch2date(2024.164) = 2024, 3, 1 *
1817# date2epoch(2024, 3, 1) = 2024.167, epoch2date(2024.167) = 2024, 3, 2 *
1818# date2epoch(2024, 3, 15) = 2024.205, epoch2date(2024.205) = 2024, 3, 16 *
1819# date2epoch(2024, 3, 30) = 2024.246, epoch2date(2024.246) = 2024, 3, 31 *
1820# date2epoch(2024, 3, 31) = 2024.249, epoch2date(2024.249) = 2024, 4, 1 *
1821# date2epoch(2024, 4, 1) = 2024.251, epoch2date(2024.251) = 2024, 4, 1
1822# date2epoch(2024, 4, 15) = 2024.290, epoch2date(2024.290) = 2024, 4, 15
1823# date2epoch(2024, 4, 29) = 2024.328, epoch2date(2024.328) = 2024, 4, 29
1824# date2epoch(2024, 4, 30) = 2024.331, epoch2date(2024.331) = 2024, 4, 30
1825# date2epoch(2024, 5, 1) = 2024.333, epoch2date(2024.333) = 2024, 5, 1
1826# date2epoch(2024, 5, 15) = 2024.372, epoch2date(2024.372) = 2024, 5, 15
1827# date2epoch(2024, 5, 30) = 2024.413, epoch2date(2024.413) = 2024, 5, 30
1828# date2epoch(2024, 5, 31) = 2024.415, epoch2date(2024.415) = 2024, 6, 1 *
1829# date2epoch(2024, 6, 1) = 2024.418, epoch2date(2024.418) = 2024, 6, 2 *
1830# date2epoch(2024, 6, 15) = 2024.456, epoch2date(2024.456) = 2024, 6, 16 *
1831# date2epoch(2024, 6, 29) = 2024.495, epoch2date(2024.495) = 2024, 6, 30 *
1832# date2epoch(2024, 6, 30) = 2024.497, epoch2date(2024.497) = 2024, 7, 1 *
1833# date2epoch(2024, 7, 1) = 2024.500, epoch2date(2024.500) = 2024, 7, 1
1834# date2epoch(2024, 7, 15) = 2024.538, epoch2date(2024.538) = 2024, 7, 16 *
1835# date2epoch(2024, 7, 30) = 2024.579, epoch2date(2024.579) = 2024, 7, 30
1836# date2epoch(2024, 7, 31) = 2024.582, epoch2date(2024.582) = 2024, 7, 31
1837# date2epoch(2024, 8, 1) = 2024.585, epoch2date(2024.585) = 2024, 8, 1
1838# date2epoch(2024, 8, 15) = 2024.623, epoch2date(2024.623) = 2024, 8, 15
1839# date2epoch(2024, 8, 30) = 2024.664, epoch2date(2024.664) = 2024, 8, 31 *
1840# date2epoch(2024, 8, 31) = 2024.667, epoch2date(2024.667) = 2024, 9, 1 *
1841# date2epoch(2024, 9, 1) = 2024.669, epoch2date(2024.669) = 2024, 9, 2 *
1842# date2epoch(2024, 9, 15) = 2024.708, epoch2date(2024.708) = 2024, 9, 16 *
1843# date2epoch(2024, 9, 29) = 2024.746, epoch2date(2024.746) = 2024, 9, 30 *
1844# date2epoch(2024, 9, 30) = 2024.749, epoch2date(2024.749) = 2024, 10, 1 *
1845# date2epoch(2024, 10, 1) = 2024.751, epoch2date(2024.751) = 2024, 10, 1
1846# date2epoch(2024, 10, 15) = 2024.790, epoch2date(2024.790) = 2024, 10, 15
1847# date2epoch(2024, 10, 30) = 2024.831, epoch2date(2024.831) = 2024, 10, 30
1848# date2epoch(2024, 10, 31) = 2024.833, epoch2date(2024.833) = 2024, 10, 31
1849# date2epoch(2024, 11, 1) = 2024.836, epoch2date(2024.836) = 2024, 11, 1
1850# date2epoch(2024, 11, 15) = 2024.874, epoch2date(2024.874) = 2024, 11, 15
1851# date2epoch(2024, 11, 29) = 2024.913, epoch2date(2024.913) = 2024, 11, 29
1852# date2epoch(2024, 11, 30) = 2024.915, epoch2date(2024.915) = 2024, 12, 1 *
1853# date2epoch(2024, 12, 1) = 2024.918, epoch2date(2024.918) = 2024, 12, 2 *
1854# date2epoch(2024, 12, 15) = 2024.956, epoch2date(2024.956) = 2024, 12, 16 *
1855# date2epoch(2024, 12, 30) = 2024.997, epoch2date(2024.997) = 2024, 12, 31 *
1856# date2epoch(2024, 12, 31) = 2025.000, epoch2date(2025.000) = 2025, 1, 1 *
1858# 1 WGS84g1150@2004xITRF2000 xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1859# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1860# 2 NAD83cors96@1997xNAD83 xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1861# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1862# 3 ITRF88@2015xETRF2014 xform=xform(tx=-25.9, ty=3.0, tz=171.3, s=-11.89, sx=2.11, sy=13.806, sz=-20.38)
1863# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1864# 4 ITRF89@2015xETRF2000 xform=xform(tx=24.3, ty=19.7, tz=63.7, s=-6.12, sx=2.106, sy=12.74, sz=-20.952)
1865# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1866# 5 ITRF89@2015xETRF2014 xform=xform(tx=-30.9, ty=-33.0, tz=147.3, s=-8.79, sx=2.21, sy=13.806, sz=-20.38)
1867# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1868# 6 ITRF89@2015xETRF2020 xform=xform(tx=32.3, ty=33.9, tz=-148.7, s=9.21, sx=2.236, sy=13.494, sz=-19.218)
1869# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1870# 7 ITRF89@1989xETRF89 xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1871# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
1872# 8 ITRF90@1984xWGS84 xform=xform(tx=60.0, ty=-517.0, tz=-223.0, s=-11.0, sx=18.3, sy=-0.3, sz=7.0)
1873# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1874# 9 ITRF90@2015xETRF2000 xform=xform(tx=29.3, ty=43.7, tz=25.7, s=-2.72, sx=2.106, sy=12.74, sz=-20.952)
1875# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1876# 10 ITRF90@1989xETRF90 xform=xform(tx=19.0, ty=28.0, tz=-23.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1877# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
1878# 11 ITRF90@1997xNAD83 xform=xform(tx=973.0, ty=-1919.2, tz=-482.9, s=-0.9, sx=-25.79, sy=-9.65, sz=-11.66)
1879# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=-0.053, sy=0.742, sz=0.032)
1880# 12 ITRF91@2015xETRF2000 xform=xform(tx=27.3, ty=39.7, tz=9.7, s=-2.42, sx=2.106, sy=12.74, sz=-20.952)
1881# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1882# 13 ITRF91@1989xETRF91 xform=xform(tx=21.0, ty=25.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1883# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
1884# 14 ITRF92@2015xETRF2000 xform=xform(tx=39.3, ty=53.7, tz=3.7, s=-1.02, sx=2.106, sy=12.74, sz=-20.952)
1885# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1886# 15 ITRF92@2015xETRF2014 xform=xform(tx=-15.9, ty=1.0, tz=87.3, s=-3.69, sx=2.21, sy=13.806, sz=-20.38)
1887# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1888# 16 ITRF92@2015xETRF2020 xform=xform(tx=17.3, ty=-0.1, tz=-88.7, s=4.11, sx=2.236, sy=13.494, sz=-19.218)
1889# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1890# 17 ITRF92@1989xETRF92 xform=xform(tx=38.0, ty=40.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1891# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
1892# 18 ITRF93@2015xETRF2000 xform=xform(tx=119.6, ty=49.9, tz=-10.9, s=-2.22, sx=5.466, sy=17.07, sz=-21.342)
1893# rates=rates(tx=2.9, ty=0.2, tz=0.6, s=-0.01, sx=0.191, sy=0.68, sz=-0.862)
1894# 19 ITRF93@2015xETRF2014 xform=xform(tx=64.4, ty=-2.8, tz=72.7, s=-4.89, sx=5.57, sy=18.136, sz=-20.77)
1895# rates=rates(tx=2.8, ty=0.1, tz=2.5, s=-0.12, sx=0.195, sy=0.721, sz=-0.84)
1896# 20 ITRF93@2015xETRF2020 xform=xform(tx=-63.0, ty=3.7, tz=-74.1, s=5.31, sx=-1.124, sy=9.164, sz=-18.828)
1897# rates=rates(tx=-2.8, ty=0.0, tz=-2.7, s=0.12, sx=-0.024, sy=0.329, sz=-0.683)
1898# 21 ITRF93@1989xETRF93 xform=xform(tx=19.0, ty=53.0, tz=-21.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1899# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.32, sy=0.78, sz=-0.67)
1900# 22 ITRF94@2015xETRF2000 xform=xform(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
1901# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1902# 23 ITRF94@2015xETRF2014 xform=xform(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
1903# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1904# 24 ITRF94@2015xETRF2020 xform=xform(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
1905# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1906# 25 ITRF94@1989xETRF94 xform=xform(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1907# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1908# 26 ITRF96@1989xETRF96 xform=xform(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1909# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1910# 27 ITRF97@1989xETRF97 xform=xform(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1911# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1912# 28 ITRF2000@1994xGDA94 xform=xform(tx=-45.91, ty=-29.85, tz=-20.37, s=7.07, sx=-1.6705, sy=0.4594, sz=1.9356)
1913# rates=rates(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
1914# 29 ITRF2000@2015xETRF2000 xform=xform(tx=54.0, ty=51.0, tz=-48.0, s=0.0, sx=2.106, sy=12.74, sz=-20.592)
1915# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.081, sy=0.49, sz=-0.792)
1916# 30 ITRF88@2015xETRF2000 xform=xform(tx=29.3, ty=55.7, tz=87.7, s=-9.22, sx=2.006, sy=12.74, sz=-20.952)
1917# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1918# 31 ITRF88@2015xETRF2020 xform=xform(tx=27.3, ty=-2.1, tz=-172.7, s=12.31, sx=2.336, sy=13.494, sz=-19.218)
1919# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1920# 32 ITRF96@2015xETRF2000 xform=xform(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
1921# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1922# 33 ITRF97@2015xETRF2000 xform=xform(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
1923# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1924# 34 ITRF2000@2015xETRF2014 xform=xform(tx=-1.2, ty=-1.7, tz=35.6, s=-2.67, sx=2.21, sy=13.806, sz=-20.02)
1925# rates=rates(tx=-0.1, ty=-0.1, tz=1.9, s=-0.11, sx=0.085, sy=0.531, sz=-0.77)
1926# 35 ITRF90@2015xETRF2014 xform=xform(tx=-25.9, ty=-9.0, tz=109.3, s=-5.39, sx=2.21, sy=13.806, sz=-20.38)
1927# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1928# 36 ITRF90@2015xETRF2020 xform=xform(tx=27.3, ty=9.9, tz=-110.7, s=5.81, sx=2.236, sy=13.494, sz=-19.218)
1929# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1930# 37 ITRF91@2015xETRF2014 xform=xform(tx=-27.9, ty=-13.0, tz=93.3, s=-5.09, sx=2.21, sy=13.806, sz=-20.38)
1931# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1932# 38 ITRF96@2015xETRF2014 xform=xform(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
1933# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1934# 39 ITRF97@2015xETRF2014 xform=xform(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
1935# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1936# 40 ITRF2000@2015xETRF2020 xform=xform(tx=2.6, ty=2.6, tz=-37.0, s=3.09, sx=2.236, sy=13.494, sz=-19.578)
1937# rates=rates(tx=0.1, ty=0.2, tz=-2.1, s=0.11, sx=0.086, sy=0.519, sz=-0.753)
1938# 41 ITRF91@2015xETRF2020 xform=xform(tx=29.3, ty=13.9, tz=-94.7, s=5.51, sx=2.236, sy=13.494, sz=-19.218)
1939# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1940# 42 ITRF96@2015xETRF2020 xform=xform(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
1941# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1942# 43 ITRF97@2015xETRF2020 xform=xform(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
1943# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1944# 44 ITRF2000@2020xGDA2020 xform=xform(tx=-105.52, ty=51.58, tz=231.68, s=3.55, sx=4.2175, sy=6.3941, sz=0.8617)
1945# rates=rates(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
1946# 45 ITRF2000@1988xITRF88 xform=xform(tx=2.47, ty=1.15, tz=-9.79, s=8.95, sx=0.1, sy=0.0, sz=-0.18)
1947# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1948# 46 ITRF2000@1988xITRF89 xform=xform(tx=2.97, ty=4.75, tz=-7.39, s=5.85, sx=0.0, sy=0.0, sz=-0.18)
1949# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1950# 47 ITRF2000@1988xITRF90 xform=xform(tx=2.47, ty=2.35, tz=-3.59, s=2.45, sx=0.0, sy=0.0, sz=-0.18)
1951# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1952# 48 ITRF2000@1988xITRF91 xform=xform(tx=26.7, ty=27.5, tz=-19.9, s=2.15, sx=0.0, sy=0.0, sz=-0.18)
1953# rates=rates(tx=0.0, ty=-0.6, tz=-1.4, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1954# 49 ITRF2000@1988xITRF92 xform=xform(tx=1.47, ty=1.35, tz=-1.39, s=0.75, sx=0.0, sy=0.0, sz=-0.18)
1955# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1956# 50 ITRF2000@1988xITRF93 xform=xform(tx=12.7, ty=6.5, tz=-20.9, s=1.95, sx=-0.39, sy=0.8, sz=-1.14)
1957# rates=rates(tx=-2.9, ty=-0.2, tz=-0.6, s=0.01, sx=-0.11, sy=-0.19, sz=0.07)
1958# 51 ITRF2000@1997xITRF94 xform=xform(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
1959# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1960# 52 ITRF2000@1997xITRF96 xform=xform(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
1961# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1962# 53 ITRF97@1997xITRF96 xform=xform(tx=-2.07, ty=-0.21, tz=9.95, s=-0.93496, sx=0.1267, sy=-0.22355, sz=-0.06065)
1963# rates=rates(tx=0.69, ty=-0.1, tz=1.86, s=-0.19201, sx=0.01347, sy=-0.01514, sz=0.00027)
1964# 54 ITRF2000@1997xITRF97 xform=xform(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
1965# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=-0.02)
1966# 55 ITRF2000@1997xNAD83 xform=xform(tx=995.6, ty=-1901.3, tz=-521.5, s=0.615, sx=-25.915, sy=-9.426, sz=-11.599)
1967# rates=rates(tx=0.7, ty=-0.7, tz=0.5, s=-0.182, sx=-0.06667, sy=0.75744, sz=0.05133)
1968# 56 ITRF2005@2015xETRF2000 xform=xform(tx=51.1, ty=51.7, tz=-80.8, s=1.6, sx=2.106, sy=12.74, sz=-20.592)
1969# rates=rates(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
1970# 57 ITRF2005@1989xETRF2005 xform=xform(tx=56.0, ty=48.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1971# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.054, sy=0.518, sz=-0.781)
1972# 58 ITRF2005@1994xGDA94 xform=xform(tx=-79.73, ty=-6.86, tz=38.03, s=6.636, sx=0.0351, sy=-2.1211, sz=-2.1411)
1973# rates=rates(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
1974# 59 ITRF2005@1997xNAD83 xform=xform(tx=996.3, ty=-1902.4, tz=-521.9, s=0.775, sx=-25.915, sy=-9.426, sz=-11.599)
1975# rates=rates(tx=0.5, ty=-0.6, tz=-1.3, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
1976# 60 ITRF2005@2015xETRF2014 xform=xform(tx=-4.1, ty=-1.0, tz=2.8, s=-1.07, sx=2.21, sy=13.806, sz=-20.02)
1977# rates=rates(tx=-0.3, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
1978# 61 ITRF2005@2015xETRF2020 xform=xform(tx=5.5, ty=1.9, tz=-4.2, s=1.49, sx=2.236, sy=13.494, sz=-19.578)
1979# rates=rates(tx=0.3, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
1980# 62 ITRF2005@2020xGDA2020 xform=xform(tx=40.32, ty=-33.85, tz=-16.72, s=4.286, sx=-1.2893, sy=-0.8492, sz=-0.3342)
1981# rates=rates(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
1982# 63 ITRF2005@2000xITRF2000 xform=xform(tx=0.1, ty=-0.8, tz=-5.8, s=0.4, sx=0.0, sy=0.0, sz=0.0)
1983# rates=rates(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
1984# 64 ITRF2008@1994xGDA94 xform=xform(tx=-84.68, ty=-19.42, tz=32.01, s=9.71, sx=-0.4254, sy=2.2578, sz=2.4015)
1985# rates=rates(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
1986# 65 ITRF2008@1997xNAD83 xform=xform(tx=993.43, ty=-1903.31, tz=-526.55, s=1.71504, sx=-25.91467, sy=-9.42645, sz=-11.59935)
1987# rates=rates(tx=0.79, ty=-0.6, tz=-1.34, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
1988# 66 ITRF96@1997xNAD83 xform=xform(tx=991.0, ty=-190.72, tz=-512.9, s=0.0, sx=25.79, sy=9.65, sz=11.66)
1989# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0532, sy=-0.7423, sz=-0.0316)
1990# 67 ITRF2008@2015xETRF2000 xform=xform(tx=53.6, ty=50.8, tz=-85.5, s=2.54, sx=2.106, sy=12.74, sz=-20.592)
1991# rates=rates(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
1992# 68 ITRF2008@2015xETRF2014 xform=xform(tx=-1.6, ty=-1.9, tz=-1.9, s=-0.13, sx=2.21, sy=13.806, sz=-20.02)
1993# rates=rates(tx=0.0, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
1994# 69 ITRF2008@2015xETRF2020 xform=xform(tx=3.0, ty=2.8, tz=0.5, s=0.55, sx=2.236, sy=13.494, sz=-19.578)
1995# rates=rates(tx=0.0, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
1996# 70 ITRF2008@2020xGDA2020 xform=xform(tx=13.79, ty=4.55, tz=15.22, s=2.5, sx=0.2808, sy=0.2677, sz=-0.4638)
1997# rates=rates(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
1998# 71 ITRF2008@2000xITRF2000 xform=xform(tx=-1.9, ty=-1.7, tz=-10.5, s=1.34, sx=0.0, sy=0.0, sz=0.0)
1999# rates=rates(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
2000# 72 ITRF2008@2000xITRF88 xform=xform(tx=22.8, ty=2.6, tz=-125.2, s=10.41, sx=0.1, sy=0.0, sz=0.06)
2001# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
2002# 73 ITRF2008@2000xITRF89 xform=xform(tx=27.8, ty=38.6, tz=-101.2, s=7.31, sx=0.0, sy=0.0, sz=0.06)
2003# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
2004# 74 ITRF2008@2000xITRF90 xform=xform(tx=22.8, ty=14.6, tz=-63.2, s=3.91, sx=0.0, sy=0.0, sz=0.06)
2005# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
2006# 75 ITRF2008@2000xITRF91 xform=xform(tx=24.8, ty=18.6, tz=-47.2, s=3.61, sx=0.0, sy=0.0, sz=0.06)
2007# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
2008# 76 ITRF2008@2000xITRF92 xform=xform(tx=12.8, ty=4.6, tz=-41.2, s=2.21, sx=0.0, sy=0.0, sz=0.06)
2009# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
2010# 77 ITRF2008@2000xITRF93 xform=xform(tx=-24.0, ty=2.4, tz=-38.6, s=3.41, sx=-1.71, sy=-1.48, sz=-0.3)
2011# rates=rates(tx=-2.8, ty=-0.1, tz=-2.4, s=0.09, sx=-0.11, sy=-0.19, sz=0.07)
2012# 78 ITRF2008@2000xITRF94 xform=xform(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
2013# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
2014# 79 ITRF2008@2000xITRF96 xform=xform(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
2015# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
2016# 80 ITRF2008@2000xITRF97 xform=xform(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
2017# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
2018# 81 ITRF2008@2005xITRF2005 xform=xform(tx=-0.5, ty=-0.9, tz=-4.7, s=0.94, sx=0.0, sy=0.0, sz=0.0)
2019# rates=rates(tx=0.3, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
2020# 82 ITRF2014@2015xETRF2000 xform=xform(tx=55.2, ty=52.7, tz=-83.6, s=2.67, sx=2.106, sy=12.74, sz=-20.592)
2021# rates=rates(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
2022# 83 ITRF2014@2015xETRF2014 xform=xform(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.21, sy=13.806, sz=-20.02)
2023# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
2024# 84 ITRF2014@2015xETRF2020 xform=xform(tx=1.4, ty=0.9, tz=-1.4, s=0.42, sx=2.236, sy=13.494, sz=-19.578)
2025# rates=rates(tx=0.0, ty=0.1, tz=-0.2, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
2026# 85 ITRF2014@2020xGDA2020 xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
2027# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=1.50379, sy=1.18346, sz=1.20716)
2028# 86 ITRF2014@2010xITRF2000 xform=xform(tx=0.7, ty=1.2, tz=-26.1, s=2.12, sx=0.0, sy=0.0, sz=0.0)
2029# rates=rates(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.0, sy=0.0, sz=0.0)
2030# 87 ITRF2014@2010xITRF2005 xform=xform(tx=2.6, ty=1.0, tz=-2.3, s=0.92, sx=0.0, sy=0.0, sz=0.0)
2031# rates=rates(tx=0.3, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
2032# 88 ITRF2014@2010xITRF2008 xform=xform(tx=1.6, ty=1.9, tz=2.4, s=-0.02, sx=0.0, sy=0.0, sz=0.0)
2033# rates=rates(tx=0.0, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
2034# 89 ITRF2014@2010xITRF88 xform=xform(tx=25.4, ty=-0.5, tz=-154.8, s=11.29, sx=0.1, sy=0.0, sz=0.26)
2035# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2036# 90 ITRF2014@2010xITRF89 xform=xform(tx=30.4, ty=35.5, tz=-130.8, s=8.19, sx=0.0, sy=0.0, sz=0.26)
2037# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2038# 91 ITRF2014@2010xITRF90 xform=xform(tx=25.4, ty=11.5, tz=-92.8, s=4.79, sx=0.0, sy=0.0, sz=0.26)
2039# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2040# 92 ITRF2014@2010xITRF91 xform=xform(tx=27.4, ty=15.5, tz=-76.8, s=4.49, sx=0.0, sy=0.0, sz=0.26)
2041# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2042# 93 ITRF2014@2010xITRF92 xform=xform(tx=15.4, ty=1.5, tz=-70.8, s=3.09, sx=0.0, sy=0.0, sz=0.26)
2043# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2044# 94 ITRF2014@2010xITRF93 xform=xform(tx=-50.4, ty=3.3, tz=-60.2, s=4.29, sx=-2.81, sy=-3.38, sz=0.4)
2045# rates=rates(tx=-2.8, ty=-0.1, tz=-2.5, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
2046# 95 ITRF2014@2010xITRF94 xform=xform(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
2047# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2048# 96 ITRF2014@2010xITRF96 xform=xform(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
2049# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2050# 97 ITRF2014@2010xITRF97 xform=xform(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
2051# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2052# 98 ITRF2020@2015xETRF2000 xform=xform(tx=53.8, ty=51.8, tz=-82.2, s=2.25, sx=2.106, sy=12.74, sz=-20.592)
2053# rates=rates(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
2054# 99 ITRF2020@2015xETRF2014 xform=xform(tx=-1.4, ty=-0.9, tz=1.4, s=0.42, sx=2.21, sy=13.806, sz=-20.02)
2055# rates=rates(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
2056# 100 ITRF2020@2015xETRF2020 xform=xform(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.236, sy=13.494, sz=-19.578)
2057# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
2058# 101 ITRF2020@2015xITRF2000 xform=xform(tx=-0.2, ty=0.8, tz=-34.2, s=2.25, sx=0.0, sy=0.0, sz=0.0)
2059# rates=rates(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.0, sy=0.0, sz=0.0)
2060# 102 ITRF2020@2015xITRF2005 xform=xform(tx=2.7, ty=0.1, tz=-1.4, s=0.65, sx=0.0, sy=0.0, sz=0.0)
2061# rates=rates(tx=0.3, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
2062# 103 ITRF2020@2015xITRF2008 xform=xform(tx=0.2, ty=1.0, tz=3.3, s=-0.29, sx=0.0, sy=0.0, sz=0.0)
2063# rates=rates(tx=0.0, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
2064# 104 ITRF2020@2015xITRF2014 xform=xform(tx=-1.4, ty=-0.9, tz=1.4, s=-0.42, sx=0.0, sy=0.0, sz=0.0)
2065# rates=rates(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.0, sy=0.0, sz=0.0)
2066# 105 ITRF2020@2015xITRF88 xform=xform(tx=24.5, ty=-3.9, tz=-169.9, s=11.47, sx=0.1, sy=0.0, sz=0.36)
2067# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2068# 106 ITRF2020@2015xITRF89 xform=xform(tx=29.5, ty=32.1, tz=-145.9, s=8.37, sx=0.0, sy=0.0, sz=0.36)
2069# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2070# 107 ITRF2020@2015xITRF90 xform=xform(tx=24.5, ty=8.1, tz=-107.9, s=4.97, sx=0.0, sy=0.0, sz=0.36)
2071# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2072# 108 ITRF2020@2015xITRF91 xform=xform(tx=26.5, ty=12.1, tz=-91.9, s=4.67, sx=0.0, sy=0.0, sz=0.36)
2073# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2074# 109 ITRF2020@2015xITRF92 xform=xform(tx=14.5, ty=-1.9, tz=-85.9, s=3.27, sx=0.0, sy=0.0, sz=0.36)
2075# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2076# 110 ITRF2020@2015xITRF93 xform=xform(tx=-65.8, ty=1.9, tz=-71.3, s=4.47, sx=-3.36, sy=-4.33, sz=0.75)
2077# rates=rates(tx=-2.8, ty=-0.2, tz=-2.3, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
2078# 111 ITRF2020@2015xITRF94 xform=xform(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
2079# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2080# 112 ITRF2020@2015xITRF96 xform=xform(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
2081# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2082# 113 ITRF2020@2015xITRF97 xform=xform(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
2083# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)