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) 2006-2022 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, _Named, \
84 _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__ = '24.05.13'
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 expected
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(name or self.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=NN):
387 '''Return the inverse of this transform.
389 @kwarg name: Optional, unique name (C{str}).
391 @return: Inverse (L{TransformXform}), unregistered.
392 '''
393 r = Transform.inverse(name=name)
394 r._Xform = r.Xform.inverse()
395 return r
397 def rename(self, name=NN):
398 '''Change this transform's name.
400 @arg name: New name (C{str}), overriding this transform's Xform's name.
402 @return: The previous name (C{str}).
403 '''
404 X = self.Xform
405 n = name or (X.toStr() if X else NN)
406 return Transform.rename(self, n)
408 def toRefFrame(self, point, name=NN): # PYCHOK signature
409 '''Convert an ellipsoidal point using this transform and Xform.
411 @arg point: The point to convert (C{Cartesian} or C{LatLon}).
413 @return: A copy of the B{C{point}}, converted I{directly} to
414 this transform's Xform's C{refName2} and C{epoch}.
416 @note: The B{C{point}}'s original C{reframe} and C{epoch} are
417 I{ignored}, its C{datum} and C{height} are preserved
418 but I{not} taken into account.
419 '''
420 _ = _xellipsoidall(point)
421 p = point.dup() if self.isunity else point.toTransform(self)
422 X = self.Xform
423 if X: # see _toRefFrame below
424 p._reframe = X.reframe2
425 p._epoch = X.epoch
426 p.rename(name or self.name)
427 return p
429 def toTransform(self, epoch1, **epoch2_inverse):
430 '''Return this transform observed at B{C{epoch1}} as a Helmert
431 L{TransformXform}, optionally at B{C{epoch2 or epoch1}}.
433 @arg epoch1: Epoch to observe I{from} (C{scalar}).
434 @kwarg epoch2_inverse: Optional C{B{epoch2}=None} to observe
435 I{to} and C{B{inverse}=False}, see method
436 L{toTransform<TRFXform.toTransform>} from
437 L{TRFXform}.
439 @return: The Helmert transform (L{TransformXform}).
441 @raise TRFError: Invalid B{C{epoch1}}, B{C{epoch2}} or
442 missing Xform.
443 '''
444 X = self.Xform
445 if X is None:
446 raise TRFError(Xform=X, txt=MISSING)
447 return X.toTransform(epoch1, **epoch2_inverse)
449 def transform2(self, x, y, z, vx=0, vy=0, vz=0, inverse=False, factor=_MM2M,
450 **Vector_and_kwds):
451 '''Transform a (cartesian) position I{with} velocities, forward or inverse.
453 @arg x: X coordinate (C{meter}).
454 @arg y: Y coordinate (C{meter}).
455 @arg z: Z coordinate (C{meter}).
456 @kwarg vx: X velocity (C{meter-per-year}).
457 @kwarg vy: Y velocity (C{meter-per-year}).
458 @kwarg vz: Z velocity (C{meter-per-year}).
459 @kwarg inverse: If C{True}, apply the inverse transform (C{bool}).
460 @kwarg factor: Factor to scale this Xform's C{rates} (C{scalar}),
461 default from C{milli-meter-} to C{meter-per-year},
462 from C{milli-arc-} to C{arc-seconds-per-year} and
463 from C{ppB-} to C{ppM-per-year}.
464 @kwarg Vector_and_kwds: An optional, (3-D) C{B{Vector}=None} or cartesian
465 class and additional C{B{Vector}} keyword arguments to
466 return the transformed position and the I{velocities}.
468 @return: 2-Tuple C{(position, velocities)}, the tranformed C{position}
469 and C{velocities}, each a L{Vector3Tuple}C{(x, y, z)} unless
470 some B{C{Vector_and_kwds}} are specified.
472 @note: If this transform's Xform is missing, the returned C{velocities}
473 are the given ones, I{un-transformed}.
475 @raise TypeError: Non-scalar B{C{factor}}.
477 @see: Soler, T. & Snay, R.A. "Transforming Positions and Velocities ...", U{equations
478 (4) and (5)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>}
479 and HTDP functions C{VTRANF} and C{VTRANF_IERS} in file U{HTDP/hdtp.f
480 <https://Geodesy.NOAA.gov/TOOLS/Htdp/Htdp.shtml>}.
481 '''
482 p = self.transform(x, y, z, inverse=inverse, **Vector_and_kwds)
483 X = self.Xform
484 if X is not None:
485 r = X.rates * factor # equ (4) ...
486 # vx', vy', vz' = (.tx + x * .s + y * .rz - z * .ry,
487 # .ty - x * .rz + y * .s + z * .rx,
488 # .tz + x * .ry - y * .rx + z * .s)
489 # using counter-/clockwise .rx, .ry, and .rz
490 V = Transform(**dict(r.items())) # unregistered
491 _ = V._s_s1(0) # XXX r.s?
492 v = V.transform(p.x, p.y, p.z, inverse=inverse)
493 # + (vx, vy, vz) like HTDP
494 vx += v.x
495 vy += v.y
496 vz += v.z
497 v = p.dup(x=vx, y=vy, z=vz, name=NN(p.name, _vs_))
498 return p, v
500 def velocities(self, factor=_MM2M, **Vector_and_kwds):
501 '''Compute the X, Y and Z I{velocities} of this transform.
503 @kwarg factor: Factor to scale this Xform's C{rates} (C{scalar}),
504 default from C{milli-meter-} to C{meter-per-year},
505 from C{milli-arc-} to C{arc-seconds-per-year} and
506 from C{ppB-} to C{ppM-per-year}.
507 @kwarg Vector_and_kwds: An optional, (3-D) C{B{Vector}=None} or
508 cartesian class and additional C{B{Vector}} keyword
509 arguments to return the I{velocities}.
511 @return: A L{Vector3Tuple}C{(x, y, z)} unless some B{C{Vector_and_kwds}}
512 are specified or C{None} if this transform's Xform is missing.
514 @raise TypeError: Non-scalar B{C{factor}}.
516 @see: Altamimi, Z. "EUREF-TN-1-Jan-31-2024", U{Appendix A, equation (3)
517 <http://ETRS89.ENSG.IGN.FR/pub/EUREF-TN-1-Jan-31-2024.pdf>} and
518 method L{transform2<TransformXform.transform2>}.
519 '''
520 v = X = self.Xform
521 if X is not None:
522 r = X.rates * factor # equ (3) ...
523 V = self.dup(tx=r.sx, ty=r.sy, tz=r.sz, _Xform=None, # Xyy-dot
524 name=NN(self.name, _vs_)) # unregistered
525 _ = V._s_s1(0)
526 v = V.transform(r.tx, r.ty, r.tz, inverse=False, # Xyy
527 **Vector_and_kwds)
528 return v
530 @property_doc_(''' the Xform (L{TRFXform}).''')
531 def Xform(self):
532 '''Get this Helmert transform's Xform (L{TRFXform} or C{None}).
533 '''
534 return self._Xform
536 @Xform.setter # PYCHOK setter!
537 def Xform(self, Xform):
538 '''Set this Helmert transform's Xform (L{TRFXform}).
540 @raise TypeError: Invalid B{C{Xform}}.
541 '''
542 _xinstanceof(TRFXform, Xform=Xform)
543 self._Xform = Xform
546class TRFXform7Tuple(_NamedTuple):
547 '''7-Tuple C{(tx, ty, tz, s, sx, sy, sz)} of conversion parameters with
548 translations C{tx}, C{ty} and C{tz} in C{milli-meter}, scale C{s} in
549 C{ppB} and rotations C{sx}, C{sy} and C{sz} in C{milli-arc-seconds}.
550 For C{rates} all are C{units-per-year}.
552 @note: The parameters are also named as C{(Tx, Ty, Tz, D, Rx, Ry, Rz)}
553 or C{(T1, T2, T3, D, R1, R2, R3)}.
555 @see: Class L{TransformXform}'s matching keyword argument names.
556 '''
557 _Names_ = _Names7 # ('tx', 'ty', 'tz', _s_, 'sx', 'sy', 'sz') == TransformXform.__init__
558 _Units_ = (_MM, _MM, _MM, _PPB, _MAS, _MAS, _MAS)
560 def __add__(self, other):
561 return self._add_sub(other, True)
563 def __eq__(self, other):
564 return isinstance(other, TRFXform7Tuple) and _equall(other, self)
565 # PYCHOK and self.name == other.name
567 def __hash__(self):
568 return _NamedTuple.__hash__(self)
570 def __mul__(self, factor):
571 _xscalar(factor=factor)
572 return type(self)((x * factor for x in self), name=_STAR_) # .fsums._mul_op
574 def __neg__(self):
575 return self.inverse()
577 def __sub__(self, other):
578 return self._add_sub(other, False)
580 def _add_sub(self, other, p_):
581 '''(INTERNAL) Return C{this +/- other} L{TRFXform7Tuple}.
582 '''
583 _xinstanceof(TRFXform7Tuple, other=other)
584 op = _operator.add if p_ else _operator.sub
585 return type(self)(map(op, self, other), name=_PLUS_ if p_ else _MINUS_)
587 def inverse(self, name=NN):
588 '''Return the inverse of this transform.
590 @kwarg name: Optional name (C{str}).
592 @return: Inverse (L{TransformXform}).
593 '''
594 n = name or _negastr(self.name)
595 return type(self)(map(neg, self), name=n)
597 @Property_RO
598 def isunity(self):
599 '''Is this a C{unity, identity} transform (C{bool}).
600 '''
601 return not any(self)
604class TRFXform(_Named):
605 '''A Terrestrial Reference Frame (TRF) converter between two
606 reference frames observed at an C{epoch}.
607 '''
608 _epoch = _EP0CH
609 _epoch_d = _0_0
610 _indir_d = NN # refName
611 _inver_d = False
612 refName1 = \
613 refName2 = NN
614 rates = \
615 xform = None
617 def __init__(self, refName1, refName2, epoch=None, xform=None,
618 rates=None, name=NN):
619 '''New L{TRFXform} TRF converter.
621 @arg refName1: Source reframe (C{str}), converting I{from}.
622 @arg refName2: Destination reframe (C{str}), converting I{to}.
623 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str}).
624 @kwarg xform: I{Transform} parameters at B{C{epoch}} (L{TRFXform7Tuple}).
625 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), like B{C{xform}},
626 but in C{units-per-year}.
627 @kwarg name: Optional name (C{str}), overriding the default from method
628 L{toStr<TRFXform.toStr>}.
630 @raise TRFError: Invalid B{C{refName1}}, B{C{refName2}} or B{C{epoch}}.
632 @raise TypeError: Invalid B{C{xform}} or B{C{rates}}.
634 @see: Functions L{trfXform}, L{trfTransform0} and L{trfTransforms}.
635 '''
636 self.refName1 = _stref(refName1=refName1)
637 self.refName2 = _stref(refName2=refName2)
638 _xinstanceof(TRFXform7Tuple, xform=xform, rates=rates)
639 self.epoch = epoch
640 self.xform = xform
641 self.rates = rates
642 self.rename(name or self.toStr())
644 def __add__(self, other):
645 return self._add_sub(other, True)
647 def __eq__(self, other):
648 return isinstance(other, TRFXform) and other.epoch == self.epoch \
649 and other.xform == self.xform \
650 and other.rates == self.rates
652# def __hash__(self):
653# return hash((self.epoch, self.xform, self.rates))
655 def __lt__(self, other): # for sorting
656 return isinstance(other, TRFXform) and (self.refName1 < other.refName1
657 or self.refName2 < other.refName2
658 or self.epoch < other.epoch)
660 def __neg__(self):
661 return self.inverse()
663 def __repr__(self):
664 return self.toRepr()
666 def __str__(self):
667 return self.toStr()
669 def __sub__(self, other):
670 return self._add_sub(other, False)
672 def _add_sub(self, other, p_, *n1_n2_n): # in _indirects below
673 '''(INTERNAL) Summate C{this +/- other} Xform at C{this.epoch}.
675 @see: U{Appendix, Table 7, last column "Sum of the previous ..."
676 <https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf">}
677 '''
678 _xinstanceof(TRFXform, other=other)
679 X1 = self
680 e1 = X1.epoch
681 X2 = other.toEpoch(e1) # if other.epoch != e1 else other
683 n1, n2, n = n1_n2_n or _n1_n2_n3(X1, X2)
685 X = type(X1)(n1, n2, epoch=e1, xform=X1.xform._add_sub(X2.xform, p_),
686 rates=X1.rates._add_sub(X2.rates, p_),
687 name=_sumstr(X1.name, X2.name, p_))
688 X._epoch_d = X1.epoched + X2.epoched
689 X._indir_d = n # reframe?
690 X._inver_d = X1.inversed and X2.inversed
691 return X
693 def _at(self, epoch):
694 '''(INTERNAL) Return C{"self.nameB{@}epoch"}.
695 '''
696 n = self.name
697 if epoch != self.epoch:
698 _e = _AT_(NN, epoch)
699 if not n.endswith(_e):
700 n = NN(n, _e)
701 return n
703 @property_doc_(''' the epoch, fractional year (L{Epoch}).''')
704 def epoch(self):
705 '''Get the epoch (L{Epoch}).
706 '''
707 return self._epoch
709 @epoch.setter # PYCHOK setter!
710 def epoch(self, epoch):
711 '''Set the epoch (L{Epoch}, C{scalar} or C{str}).
713 @raise TRFError: Invalid B{C{epoch}}.
714 '''
715 e = _Epoch(epoch)
716 if self._epoch != e:
717 self.rename(self._at(e))
718 self._epoch = e
720 @property_RO
721 def epoched(self):
722 '''Get this Xform's aggregate I{epoch} deltas (C{float}).
723 '''
724 return self._epoch_d
726 @property_RO
727 def indirected(self):
728 '''Is this an I{indirected} Xform? (C{str} of space-separated
729 refNames) or C{NN}.
730 '''
731 return self._indir_d
733 def inverse(self, name=NN):
734 '''Return this Xform {inversed}, C{refName1} and C{-2} swapped.
736 @return: The inverse (L{TRFXform}).
737 '''
738 n = name or _negastr(self.name)
739 X = self.dup(refName1=self.refName2, xform=-self.xform,
740 refName2=self.refName1, rates=-self.rates,
741 name=n, _inver_d=not self.inversed)
742# X = type(self)(self.refName2, self.refName1, epoch= self.epoch,
743# xform=-self.xform,
744# rates=-self.rates, name=n)
745# if self.epoched:
746# X._epoch_d = self.epoched
747# if self.indirected:
748# X._indir_d = self.indirected
749# if not self.inversed:
750# X._inver_d = True
751 return X
753 @property_RO
754 def inversed(self):
755 '''Is this an I{inversed} Xform? (C{bool}).
756 '''
757 return self._inver_d
759 def _reframe(self, name, datum=_GRS80):
760 '''(INTERNAL) Get an un-/registered frame.
761 '''
762 r = RefFrames.get(name)
763 if r is None or r.datum != datum:
764 r = RefFrame(self.epoch, datum)
765 r.name = name # unregistered
766 return r
768 @property_RO
769 def reframe1(self):
770 '''Get the un-/registered I{from} frame (C{RefFrame}).
771 '''
772 return self._reframe(self.refName1)
774 @property_RO
775 def reframe2(self):
776 '''Get the un-/registered I{to} frame (C{RefFrame}).
777 '''
778 return self._reframe(self.refName2)
780 def rename(self, name=NN):
781 '''Change this Xform's name.
783 @arg name: New name (C{str}), overriding the base
784 name C{"refName1B{@}epochB{x}refName2"}.
786 @return: The old name (C{str}).
787 '''
788 return _Named.rename(self, name or self.toStr())
790 def toEpoch(self, epoch):
791 '''Convert this Xform to B{C{epoch}}, if needed.
793 @arg epoch: Epoch, fractional year (C{Epoch}, C{scalar}
794 or C{str}).
796 @return: This Xform or a copy converted to B{C{epoch}}.
798 @raise TRFError: Invalid B{C{epoch}}.
799 '''
800 e = _Epoch(epoch)
801 X, d = self, e - self.epoch
802 if d:
803 t = X.xform + X.rates * d
804 X = X.dup(epoch=e, xform=t, name=X._at(e))
805 X._epoch_d += fabs(d)
806 return X
808 def toHelmert(self, factor=_MM2M):
809 '''Return the Helmert transform from this Xform scaled accordingly.
811 @kwarg factor: Factor to scale this Xform's C{xform} (C{scalar}),
812 default from C{milli-meter-} to C{meter-}, from
813 C{milli-arc-} to C{arc-seconds} and from C{ppB}
814 to C{ppM}.
816 @return: The Helmert transform (L{TransformXform}).
817 '''
818 h = self.xform * factor
819 H = TransformXform(**dict(h.items()))
820 H.name = self.name # unregistered
821 H.Xform = self
822 return H
824 def toRefFrame(self, point, datum=_GRS80, **epoch_epoch2_name):
825 '''Convert an ellipsoidal point from this Xform's C{refName1} and
826 C{epoch} to this Xform's C{refName2} and C{epoch2 or epoch}.
828 @arg point: The point to convert (C{Cartesian} or C{LatLon}).
829 @kwarg datum: Optional datum to define a temporary L{RefFrame} from
830 this Xform's C{refName1} or C{refName2} (C{datum}).
831 @kwarg epoch_epoch2_name: Optional keyword arguments C{B{epoch}=None},
832 B{C{epoch2}=None} and C{B{name}=refName1}.
834 @return: A copy of the B{C{point}}, converted and renamed.
836 @see: Method L{RefFrame.toRefFrame} for more details.
837 '''
838 r1 = self._reframe(self.refName1, datum=datum)
839 r2 = self._reframe(self.refName2, datum=datum)
840 return _toRefFrame(point, r2, reframe=r1,
841 **_xkwds(epoch_epoch2_name, name=r1.name))
843 def toRepr(self, **unused): # PYCHOK signature
844 '''Return the represention of this Xform (C{str}).
845 '''
846 return unstr(self.classname, name=self.name, epoch=self.epoch)
848 def toStr(self, epoch=None, **unused): # PYCHOK signature
849 '''Return this Xform as C{"refName1B{@}epochB{x}refName2"} (C{str}).
851 @kwarg epoch: Epoch (C{Epoch}, C{scalar} or C{str}), overriding
852 this Xform's epoch.
853 '''
854 e = self.epoch if epoch is None else _Epoch(epoch)
855 return NN(_AT_(self.refName1, e), _x_, self.refName2)
857 def toTransform(self, epoch=None, epoch2=None, inverse=False):
858 '''Combine this Xform observed at B{C{epoch}} into a Helmert
859 L{TransformXform}, optionally at B{C{epoch2 or epoch}}.
861 @kwarg epoch: Epoch to observe I{from} (C{scalar}),
862 overriding this converter's epoch.
863 @kwarg epoch2: Optional epoch to observe I{to} (C{scalar}),
864 overriding B{C{epoch}}.
865 @kwarg inverse: Use the Xform's inverse (C{bool}).
867 @return: The Helmert transform (L{TransformXform}).
869 @raise TRFError: Invalid B{C{epoch}} or B{C{epoch2}}.
871 @see: Method L{toHelmert}.
872 '''
873 if epoch2 is None:
874 e = self.epoch if epoch is None else epoch
875 elif isinstance(epoch2, Epoch):
876 e = epoch2
877 else:
878 e = Epoch(epoch2=epoch2)
879 X = self.toEpoch(e)
880 if inverse:
881 X = X.inverse()
882 return X.toHelmert()
885def date2epoch(year, month, day):
886 '''Return the C{epoch} for a calendar day.
888 @arg year: Year of the date (C{scalar}).
889 @arg month: Month in the B{C{year}} (C{scalar}, 1..12).
890 @arg day: Day in the B{C{month}} (C{scalar}, 1..31).
892 @return: Epoch, the fractional year (C{float}).
894 @raise TRFError: Invalid B{C{year}}, B{C{month}} or B{C{day}}.
896 @note: Any B{C{year}} is considered a leap year, i.e. having
897 29 days in February.
898 '''
899 try:
900 y, m, d = map1(int, year, month, day)
901 if y > 0 and 1 <= m <= 12 and 1 <= d <= _mDays[m]:
902 e = y + float(sum(_mDays[:m]) + d) / _366_0
903 return Epoch(e, low=0)
905 raise ValueError # _invalid_
906 except (TRFError, TypeError, ValueError) as x:
907 raise TRFError(year=year, month=month, day=day, cause=x)
910def _direct(n1, n2):
911 '''(INTERNAL) Get the C{n1} to C{n2} Xform or C{None}.
912 '''
913 r = RefFrames.get(n1)
914 return r._Xto.get(n2, None) if r else None
917def _Epoch(e, **kwds):
918 '''(INTERNAL) Get the C{Epoch(B{e})}.
919 '''
920 return e if isinstance(e, Epoch) and not kwds else Epoch(e, **kwds)
923def epoch2date(epoch):
924 '''Return the date for a reference frame C{epoch}.
926 @arg epoch: Fractional year (C{scalar}).
928 @return: 3-Tuple C{(year, month, day)}.
930 @raise TRFError: Invalid B{C{epoch}}.
932 @note: Any B{C{year}} is considered a leap year, i.e. having
933 29 days in February.
934 '''
935 e = Epoch(epoch, low=0)
936 y = int(e)
937 d = int(_ceil((e - y) * _366_0))
938 for m, n in enumerate(_mDays[1:]):
939 if d > n:
940 d -= n
941 else:
942 break
943 return y, (m + 1), max(1, d)
946def _eXhaustives(n1, n2):
947 '''(INTERNAL) Yield all I{coalesced} Xforms from C{n1} to {n2}
948 via I{any number of} intermediate reframe conversions.
949 '''
950 def _k2(item):
951 return -item[1].epoch # most recent first
953 R = dict(RefFrames)
954 r = R.pop(n1, None)
955 if r:
956 Xs = list(sorted(tuple(r._Xitems(2, R)), key=_k2))
957 while Xs:
958 n, X = Xs.pop(0)
959 if n == n2:
960 yield _n_pop(X)
961 else:
962 r = R.pop(n, None)
963 if r:
964 for n, x in r._Xitems(2, R):
965 Xs.append((n, X + x))
968def _indirects(n1, n2):
969 '''(INTERNAL) Yield all Xforms between C{n1} and C{n2} via
970 I{one} intermediate reframe C{n} conversion.
971 '''
972 def _X4(_Xto, n2):
973 _d = _direct
974 for n, X1 in _Xto.items():
975 X2 = _d(n, n2)
976 if X2:
977 yield X1, X2, n, True # X1 + X2
978 X2 = _d(n2, n)
979 if X2:
980 yield X1, X2, n, False # X1 - X2
982 r1 = RefFrames.get(n1)
983 if r1:
984 for X1, X2, n, p_ in _X4(r1._Xto, n2):
985 e1, e2 = X1.epoch, X2.epoch
986 if e1 < e2: # X1 to e2
987 X1 = X1.toEpoch(e2)
988# elif e1 > e2: # X2 to e1
989# X2 = X2.toEpoch(e1)
990 yield X1._add_sub(X2, p_, n1, n2, n)
993def _n1_n2_n3(X1, X2):
994 '''(INTERNAL) L{TRFXform._add_sub} helper.
995 '''
996 n = X1.indirected
997 n = _SPACE_(n, X1.refName2) if n else X1.refName2
998 return X1.refName1, X2.refName2, n
1001def _n_pop(X):
1002 '''(INTERNAL) Pop L{TRFXform.indirected}'s ends.
1003 '''
1004 p, n = None, X.indirected.split()
1005 if n and n[-1] == X.refName2:
1006 p = n.pop()
1007 if n and n[ 0] == X.refName1:
1008 p = n.pop(0)
1009 if p:
1010 X._indir_d = _SPACE_.join(n) if n else NN
1011 return X
1014def _reframe(**name_reframe):
1015 '''(INTERNAL) Get a C{reframe}.
1016 '''
1017 _, r = _xkwds_item2(name_reframe)
1018 if isstr(r) and r: # not NN
1019 r = RefFrames.get(r)
1020 if r and isinstance(r, RefFrame):
1021 return r
1022 raise TRFError(**name_reframe) # _invalid_
1025def _stref(**name_refname):
1026 '''(INTERNAL) Check a reference frame name.
1027 '''
1028 _, n = _xkwds_item2(name_refname)
1029 if isstr(n) and isidentifier(n):
1030 return str(n)
1031 raise TRFError(**name_refname) # _invalid_
1034def _sumstr(name1, name2, p_):
1035 '''(INTERNAL) "Sum" of C{name1 + ('+' if p_ else '-') + name2}.
1036 '''
1037 if name2:
1038 n = name2 if p_ else _negastr(name2)
1039 p = NN if n.startswith(_MINUS_) or \
1040 n.startswith(_PLUS_) else _PLUS_
1041 name1 = NN(name1, p, n)
1042 return name1
1045def _toRefFrame(point, reframe2, reframe=None, epoch=None,
1046 epoch2=None, name=NN, **LatLon_kwds):
1047 '''(INTERNAL) Convert an ellipsoidal point to C{reframe2}
1048 and C{epoch2 or epoch or pont.epoch or reframe.epoch}.
1049 '''
1050 ll = _xellipsoidall(point)
1051 r1 = reframe or point.reframe
1052 if not r1:
1053 t = _SPACE_(_DOT_(repr(point), _reframe_), MISSING)
1054 raise TRFError(_no_(_conversion_), txt=t)
1056 _xinstanceof(RefFrame, reframe2=reframe2, reframe=r1)
1058 e1 = _Epoch(epoch or point.epoch or r1.epoch)
1059 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2)
1060 t0 = _toTransform0(r1.name, e1, reframe2.name, e2)
1061 if t0 is None:
1062 t = _SPACE_(RefFrame.__name__, _AT_(r1.name, e1),
1063 _to_, _AT_(reframe2.name, e2))
1064 raise TRFError(_no_(_conversion_), txt=t)
1066 if t0: # is not ()
1067 if t0.isunity:
1068 p = point.dup()
1069 elif point.datum:
1070 p = point.toCartesian() if ll else point
1071 p = p.toDatum( r1.datum).toTransform(t0) \
1072 .toDatum(reframe2.datum).toDatum(point.datum)
1073 if ll:
1074 p = p.toLatLon(LatLon=point.classof, **LatLon_kwds)
1075 elif ll: # and LatLon_kwds
1076 p = point.toTransform(t0, **LatLon_kwds)
1077 else:
1078 p = point.toTransform(t0)
1079 p._reframe = reframe2 # see TRFXform.toRefFrame above
1080 p._epoch = _xattr(t0.Xform, epoch=e2)
1081 p.rename(name or reframe2.name)
1082 else:
1083 p = point.dup(_reframe=reframe2, # ditto
1084 _epoch=e2, name=name) if name else point
1085 return p
1088def _toTransform0(n1, e1, n2, e2, **indirect_inverse):
1089 '''(INTERNAL) Return a L{TransformXform}, 0-tuple or C{None}.
1090 '''
1091 if n1 == n2 and e1 == e2:
1092 return () # unity?
1094 for X in _toTransforms(n1, e1, n2, e2, **indirect_inverse):
1095 return X # first OK?
1097 if (n1.startswith(_ITRF_) and n2.startswith(_WGS84_)) or \
1098 (n2.startswith(_ITRF_) and n1.startswith(_WGS84_)): # and e1 == e2?
1099 return () # unity?
1101 return None
1104def _toTransforms(n1, e1, n2, e2, indirect=True, inverse=True, exhaust=False): # MCCABE 16
1105 '''(INTERNAL) Yield all possible Helmert transforms, if any.
1106 '''
1107 class Ts(list): # L{TransformXform}s de-dup
1108 def __call__(self, Xs, e1=e1, e2=e2, **inverse):
1109 for X in Xs:
1110 if X:
1111 T = X.toTransform(e1, epoch2=e2, **inverse)
1112 if T not in self:
1113 self.append(T)
1114 yield T
1116# def __contains__(self, T):
1117# _xinstanceof(TransformXform, T=T)
1118# return any(t == T for t in self)
1120 def _k(X):
1121 return -X.epoch # most recent first
1123 _Ts = Ts()
1125 for T in _Ts((_direct(n1, n2),), inverse=False):
1126 yield T
1127 if inverse:
1128 for T in _Ts((_direct(n2, n1),), inverse=True):
1129 yield T
1131 if indirect:
1132 for T in _Ts(sorted(_indirects(n1, n2), key=_k), inverse=False):
1133 yield T
1134 if inverse:
1135 for T in _Ts(sorted(_indirects(n2, n1), key=_k), inverse=True):
1136 yield T
1138 if exhaust:
1139 for T in _Ts(_eXhaustives(n1, n2), inverse=False):
1140 yield T
1141 for T in _Ts(_eXhaustives(n2, n1), inverse=True):
1142 yield T
1145def trfTransform0(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True, exhaust=False):
1146 '''Get a Helmert transform to convert one C{reframe} observed at C{epoch}
1147 to an other C{reframe2} at observed at C{epoch2 or epoch}.
1149 @return: A L{TransformXform} instance, a C{0-tuple} for I{unity, identity} or
1150 C{None} if no conversion exists.
1152 @see: Function L{trfTransforms} for futher details.
1153 '''
1154 return _trfT0s(_toTransform0, reframe, reframe2, epoch, epoch2,
1155 indirect=indirect, inverse=inverse, exhaust=exhaust)
1158def trfTransforms(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True, exhaust=False):
1159 '''Yield all Helmert transform to convert one C{reframe} observed at C{epoch}
1160 to an other C{reframe2} at observed at C{epoch2 or epoch}.
1162 @arg reframe: The frame to convert I{from} (L{RefFrame} or C{str}).
1163 @arg reframe2: The frame to convert I{to} (L{RefFrame} or C{str}).
1164 @arg epoch: Epoch to observe I{from} (L{Epoch}, C{scalar} or C{str}),
1165 otherwise C{B{reframe}}'s C{epoch}.
1166 @kwarg epoch2: Optional epoch to observe I{to} (L{Epoch}, C{scalar} or C{str}),
1167 otherwise B{C{epoch}}.
1168 @kwarg indirect: If C{True}, include transforms via I{one} intermediate reframe,
1169 otherwise only I{direct} B{C{reframe}} to B{C{reframe2}}
1170 transforms (C{bool}).
1171 @kwarg inverse: If C{True}, include inverse, otherwise only forward transforms
1172 (C{bool}).
1173 @kwarg exhaust: If C{True}, exhaustively generate all transforms, forward and
1174 inverse and via any number of intermediate reframes (C{bool}).
1176 @return: A L{TransformXform} instance for each available conversion, without
1177 duplicates.
1179 @raise TRFError: Invalid B{C{reframe}}, B{C{reframe2}}, B{C{epoch}} or B{C{epoch2}}.
1181 @raise TypeError: Invalid B{C{reframe}} or B{C{reframe2}}.
1182 '''
1183 return _trfT0s(_toTransforms, reframe, reframe2, epoch, epoch2,
1184 indirect=indirect, inverse=inverse, exhaust=exhaust)
1187def _trfT0s(_toT0s, reframe, reframe2, epoch, epoch2, **indirect_inverse_exhaust):
1188 '''(INTERNAL) Handle C{trfTransforms0} and C{trfTransforms} calls.
1189 '''
1190 r1 = _reframe(reframe=reframe)
1191 e1 = r1.epoch if epoch is None else _Epoch(epoch)
1192 r2 = _reframe(reframe2=reframe2)
1193 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2)
1194 return _toT0s(r1.name, e1, r2.name, e2, **indirect_inverse_exhaust)
1197def trfXform(reframe1, reframe2, epoch=None, xform=None, rates=None, raiser=True):
1198 '''Define a new Terrestrial Reference Frame (TRF) converter or get an
1199 existing one.
1201 @arg reframe1: Source frame (L{RefFrame} or C{str}), converting I{from}.
1202 @arg reframe2: Destination frame (L{RefFrame} or C{str}), converting I{to}.
1203 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str})
1204 or C{None} for C{B{reframe2}}'s epoch.
1205 @kwarg xform: I{Transform} parameters (L{TRFXform7Tuple}).
1206 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), as B{C{xform}},
1207 but in C{units-per-year}.
1208 @kwarg raiser: If C{False}, do not raise an error if the converter
1209 exists, replace it (C{bool}).
1211 @return: The new TRF converter (L{TRFXform}) or if no B{C{epoch}},
1212 B{C{xform}} and B{C{rates}} are given, return the existing
1213 one (L{TRFXform}) or C{None} if not available.
1215 @raise TRFError: Invalid B{C{reframe1}}, B{C{reframe2}}, B{C{epoch}},
1216 B{C{xform}} or B{C{rates}} or the TRF converter
1217 already exists.
1218 '''
1219 try:
1220 r1 = _reframe(reframe1=reframe1)
1221 r2 = _reframe(reframe2=reframe2)
1222 if epoch is None:
1223 if xform is rates is None:
1224 return r1._Xto.get(r2.name, None)
1225 e = r2.epoch
1226 else:
1227 e = _Epoch(epoch)
1228 return _trfX(r1.name, r2.name, raiser=raiser, epoch=e,
1229 xform=xform, rates=rates)
1230 except (TypeError, ValueError) as x:
1231 t = unstr(trfXform, reframe1, reframe2, epoch=epoch)
1232 raise TRFError(t, cause=x)
1235def _trfX(n1, n2, raiser=True, **epoch_xform_rates):
1236 '''(INTERNAL) New, I{unique} L{TRFXform} converter.
1237 '''
1238 r1 = RefFrames.get(n1)
1239 if r1 is None:
1240 raise ValueError(_invalid_)
1241 r2 = RefFrames.get(n2)
1242 if r2 is None:
1243 raise ValueError(_invalid_)
1244 if raiser:
1245 if n2 in r1._Xto:
1246 raise ValueError(_exists_)
1247 if n1 in r2._Xto:
1248 raise ValueError(_SPACE_(_inverse_, _exists_))
1249 r1._Xto[n2] = X = TRFXform(n1, n2, **epoch_xform_rates)
1250 return X
1253# def velocities2neu(vx, vy, vz, lat=0, lon=0):
1254# '''Convert X, Y, and Z I{velocities} to North, East, Up.
1255#
1256# @arg vx: X velocity (C{meter-per-time}).
1257# @arg vx: Y velocity (C{meter-per-time}).
1258# @arg vx: Z velocity (C{meter-per-time}).
1259# @kwarg lat: Latitude (C{degrees}).
1260# @kwarg lon: Longitude (C{degrees}).
1261#
1262# @return: 3-Tuple C{(vnorth, veast, vup)} with the
1263# North, East and Up velocities, same units
1264# as B{C{vx}, B{C{vy}} and B{C{vx}}.
1265# '''
1266# sa, ca, sb, cb = sincos2d_(lat, lon)
1267# ve = cb * vy - sb * vx
1268# v = cb * vx + sb * vy
1269# vn = ca * vz - sa * v
1270# vu = sa * vz + ca * v
1271# return vn, ve, vu
1274# def velocities2xyz(vn, ve, vu, lat=0, lon=0):
1275# '''Convert North, East and Up I{velocities} to X, Y, Z.
1276#
1277# @arg vn: North velocity (C{meter-per-time}).
1278# @arg ve: East velocity (C{meter-per-time}).
1279# @arg vu: Up velocity (C{meter-per-time}).
1280# @kwarg lat: Latitude (C{degrees}).
1281# @kwarg lon: Longitude (C{degrees}).
1282#
1283# @return: 3-Tuple C{(vx, vy, vz)} with the X, Y
1284# and Z velocities, same units as B{C{vn},
1285# B{C{ve}} and B{C{vu}}.
1286# '''
1287# sa, ca, sb, cb = sincos2d_(lat, lon)
1288# vz = ca * vn + sa * vu
1289# v = ca * vu - sa * vn
1290# vx = cb * v - sb * ve
1291# vy = sb * v + cb * ve
1292# return vx, vy, vz
1295def _X(*ps): # deleted below
1296 return _P(ps, _xform_, _Xs) # PYCHOK del
1299def _R(*ps): # deleted below
1300 return _P(ps, _rates_, _Rs) # PYCHOK del
1303_P_0_0s = TRFXform7Tuple(_0_0s(len(_Names7)), name='unity')
1305# TRF conversions specified as an epoch and 2 sets of 7 parameters. Most from Altamimi, Z. U{"EUREF Technical
1306# Note 1: Relationship and Transformation between the International and the European Terrestrial Reference
1307# Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Appendix A, more at U{Quinsy QPS <https://
1308# confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ITRF_Transformation_Parameters.xlsx>}.
1309# See also U{Quinsy International Terrestrial Reference Frame 2014 (ITRF2014)<https://confluence.QPS.NL/qinsy/latest/
1310# en/international-terrestrial-reference-frame-2014-itrf2014-182618383.html>}.
1311_trfX(_ITRF2020_, _ITRF2014_, epoch=_E(2015), # <https://ITRF.IGN.Fr/docs/solutions/itrf2020/Transfo-ITRF2020_TRFs.txt>
1312 xform=_X( -1.4, -0.9, 1.4, -0.42, _0_0, _0_0, _0_0),
1313 rates=_R( _0_0, -0.1, 0.2, _0_0, _0_0, _0_0, _0_0))
1314_trfX(_ITRF2020_, _ITRF2008_, epoch=_E(2015),
1315 xform=_X( 0.2, 1.0, 3.3, -0.29, _0_0, _0_0, _0_0),
1316 rates=_R( _0_0, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0))
1317_trfX(_ITRF2020_, _ITRF2005_, epoch=_E(2015),
1318 xform=_X( 2.7, 0.1, -1.4, 0.65, _0_0, _0_0, _0_0),
1319 rates=_R( 0.3, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0))
1320_trfX(_ITRF2020_, _ITRF2000_, epoch=_E(2015),
1321 xform=_X( -0.2, 0.8, -34.2, 2.25, _0_0, _0_0, _0_0),
1322 rates=_R( 0.1, _0_0, -1.7, 0.11, _0_0, _0_0, _0_0))
1323_trfX(_ITRF2020_, _ITRF97_, epoch=_E(2015),
1324 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
1325 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1326_trfX(_ITRF2020_, _ITRF96_, epoch=_E(2015),
1327 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
1328 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1329_trfX(_ITRF2020_, _ITRF94_, epoch=_E(2015),
1330 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
1331 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1332_trfX(_ITRF2020_, _ITRF93_, epoch=_E(2015),
1333 xform=_X( -65.8, 1.9, -71.3, 4.47, -3.36, -4.33, 0.75),
1334 rates=_R( -2.8, -0.2, -2.3, 0.12, -0.11, -0.19, 0.07))
1335_trfX(_ITRF2020_, _ITRF92_, epoch=_E(2015),
1336 xform=_X( 14.5, -1.9, -85.9, 3.27, _0_0, _0_0, 0.36),
1337 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1338_trfX(_ITRF2020_, _ITRF91_, epoch=_E(2015),
1339 xform=_X( 26.5, 12.1, -91.9, 4.67, _0_0, _0_0, 0.36),
1340 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1341_trfX(_ITRF2020_, _ITRF90_, epoch=_E(2015),
1342 xform=_X( 24.5, 8.1, -107.9, 4.97, _0_0, _0_0, 0.36),
1343 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1344_trfX(_ITRF2020_, _ITRF89_, epoch=_E(2015),
1345 xform=_X( 29.5, 32.1, -145.9, 8.37, _0_0, _0_0, 0.36),
1346 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1347_trfX(_ITRF2020_, _ITRF88_, epoch=_E(2015),
1348 xform=_X( 24.5, -3.9, -169.9, 11.47, 0.1, _0_0, 0.36),
1349 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1351# see U{Transformation Parameters ITRF2014<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2014_ITRFs.txt>} and
1352# Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1353# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1.pdf>} Appendix A.
1354_trfX(_ITRF2014_, _ITRF2008_, epoch=(2010), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2014/tp_14-08.php>
1355 xform=_X( 1.6, 1.9, 2.4, -0.02, _0_0, _0_0, _0_0),
1356 rates=_R( _0_0, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0))
1357_trfX(_ITRF2014_, _ITRF2005_, epoch=_E(2010),
1358 xform=_X( 2.6, _1_0, -2.3, 0.92, _0_0, _0_0, _0_0),
1359 rates=_R( 0.3, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0))
1360_trfX(_ITRF2014_, _ITRF2000_, epoch=_E(2010),
1361 xform=_X( 0.7, 1.2, -26.1, 2.12, _0_0, _0_0, _0_0),
1362 rates=_R( 0.1, 0.1, -1.9, 0.11, _0_0, _0_0, _0_0))
1363_trfX(_ITRF2014_, _ITRF97_, epoch=_E(2010),
1364 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1365 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1366_trfX(_ITRF2014_, _ITRF96_, epoch=_E(2010),
1367 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1368 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1369_trfX(_ITRF2014_, _ITRF94_, epoch=_E(2010),
1370 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1371 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1372_trfX(_ITRF2014_, _ITRF93_, epoch=_E(2010),
1373 xform=_X( -50.4, 3.3, -60.2, 4.29, -2.81, -3.38, 0.4),
1374 rates=_R( -2.8, -0.1, -2.5, 0.12, -0.11, -0.19, 0.07))
1375_trfX(_ITRF2014_, _ITRF92_, epoch=_E(2010),
1376 xform=_X( 15.4, 1.5, -70.8, 3.09, _0_0, _0_0, 0.26),
1377 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1378_trfX(_ITRF2014_, _ITRF91_, epoch=_E(2010),
1379 xform=_X( 27.4, 15.5, -76.8, 4.49, _0_0, _0_0, 0.26),
1380 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1381_trfX(_ITRF2014_, _ITRF90_, epoch=_E(2010),
1382 xform=_X( 25.4, 11.5, -92.8, 4.79, _0_0, _0_0, 0.26),
1383 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1384_trfX(_ITRF2014_, _ITRF89_, epoch=_E(2010),
1385 xform=_X( 30.4, 35.5, -130.8, 8.19, _0_0, _0_0, 0.26),
1386 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1387_trfX(_ITRF2014_, _ITRF88_, epoch=_E(2010),
1388 xform=_X( 25.4, -0.5, -154.8, 11.29, 0.1, _0_0, 0.26),
1389 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1391# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1392# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 1st and 2nd column
1393_trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2005),
1394 xform=_X( -0.5, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1395 rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1396# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(1997),
1397# xform=_X( -2.9, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1398# rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1399# see U{Transformation Parameters ITRF2008<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2008_ITRFs.txt>}
1400# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2008/tp_08-05.php>
1401# xform=_X( -2.0, -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_trfX(_ITRF2008_, _ITRF2000_, epoch=_E(2000),
1404 xform=_X( -1.9, -1.7, -10.5, 1.34, _0_0, _0_0, _0_0),
1405 rates=_R( 0.1, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1406_trfX(_ITRF2008_, _ITRF97_, epoch=_E(2000),
1407 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1408 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1409_trfX(_ITRF2008_, _ITRF96_, epoch=_E(2000),
1410 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1411 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1412_trfX(_ITRF2008_, _ITRF94_, epoch=_E(2000),
1413 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1414 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1415_trfX(_ITRF2008_, _ITRF93_, epoch=_E(2000),
1416 xform=_X( -24.0, 2.4, -38.6, 3.41, -1.71, -1.48, -0.3),
1417 rates=_R( -2.8, -0.1, -2.4, 0.09, -0.11, -0.19, 0.07))
1418_trfX(_ITRF2008_, _ITRF92_, epoch=_E(2000),
1419 xform=_X( 12.8, 4.6, -41.2, 2.21, _0_0, _0_0, 0.06),
1420 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1421_trfX(_ITRF2008_, _ITRF91_, epoch=_E(2000),
1422 xform=_X( 24.8, 18.6, -47.2, 3.61, _0_0, _0_0, 0.06),
1423 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1424_trfX(_ITRF2008_, _ITRF90_, epoch=_E(2000),
1425 xform=_X( 22.8, 14.6, -63.2, 3.91, _0_0, _0_0, 0.06),
1426 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1427_trfX(_ITRF2008_, _ITRF89_, epoch=_E(2000),
1428 xform=_X( 27.8, 38.6, -101.2, 7.31, _0_0, _0_0, 0.06),
1429 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1430_trfX(_ITRF2008_, _ITRF88_, epoch=_E(2000),
1431 xform=_X( 22.8, 2.6, -125.2, 10.41, 0.1, _0_0, 0.06),
1432 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1434# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1435# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 3rd column
1436# _trfX(_ITRF2005_, _ITRF2000_, epoch=_E(1997),
1437# xform=_X( 0.7, -1.1, -0.4, 0.16, -0.2, 0.1 -1.8),
1438# rates=_R( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1439_trfX(_ITRF2005_, _ITRF2000_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2005/tp_05-00.php>
1440 xform=_X( 0.1, -0.8, -5.8, 0.4, _0_0, _0_0, _0_0),
1441 rates=_R( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1443_trfX(_ITRF2000_, _ITRF97_, epoch=_E(1997),
1444 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1445 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, -0.02)) # 0.02?
1446_trfX(_ITRF2000_, _ITRF96_, epoch=_E(1997),
1447 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1448 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1449_trfX(_ITRF2000_, _ITRF94_, epoch=_E(1997),
1450 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1451 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1452_trfX(_ITRF2000_, _ITRF93_, epoch=_E(1988),
1453 xform=_X( 12.7, 6.5, -20.9, 1.95, -0.39, 0.8, -1.14),
1454 rates=_R( -2.9, -0.2, -0.6, 0.01, -0.11, -0.19, 0.07))
1455_trfX(_ITRF2000_, _ITRF92_, epoch=_E(1988),
1456 xform=_X( 1.47, 1.35, -1.39, 0.75, _0_0, _0_0, -0.18),
1457 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1458_trfX(_ITRF2000_, _ITRF91_, epoch=_E(1988),
1459 xform=_X( 26.7, 27.5, -19.9, 2.15, _0_0, _0_0, -0.18),
1460 rates=_R( _0_0, -0.6, -1.4, 0.01, _0_0, _0_0, 0.02))
1461_trfX(_ITRF2000_, _ITRF90_, epoch=_E(1988),
1462 xform=_X( 2.47, 2.35, -3.59, 2.45, _0_0, _0_0, -0.18),
1463 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1464_trfX(_ITRF2000_, _ITRF89_, epoch=_E(1988),
1465 xform=_X( 2.97, 4.75, -7.39, 5.85, _0_0, _0_0, -0.18),
1466 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1467_trfX(_ITRF2000_, _ITRF88_, epoch=_E(1988),
1468 xform=_X( 2.47, 1.15, -9.79, 8.95, 0.1, _0_0, -0.18),
1469 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1471# Soler, T .& Snay R.A. U{"Transforming Positions and Velocities between the International Terrestrial
1472# Reference Frame of 2000 and North American Datum of 1983"<https://www.ResearchGate.net/publication/245291390>},
1473# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1474# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 5th and 6th column
1475_trfX(_ITRF97_, _ITRF96_, epoch=_E(1997),
1476 xform=_X( -2.07, -0.21, 9.95, -0.93496, 0.1267, -0.22355, -0.06065,),
1477 rates=_R( 0.69, -0.1, 1.86, -0.19201, 0.01347, -0.01514, 0.00027))
1478_trfX(_ITRF96_, _NAD83_, epoch=_E(1997),
1479 xform=_X( 991.0, -190.72, -512.9, _0_0, 25.79, 9.65, 11.66,),
1480 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.0532, -0.7423, -0.0316,))
1482# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1483# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 1.
1484# _trfX(_ITRF2020_, _ETRF2020_, epoch=_E(1989), # see Table 2 below
1485# xform=_P_0_0s,
1486# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753))
1487# _trfX(_ITRF2014_, _ETRF2014_, epoch=_E(1989), # see Table 3 below
1488# xform=_P_0_0s,
1489# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77))
1490_trfX(_ITRF2005_, _ETRF2005_, epoch=_E(1989),
1491 xform=_X( 56.0, 48.0, -37.0, _0_0, _0_0, _0_0, _0_0),
1492 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.054, 0.518, -0.781))
1493# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(1989), # see Table 4 below
1494# xform=_X( 54.0, 51.0, -48.0, _0_0, _0_0, _0_0, _0_0),
1495# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1496_trfX(_ITRF97_, _ETRF97_, epoch=_E(1989),
1497 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1498 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1499_trfX(_ITRF96_, _ETRF96_, epoch=_E(1989),
1500 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1501 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1502_trfX(_ITRF94_, _ETRF94_, epoch=_E(1989),
1503 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1504 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1505_trfX(_ITRF93_, _ETRF93_, epoch=_E(1989),
1506 xform=_X( 19.0, 53.0, -21.0, _0_0, _0_0, _0_0, _0_0),
1507 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.32, 0.78, -0.67))
1508_trfX(_ITRF92_, _ETRF92_, epoch=_E(1989),
1509 xform=_X( 38.0, 40.0, -37.0, 0.0, 0.0, 0.0, 0.0),
1510 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68))
1511_trfX(_ITRF91_, _ETRF91_, epoch=_E(1989),
1512 xform=_X( 21.0, 25.0, -37.0, _0_0, _0_0, _0_0, _0_0),
1513 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68))
1514_trfX(_ITRF90_, _ETRF90_, epoch=_E(1989),
1515 xform=_X( 19.0, 28.0, -23.0, _0_0, _0_0, _0_0, _0_0),
1516 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71))
1517_trfX(_ITRF89_, _ETRF89_, epoch=_E(1989),
1518 xform=_P_0_0s,
1519 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71))
1521# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1522# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 2.
1523_trfX(_ITRF2020_, _ETRF2020_, epoch=_E(2015),
1524 xform=_X( _0_0, _0_0, _0_0, _0_0, 2.236, 13.494, -19.578),
1525 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753))
1526_trfX(_ITRF2014_, _ETRF2020_, epoch=_E(2015),
1527 xform=_X( 1.4, 0.9, -1.4, 0.42, 2.236, 13.494, -19.578),
1528 rates=_R( _0_0, 0.1, -0.2, _0_0, 0.086, 0.519, -0.753))
1529_trfX(_ITRF2008_, _ETRF2020_, epoch=_E(2015),
1530 xform=_X( 3.0, 2.8, 0.5, 0.55, 2.236, 13.494, -19.578),
1531 rates=_R( _0_0, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753))
1532_trfX(_ITRF2005_, _ETRF2020_, epoch=_E(2015),
1533 xform=_X( 5.5, 1.9, -4.2, 1.49, 2.236, 13.494, -19.578),
1534 rates=_R( 0.3, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753))
1535_trfX(_ITRF2000_, _ETRF2020_, epoch=_E(2015),
1536 xform=_X( 2.6, 2.6, -37.0, 3.09, 2.236, 13.494, -19.578),
1537 rates=_R( 0.1, 0.2, -2.1, 0.11, 0.086, 0.519, -0.753))
1538_trfX(_ITRF97_, _ETRF2020_, epoch=_E(2015),
1539 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1540 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1541_trfX(_ITRF96_, _ETRF2020_, epoch=_E(2015),
1542 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1543 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1544_trfX(_ITRF94_, _ETRF2020_, epoch=_E(2015),
1545 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1546 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1547_trfX(_ITRF93_, _ETRF2020_, epoch=_E(2015),
1548 xform=_X( -63.0, 3.7, -74.1, 5.31, -1.124, 9.164, -18.828),
1549 rates=_R( -2.8, _0_0, -2.7, 0.12, -0.024, 0.329, -0.683))
1550_trfX(_ITRF92_, _ETRF2020_, epoch=_E(2015),
1551 xform=_X( 17.3, -0.1, -88.7, 4.11, 2.236, 13.494, -19.218),
1552 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1553_trfX(_ITRF91_, _ETRF2020_, epoch=_E(2015),
1554 xform=_X( 29.3, 13.9, -94.7, 5.51, 2.236, 13.494, -19.218),
1555 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1556_trfX(_ITRF90_, _ETRF2020_, epoch=_E(2015),
1557 xform=_X( 27.3, 9.9, -110.7, 5.81, 2.236, 13.494, -19.218),
1558 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1559_trfX(_ITRF89_, _ETRF2020_, epoch=_E(2015),
1560 xform=_X( 32.3, 33.9, -148.7, 9.21, 2.236, 13.494, -19.218),
1561 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1562_trfX(_ITRF88_, _ETRF2020_, epoch=_E(2015),
1563 xform=_X( 27.3, -2.1, -172.7, 12.31, 2.336, 13.494, -19.218),
1564 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1566# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1567# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 3.
1568_trfX(_ITRF2020_, _ETRF2014_, epoch=_E(2015),
1569 xform=_X( -1.4, -0.9, 1.4, 0.42, 2.21, 13.806, -20.02),
1570 rates=_R( _0_0, -0.1, 0.2, _0_0, 0.085, 0.531, -0.77))
1571_trfX(_ITRF2014_, _ETRF2014_, epoch=_E(2015),
1572 xform=_X( _0_0, _0_0, _0_0, _0_0, 2.21, 13.806, -20.02),
1573 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77))
1574_trfX(_ITRF2008_, _ETRF2014_, epoch=_E(2015),
1575 xform=_X( -1.6, -1.9, -1.9, -0.13, 2.21, 13.806, -20.02),
1576 rates=_R( _0_0, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77))
1577_trfX(_ITRF2005_, _ETRF2014_, epoch=_E(2015),
1578 xform=_X( -4.1, -1.0, 2.8, -1.07, 2.21, 13.806, -20.02),
1579 rates=_R( -0.3, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77))
1580_trfX(_ITRF2000_, _ETRF2014_, epoch=_E(2015),
1581 xform=_X( -1.2, -1.7, 35.6, -2.67, 2.21, 13.806, -20.02),
1582 rates=_R( -0.1, -0.1, 1.9, -0.11, 0.085, 0.531, -0.77))
1583_trfX(_ITRF97_, _ETRF2014_, epoch=_E(2015),
1584 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1585 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1586_trfX(_ITRF96_, _ETRF2014_, epoch=_E(2015),
1587 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1588 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1589_trfX(_ITRF94_, _ETRF2014_, epoch=_E(2015),
1590 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1591 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1592_trfX(_ITRF93_, _ETRF2014_, epoch=_E(2015),
1593 xform=_X( 64.4, -2.8, 72.7, -4.89, 5.570, 18.136, -20.77),
1594 rates=_R( 2.8, 0.1, 2.5, -0.12, 0.195, 0.721, -0.84))
1595_trfX(_ITRF92_, _ETRF2014_, epoch=_E(2015),
1596 xform=_X( -15.9, 1.0, 87.3, -3.69, 2.21, 13.806, -20.38),
1597 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1598_trfX(_ITRF91_, _ETRF2014_, epoch=_E(2015),
1599 xform=_X( -27.9, -13.0, 93.3, -5.09, 2.21, 13.806, -20.38),
1600 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1601_trfX(_ITRF90_, _ETRF2014_, epoch=_E(2015),
1602 xform=_X( -25.9, -9.0, 109.3, -5.39, 2.21, 13.806, -20.38),
1603 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1604_trfX(_ITRF89_, _ETRF2014_, epoch=_E(2015),
1605 xform=_X( -30.9, -33.0, 147.3, -8.79, 2.21, 13.806, -20.38),
1606 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1607_trfX(_ITRF88_, _ETRF2014_, epoch=_E(2015),
1608 xform=_X( -25.9, 3.0, 171.3, -11.89, 2.11, 13.806, -20.38),
1609 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1611# see U{Altamimi, Z. "EUREF Technical Note 1: Relationship and Transformation between the International and
1612# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 4,
1613# U{Boucher, C. & Altamimi, Z. "Memo: Specifications for reference frame fixing in the analysis of a EUREF GPS
1614# campaign" (2011) <https://ETRS89.ENSG.IGN.Fr/memo-V8.pdf>} and U{Altamimi, Z. "Key results of ITRF2014 and
1615# implication to ETRS89 realization", EUREF2016<https://www.EUREF.EU/symposia/2016SanSebastian/01-02-Altamimi.pdf>}.
1616_trfX(_ITRF2020_, _ETRF2000_, epoch=_E(2015),
1617 xform=_X( 53.8, 51.8, -82.2, 2.25, 2.106, 12.74, -20.592),
1618 rates=_R( 0.1, _0_0, -1.7, 0.11, 0.081, 0.49, -0.792))
1619# _trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2000),
1620# xform=_X( 53.7, 51.2, -55.1, 1.02, 0.891, 5.39, -8.712),
1621# rates=_R( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792))
1622_trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2015),
1623 xform=_X( 55.2, 52.7, -83.6, 2.67, 2.106, 12.74, -20.592),
1624 rates=_R( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792))
1625# _trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2000),
1626# xform=_X( 52.1, 49.3, -58.5, 1.34, 0.891, 5.39, -8.712),
1627# rates=_R( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1628_trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2015),
1629 xform=_X( 53.6, 50.8, -85.5, 2.54, 2.106, 12.74, -20.592),
1630 rates=_R( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1631# _trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2000),
1632# xform=_X( 54.1, 50.2, -53.8, 0.4, 0.891, 5.39, -8.712),
1633# rates=_R( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1634_trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2015),
1635 xform=_X( 51.1, 51.7, -80.8, 1.6, 2.106, 12.74, -20.592),
1636 rates=_R( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1637# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2000),
1638# xform=_X( 54.0, 51.0, -48.0, _0_0, 0.891, 5.39, -8.712),
1639# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1640_trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2015),
1641 xform=_X( 54.0, 51.0, -48.0, _0_0, 2.106, 12.74, -20.592),
1642 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1643_trfX(_ITRF97_, _ETRF2000_, epoch=_E(2015),
1644 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1645 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1646_trfX(_ITRF96_, _ETRF2000_, epoch=_E(2015),
1647 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1648 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1649_trfX(_ITRF94_, _ETRF2000_, epoch=_E(2015),
1650 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1651 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1652_trfX(_ITRF93_, _ETRF2000_, epoch=_E(2015),
1653 xform=_X( 119.6, 49.9, -10.9, -2.22, 5.466, 17.07, -21.342),
1654 rates=_R( 2.9, 0.2, 0.6, -0.01, 0.191, 0.68, -0.862))
1655_trfX(_ITRF92_, _ETRF2000_, epoch=_E(2015),
1656 xform=_X( 39.3, 53.7, 3.7, -1.02, 2.106, 12.74, -20.952),
1657 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1658_trfX(_ITRF91_, _ETRF2000_, epoch=_E(2015),
1659 xform=_X( 27.3, 39.7, 9.7, -2.42, 2.106, 12.74, -20.952),
1660 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1661_trfX(_ITRF90_, _ETRF2000_, epoch=_E(2015),
1662 xform=_X( 29.3, 43.7, 25.7, -2.72, 2.106, 12.74, -20.952),
1663 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1664_trfX(_ITRF89_, _ETRF2000_, epoch=_E(2015),
1665 xform=_X( 24.3, 19.7, 63.7, -6.12, 2.106, 12.74, -20.952),
1666 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1667_trfX(_ITRF88_, _ETRF2000_, epoch=_E(2015),
1668 xform=_X( 29.3, 55.7, 87.7, -9.22, 2.006, 12.74, -20.952),
1669 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1671# GDA2020 "Geocentric Datum of Australia 2020 Technical Manual", v1.5, 2020-12-09, Table 3.3 and 3.4
1672# <https://www.ICSM.gov.AU/sites/default/files/2020-12/GDA2020%20Technical%20Manual%20V1.5_4.pdf>
1673# (the GDA2020 xforms are different but the rates are the same as GDA94, further below)
1674_trfX(_ITRF2014_, _GDA2020_, epoch=_E(2020),
1675 xform=_P_0_0s,
1676 rates=_R( _0_0, _0_0, _0_0, _0_0, 1.50379, 1.18346, 1.20716))
1677_trfX(_ITRF2008_, _GDA2020_, epoch=_E(2020),
1678 xform=_X( 13.79, 4.55, 15.22, 2.5, 0.2808, 0.2677, -0.4638),
1679 rates=_R( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))
1680_trfX(_ITRF2005_, _GDA2020_, epoch=_E(2020),
1681 xform=_X( 40.32, -33.85, -16.72, 4.286, -1.2893, -0.8492, -0.3342),
1682 rates=_R( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))
1683_trfX(_ITRF2000_, _GDA2020_, epoch=_E(2020),
1684 xform=_X(-105.52, 51.58, 231.68, 3.55, 4.2175, 6.3941, 0.8617),
1685 rates=_R( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))
1687# see Table 2 in U{Dawson, J. & Woods, A. "ITRF to GDA94 coordinate transformations", Journal of Applied
1688# Geodesy 4 (2010), 189-199<https://www.ResearchGate.net/publication/258401581_ITRF_to_GDA94_coordinate_transformations>}
1689# (note, sign of rotations for GDA94 reversed as "Australia assumes rotation to be of coordinate axes",
1690# rather than the more conventional "position around the coordinate axes")
1691_trfX(_ITRF2008_, _GDA94_, epoch=_E(1994),
1692 xform=_X( -84.68, -19.42, 32.01, 9.71, -0.4254, 2.2578, 2.4015),
1693 rates=_R( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))
1694_trfX(_ITRF2005_, _GDA94_, epoch=_E(1994),
1695 xform=_X( -79.73, -6.86, 38.03, 6.636, 0.0351, -2.1211, -2.1411),
1696 rates=_R( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))
1697_trfX(_ITRF2000_, _GDA94_, epoch=_E(1994),
1698 xform=_X( -45.91, -29.85, -20.37, 7.07, -1.6705, 0.4594, 1.9356),
1699 rates=_R( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))
1701# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
1702# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 and Pearson, C. & Snay, R. U{"Introducing
1703# HTDP 3.1 to transform coordinates across time and spatial reference frames"<https://Geodesy.NOAA.gov/
1704# TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 7th column
1705_trfX(_ITRF2008_, _NAD83_, epoch=_E(1997),
1706 xform=_X( 993.43, -1903.31, -526.55, 1.71504, -25.91467, -9.42645, -11.59935),
1707 rates=_R( 0.79, -0.6, -1.34, -0.10201, -0.06667, 0.75744, 0.05133))
1708# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
1709# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83
1710_trfX(_ITRF2005_, _NAD83_, epoch=_E(1997),
1711 xform=_X( 996.3, -1902.4, -521.9, 0.775, -25.915, -9.426, -11.599),
1712 rates=_R( 0.5, -0.6, -1.3, -0.10201, -0.06667, 0.75744, 0.05133))
1713# see U{Solar, T. & Snay, R.A. "Transforming Positions and Velocities between the International Terrestrial Reference
1714# Frame of 2000 and North American Datum of 1983" (2004)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>}
1715_trfX(_ITRF2000_, _NAD83_, epoch=_E(1997), # note NAD83(CORS96)
1716 xform=_X( 995.6, -1901.3, -521.5, 0.615, -25.915, -9.426, -11.599),
1717 rates=_R( 0.7, -0.7, _0_5, -0.182, -0.06667, 0.75744, 0.05133))
1718_trfX(_ITRF90_, _NAD83_, epoch=_E(1997),
1719 xform=_X( 973.0, -1919.2, -482.9, -0.9, -25.79, -9.65, -11.66),
1720 rates=_R( _0_0, _0_0, _0_0, _0_0, -0.053, 0.742, 0.032))
1721_trfX(_ITRF90_, _WGS84_, epoch=_E(1984), # coverage
1722 xform=_X( 60.0, -517.0, -223.0, -11.0, 18.3, -0.3, 7.0),
1723 rates=_P_0_0s)
1725# equivalents U{"Transformations Between NAD83 and WGS84"<https://www.NGS.NOAA.gov/CORS/Articles/WGS84NAD83.pdf>}
1726trfXform(_NAD83cors96_, _NAD83_, epoch=_E(1997), xform=_P_0_0s, rates=_P_0_0s)
1727trfXform(_WGS84g1150_, _ITRF2000_, epoch=_E(2004), xform=_P_0_0s, rates=_P_0_0s)
1729del _E, _Es, _i, _P, _P_0_0s, _R, _Rs, _X, _Xs
1731if __name__ == '__main__':
1733 def _main():
1734 from pygeodesy.basics import _args_kwds_names
1735 from pygeodesy.interns import _COLONSPACE_,_COMMA_, _NL_, _NLATvar_, _vs_
1736 from pygeodesy import printf
1737 from time import localtime
1739 D = date2epoch.__name__
1740 E = epoch2date.__name__
1741 y = localtime()[0]
1742 for m in range(1, 13):
1743 for d in (1, 15, _mDays[m] - 1, _mDays[m]):
1744 f = '%s(%d,%3d,%3d)' % (D, y, m, d)
1745 e = date2epoch(y, m, d)
1746 t = epoch2date(e)
1747 x = NN if t == (y, m, d) else _STAR_
1748 e = '%.3f' % (e,)
1749 e = '%s, %s(%s)' % (e, E, e)
1750 t = '%d,%3d,%3d' % t
1751 printf('# %s = %s = %s %s', f, e, t, x)
1753 # __doc__ of this file, force all into registery
1754 def _RFs():
1755 yield NN
1756 for t in RefFrames.toRepr(all=True).split(_NL_):
1757 t = t.strip(_COMMA_)
1758 n = t.split(_COLONSPACE_)[0].split(_DOT_)[1]
1759 r = RefFrames.get(n)
1760 x = len(r.Xforms()), -len(r.Xforms(inverse=True))
1761 yield '%s .Xforms=%s' % (t, x)
1763 printf(_NLATvar_.join(sorted(_RFs())), nt=1)
1765 X, t = (), 0 # all form
1766 for r in RefFrames.values():
1767 X += tuple(r._Xto.values())
1768 for X in sorted(X):
1769 t += 1
1770 printf('#%4d %-24s xform=%r', t, X.name, X.xform)
1771 printf('#%29s rates=%r', _SPACE_, X.rates)
1773 t = _args_kwds_names(Transform.__init__)
1774 for n in TRFXform7Tuple._Names_:
1775 if n not in t:
1776 raise AssertionError(_SPACE_(n, _vs_, t))
1778 _main()
1779 del _main
1781# **) MIT License
1782#
1783# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1784#
1785# Permission is hereby granted, free of charge, to any person obtaining a
1786# copy of this software and associated documentation files (the "Software"),
1787# to deal in the Software without restriction, including without limitation
1788# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1789# and/or sell copies of the Software, and to permit persons to whom the
1790# Software is furnished to do so, subject to the following conditions:
1791#
1792# The above copyright notice and this permission notice shall be included
1793# in all copies or substantial portions of the Software.
1794#
1795# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1796# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1797# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1798# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1799# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1800# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1801# OTHER DEALINGS IN THE SOFTWARE.
1803# % python -m pygeodesy.trf
1804#
1805# date2epoch(2024, 1, 1) = 2024.003, epoch2date(2024.003) = 2024, 1, 1
1806# date2epoch(2024, 1, 15) = 2024.041, epoch2date(2024.041) = 2024, 1, 15
1807# date2epoch(2024, 1, 30) = 2024.082, epoch2date(2024.082) = 2024, 1, 30
1808# date2epoch(2024, 1, 31) = 2024.085, epoch2date(2024.085) = 2024, 1, 31
1809# date2epoch(2024, 2, 1) = 2024.087, epoch2date(2024.087) = 2024, 2, 2 *
1810# date2epoch(2024, 2, 15) = 2024.126, epoch2date(2024.126) = 2024, 2, 16 *
1811# date2epoch(2024, 2, 28) = 2024.161, epoch2date(2024.161) = 2024, 2, 28
1812# date2epoch(2024, 2, 29) = 2024.164, epoch2date(2024.164) = 2024, 3, 1 *
1813# date2epoch(2024, 3, 1) = 2024.167, epoch2date(2024.167) = 2024, 3, 2 *
1814# date2epoch(2024, 3, 15) = 2024.205, epoch2date(2024.205) = 2024, 3, 16 *
1815# date2epoch(2024, 3, 30) = 2024.246, epoch2date(2024.246) = 2024, 3, 31 *
1816# date2epoch(2024, 3, 31) = 2024.249, epoch2date(2024.249) = 2024, 4, 1 *
1817# date2epoch(2024, 4, 1) = 2024.251, epoch2date(2024.251) = 2024, 4, 1
1818# date2epoch(2024, 4, 15) = 2024.290, epoch2date(2024.290) = 2024, 4, 15
1819# date2epoch(2024, 4, 29) = 2024.328, epoch2date(2024.328) = 2024, 4, 29
1820# date2epoch(2024, 4, 30) = 2024.331, epoch2date(2024.331) = 2024, 4, 30
1821# date2epoch(2024, 5, 1) = 2024.333, epoch2date(2024.333) = 2024, 5, 1
1822# date2epoch(2024, 5, 15) = 2024.372, epoch2date(2024.372) = 2024, 5, 15
1823# date2epoch(2024, 5, 30) = 2024.413, epoch2date(2024.413) = 2024, 5, 30
1824# date2epoch(2024, 5, 31) = 2024.415, epoch2date(2024.415) = 2024, 6, 1 *
1825# date2epoch(2024, 6, 1) = 2024.418, epoch2date(2024.418) = 2024, 6, 2 *
1826# date2epoch(2024, 6, 15) = 2024.456, epoch2date(2024.456) = 2024, 6, 16 *
1827# date2epoch(2024, 6, 29) = 2024.495, epoch2date(2024.495) = 2024, 6, 30 *
1828# date2epoch(2024, 6, 30) = 2024.497, epoch2date(2024.497) = 2024, 7, 1 *
1829# date2epoch(2024, 7, 1) = 2024.500, epoch2date(2024.500) = 2024, 7, 1
1830# date2epoch(2024, 7, 15) = 2024.538, epoch2date(2024.538) = 2024, 7, 16 *
1831# date2epoch(2024, 7, 30) = 2024.579, epoch2date(2024.579) = 2024, 7, 30
1832# date2epoch(2024, 7, 31) = 2024.582, epoch2date(2024.582) = 2024, 7, 31
1833# date2epoch(2024, 8, 1) = 2024.585, epoch2date(2024.585) = 2024, 8, 1
1834# date2epoch(2024, 8, 15) = 2024.623, epoch2date(2024.623) = 2024, 8, 15
1835# date2epoch(2024, 8, 30) = 2024.664, epoch2date(2024.664) = 2024, 8, 31 *
1836# date2epoch(2024, 8, 31) = 2024.667, epoch2date(2024.667) = 2024, 9, 1 *
1837# date2epoch(2024, 9, 1) = 2024.669, epoch2date(2024.669) = 2024, 9, 2 *
1838# date2epoch(2024, 9, 15) = 2024.708, epoch2date(2024.708) = 2024, 9, 16 *
1839# date2epoch(2024, 9, 29) = 2024.746, epoch2date(2024.746) = 2024, 9, 30 *
1840# date2epoch(2024, 9, 30) = 2024.749, epoch2date(2024.749) = 2024, 10, 1 *
1841# date2epoch(2024, 10, 1) = 2024.751, epoch2date(2024.751) = 2024, 10, 1
1842# date2epoch(2024, 10, 15) = 2024.790, epoch2date(2024.790) = 2024, 10, 15
1843# date2epoch(2024, 10, 30) = 2024.831, epoch2date(2024.831) = 2024, 10, 30
1844# date2epoch(2024, 10, 31) = 2024.833, epoch2date(2024.833) = 2024, 10, 31
1845# date2epoch(2024, 11, 1) = 2024.836, epoch2date(2024.836) = 2024, 11, 1
1846# date2epoch(2024, 11, 15) = 2024.874, epoch2date(2024.874) = 2024, 11, 15
1847# date2epoch(2024, 11, 29) = 2024.913, epoch2date(2024.913) = 2024, 11, 29
1848# date2epoch(2024, 11, 30) = 2024.915, epoch2date(2024.915) = 2024, 12, 1 *
1849# date2epoch(2024, 12, 1) = 2024.918, epoch2date(2024.918) = 2024, 12, 2 *
1850# date2epoch(2024, 12, 15) = 2024.956, epoch2date(2024.956) = 2024, 12, 16 *
1851# date2epoch(2024, 12, 30) = 2024.997, epoch2date(2024.997) = 2024, 12, 31 *
1852# date2epoch(2024, 12, 31) = 2025.000, epoch2date(2025.000) = 2025, 1, 1 *
1854# 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)
1855# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1856# 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)
1857# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1858# 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)
1859# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1860# 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)
1861# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1862# 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)
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# 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)
1865# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1866# 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)
1867# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
1868# 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)
1869# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1870# 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)
1871# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1872# 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)
1873# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
1874# 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)
1875# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=-0.053, sy=0.742, sz=0.032)
1876# 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)
1877# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1878# 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)
1879# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
1880# 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)
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# 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)
1883# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1884# 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)
1885# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1886# 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)
1887# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
1888# 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)
1889# rates=rates(tx=2.9, ty=0.2, tz=0.6, s=-0.01, sx=0.191, sy=0.68, sz=-0.862)
1890# 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)
1891# rates=rates(tx=2.8, ty=0.1, tz=2.5, s=-0.12, sx=0.195, sy=0.721, sz=-0.84)
1892# 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)
1893# rates=rates(tx=-2.8, ty=0.0, tz=-2.7, s=0.12, sx=-0.024, sy=0.329, sz=-0.683)
1894# 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)
1895# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.32, sy=0.78, sz=-0.67)
1896# 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)
1897# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1898# 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)
1899# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1900# 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)
1901# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1902# 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)
1903# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1904# 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)
1905# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1906# 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)
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# 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)
1909# rates=rates(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
1910# 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)
1911# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.081, sy=0.49, sz=-0.792)
1912# 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)
1913# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1914# 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)
1915# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1916# 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)
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# 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)
1919# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1920# 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)
1921# rates=rates(tx=-0.1, ty=-0.1, tz=1.9, s=-0.11, sx=0.085, sy=0.531, sz=-0.77)
1922# 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)
1923# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1924# 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)
1925# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1926# 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)
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# 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)
1929# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1930# 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)
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# 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)
1933# rates=rates(tx=0.1, ty=0.2, tz=-2.1, s=0.11, sx=0.086, sy=0.519, sz=-0.753)
1934# 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)
1935# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1936# 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)
1937# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1938# 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)
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# 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)
1941# rates=rates(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
1942# 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)
1943# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1944# 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)
1945# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1946# 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)
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# 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)
1949# rates=rates(tx=0.0, ty=-0.6, tz=-1.4, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1950# 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)
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# 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)
1953# rates=rates(tx=-2.9, ty=-0.2, tz=-0.6, s=0.01, sx=-0.11, sy=-0.19, sz=0.07)
1954# 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)
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# 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)
1957# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1958# 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)
1959# rates=rates(tx=0.69, ty=-0.1, tz=1.86, s=-0.19201, sx=0.01347, sy=-0.01514, sz=0.00027)
1960# 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)
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# 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)
1963# rates=rates(tx=0.7, ty=-0.7, tz=0.5, s=-0.182, sx=-0.06667, sy=0.75744, sz=0.05133)
1964# 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)
1965# rates=rates(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
1966# 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)
1967# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.054, sy=0.518, sz=-0.781)
1968# 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)
1969# rates=rates(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
1970# 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)
1971# rates=rates(tx=0.5, ty=-0.6, tz=-1.3, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
1972# 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)
1973# rates=rates(tx=-0.3, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
1974# 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)
1975# rates=rates(tx=0.3, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
1976# 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)
1977# rates=rates(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
1978# 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)
1979# rates=rates(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
1980# 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)
1981# rates=rates(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
1982# 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)
1983# rates=rates(tx=0.79, ty=-0.6, tz=-1.34, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
1984# 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)
1985# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0532, sy=-0.7423, sz=-0.0316)
1986# 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)
1987# rates=rates(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
1988# 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)
1989# rates=rates(tx=0.0, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
1990# 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)
1991# rates=rates(tx=0.0, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
1992# 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)
1993# rates=rates(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
1994# 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)
1995# rates=rates(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
1996# 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)
1997# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1998# 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)
1999# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
2000# 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)
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# 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)
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# 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)
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# 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)
2007# rates=rates(tx=-2.8, ty=-0.1, tz=-2.4, s=0.09, sx=-0.11, sy=-0.19, sz=0.07)
2008# 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)
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# 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)
2011# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
2012# 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)
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# 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)
2015# rates=rates(tx=0.3, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
2016# 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)
2017# rates=rates(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
2018# 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)
2019# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
2020# 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)
2021# rates=rates(tx=0.0, ty=0.1, tz=-0.2, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
2022# 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)
2023# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=1.50379, sy=1.18346, sz=1.20716)
2024# 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)
2025# rates=rates(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.0, sy=0.0, sz=0.0)
2026# 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)
2027# rates=rates(tx=0.3, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
2028# 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)
2029# rates=rates(tx=0.0, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
2030# 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)
2031# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2032# 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)
2033# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2034# 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)
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# 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)
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# 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)
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# 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)
2041# rates=rates(tx=-2.8, ty=-0.1, tz=-2.5, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
2042# 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)
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# 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)
2045# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2046# 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)
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# 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)
2049# rates=rates(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
2050# 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)
2051# rates=rates(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
2052# 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)
2053# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
2054# 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)
2055# rates=rates(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.0, sy=0.0, sz=0.0)
2056# 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)
2057# rates=rates(tx=0.3, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
2058# 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)
2059# rates=rates(tx=0.0, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
2060# 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)
2061# rates=rates(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.0, sy=0.0, sz=0.0)
2062# 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)
2063# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2064# 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)
2065# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2066# 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)
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# 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)
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# 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)
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# 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)
2073# rates=rates(tx=-2.8, ty=-0.2, tz=-2.3, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
2074# 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)
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# 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)
2077# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
2078# 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)
2079# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)