Coverage for pygeodesy/trf.py: 94%
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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
9U{latlon-ellipsoidal-referenceframe.js<https://GitHub.com/ChrisVeness/geodesy/blob/master/
10latlon-ellipsoidal-referenceframe.js>} and U{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, isstr, _xinstanceof, _xisscalar, _zip
73from pygeodesy.constants import _float as _F, _0_0s, _0_0, _0_001, _0_5, _1_0, _N_1_0
74from pygeodesy.datums import Datums, _earth_datum, _GDA2020_, _minus, _Names7, \
75 Transform, _S1_S, _WGS84
76from pygeodesy.errors import TRFError, _xattr, _xellipsoidall, _xkwds
77from pygeodesy.interns import MISSING, NN, _AT_, _COMMASPACE_, _conversion_, \
78 _datum_, _DOT_, _exists_, _invalid_, _MINUS_, \
79 _NAD83_, _no_, _PLUS_, _reframe_, _s_, _SPACE_, \
80 _STAR_, _to_, _WGS84_, _x_, _intern as _i
81from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS
82from pygeodesy.named import ADict, classname, _lazyNamedEnumItem as _lazy, _Named, \
83 _NamedEnum, _NamedEnumItem, _NamedTuple, Fmt, unstr
84from pygeodesy.props import deprecated_method, property_doc_, Property_RO, property_RO
85# from pygeodesy.streprs import Fmt, unstr # from .named
86from pygeodesy.units import Epoch, Float
88from math import ceil as _ceil
90__all__ = _ALL_LAZY.trf
91__version__ = '24.02.22'
93_EP0CH = Epoch(0, low=0)
94_Es = {_EP0CH: _EP0CH} # L{Epoch}s, deleted below
95_GRS80 = Datums.GRS80
96_inverse_ = 'inverse'
97_MAS = _MM = _PPB = Float # Units
98_MM2M = _0_001 # scale mm2m, ppb2ppM, mas2as
99_mDays = (0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 0)
100_366_0 = _F(sum(_mDays))
101_rates_ = 'rates' # PYCHOK used!
102_Rs = {} # L{TRFXform7Tuple}s, deleted below
103_S_S1 = _N_1_0 / _S1_S # Transform.s for .s1 == 0
104_v_ = 'v'
105_xform_ = 'xform' # PYCHOK used!
106_Xs = {} # L{TRFXform7Tuple}s, deleted below
108_ETRF88_ = _i('ETRF88')
109_ETRF89_ = _i('ETRF89')
110_ETRF90_ = _i('ETRF90')
111_ETRF91_ = _i('ETRF91')
112_ETRF92_ = _i('ETRF92')
113_ETRF93_ = _i('ETRF93')
114_ETRF94_ = _i('ETRF94')
115_ETRF96_ = _i('ETRF96')
116_ETRF97_ = _i('ETRF97')
117_ETRF2000_ = _i('ETRF2000')
118_ETRF2005_ = _i('ETRF2005')
119_ETRF2008_ = _i('ETRF2008')
120_ETRF2014_ = _i('ETRF2014')
121_ETRF2020_ = _i('ETRF2020')
122_GDA94_ = _i('GDA94')
123_ITRF_ = _i('ITRF')
124_ITRF88_ = _i('ITRF88')
125_ITRF89_ = _i('ITRF89')
126_ITRF90_ = _i('ITRF90')
127_ITRF91_ = _i('ITRF91')
128_ITRF92_ = _i('ITRF92')
129_ITRF93_ = _i('ITRF93')
130_ITRF94_ = _i('ITRF94')
131_ITRF96_ = _i('ITRF96')
132_ITRF97_ = _i('ITRF97')
133_ITRF2000_ = _i('ITRF2000')
134_ITRF2005_ = _i('ITRF2005')
135_ITRF2008_ = _i('ITRF2008')
136_ITRF2014_ = _i('ITRF2014')
137_ITRF2020_ = _i('ITRF2020')
138_NAD83cors96_ = _i('NAD83cors96')
139_WGS84g1150_ = _i('WGS84g1150')
140_WGS84g1674_ = _i('WGS84g1674')
141_WGS84g1762_ = _i('WGS84g1762')
144def _E(epoch): # deleted below
145 '''(INTERNAL) De-dup L{Epochs}s.
146 '''
147 e = Epoch(_F(epoch))
148 return _Es.setdefault(e, e) # PYCHOK del
151def _P(ps, name, _Ps): # deleted below
152 '''(INTERNAL) De-dup L{TRFXform7Tuple}s.
153 '''
154 t = TRFXform7Tuple(map(_F, ps), name=name)
155 return _Ps.setdefault(t, t)
158class RefFrame(_NamedEnumItem):
159 '''Terrestrial Reference Frame (TRF) parameters.
160 '''
161 _datum = _GRS80 # Datums.GRS80 or .WGS84 (L{Datum})
162 _epoch = _EP0CH # epoch, fractional year (L{Epoch})
164 def __init__(self, epoch, datum, name=NN):
165 '''New L{RefFrame}.
167 @arg epoch: Epoch, a fractional calendar year (C{scalar} or C{str}).
168 @arg datum: Datum or ellipsoid (L{Datum}, {Ellipsoid}, L{Ellipsoid2}
169 or L{a_f2Tuple}).
170 @kwarg name: Unique, non-empty name (C{str}).
172 @raise NameError: A L{RefFrame} with that B{C{name}} already exists.
174 @raise TRFError: Invalid B{C{epoch}}.
176 @raise TypeError: Invalid B{C{datum}}.
177 '''
178 if datum is not _GRS80:
179 _earth_datum(self, datum, raiser=_datum_)
180 self._epoch = _Epoch(epoch)
181 self._Xto = {} # dict of Xforms
182 if name:
183 self._register(RefFrames, name)
185 def __eq__(self, other):
186 return isinstance(other, RefFrame) and other.epoch == self.epoch \
187 and other.datum == self.datum
189 def __lt__(self, other): # for sorting
190 return isinstance(other, RefFrame) and (self.name < other.name
191 or self.epoch < other.epoch)
193 @deprecated_method # PYCHOK Python 3.5+
194 def __matmul__(self, point):
195 '''DEPRECATED on 2024.02.16, use method C{B{point}.toRefFrame}.'''
196 return _toRefFrame(point, self)
198 @property_RO
199 def datum(self):
200 '''Get this reference frame's datum (L{Datum}).
201 '''
202 return self._datum
204 @property_RO
205 def ellipsoid(self):
206 '''Get this reference frame's ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
207 '''
208 return self._datum.ellipsoid
210 @Property_RO
211 def epoch(self):
212 '''Get this reference frame's epoch (C{Epoch}).
213 '''
214 return self._epoch
216 def toRefFrame(self, point, reframe2, **epoch2_epoch_name):
217 '''Convert an ellipsoidal point from this reframe and from C{epoch} to
218 an other C{reframe2} and C{epoch2 or epoch}.
220 @arg point: The point to convert (C{Cartesian} or C{LatLon}).
221 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}).
222 @kwarg epoch2_epoch_name: Optional keyword arguments C{B{epoch2}=None},
223 C{B{epoch}=None} and C{B{name}=NN}.
225 @return: A copy of the B{C{point}}, converted or renamed.
227 @raise TypeError: Invalid B{C{point}}.
229 @note: The B{C{point}}'s C{reframe} and C{epoch} are overridden by
230 this reframe respectively B{C{epoch}} or this reframe's epoch.
232 @see: Ellipsoidal methods L{toRefFrame<ellipsoidalBase.LatLonEllipsoidalBase.toRefFrame>}
233 and L{toRefFrame<ellipsoidalBase.CartesianEllipsoidalBase.toRefFrame>}
234 for more details.
235 '''
236 return _toRefFrame(point, reframe2, reframe=self,
237 **_xkwds(epoch2_epoch_name, name=self.name))
239 def toStr(self, epoch=None, name=NN, **unused): # PYCHOK expected
240 '''Return this reference frame as a string.
242 @kwarg epoch: Override this reframe's epoch (C{scalar} or C{str}).
243 @kwarg name: Override name (C{str}) or C{None} to exclude the
244 reframe's name.
246 @return: This L{RefFrame}'s attributes (C{str}).
247 '''
248 D = self.datum
249 e = self.epoch if epoch is None else _Epoch(epoch)
250 t = (Fmt.EQUAL(name=repr(name or self.name)),
251 Fmt.EQUAL(epoch=e),
252 Fmt.EQUAL(datum=_DOT_(classname(D) + _s_, D.name)))
253 return _COMMASPACE_.join(t[int(name is None):])
255 def Xform(self, reframe2):
256 '''Get the converter Xform I{from} this reference frame I{to} C{reframe2}.
258 @arg reframe2: Destination frame to convert I{to} (L{RefFrame} or C{str}).
260 @return: The L{TRFXform} instance or C{None} if not available.
262 @raise TypeError: Invalid B{C{reframe2}}.
263 '''
264 _xinstanceof(RefFrame, str, reframe2=reframe2)
265 n2 = reframe2 if isstr(reframe2) else reframe2.name
266 return self._Xto.get(n2, None)
268 def Xforms(self, inverse=False):
269 '''Return all Xforms converting I{from} or I{to} this reference frame.
271 @kwarg inverse: If C{True}, get all I{inverse, to} Xforms (C{bool}).
273 @return: An L{ADict} of C{name=}L{TRFXform}s I{from} this reframe or
274 if C{B{inverse}=True} I{to} this reframe.
275 '''
276 def _Xi(n2):
277 for n1, r in RefFrames.items():
278 if n2 in r._Xto:
279 yield n1, r
281 return ADict(_Xi(self.name) if inverse else self._Xto)
284class RefFrames(_NamedEnum):
285 '''(INTERNAL) L{RefFrame} registry, I{must} be a sub-class
286 to accommodate the L{_LazyNamedEnumItem} properties.
287 '''
288 def _Lazy(self, epoch, datum=_GRS80, name=NN):
289 '''(INTERNAL) Instantiate the L{RefFrame}.
290 '''
291 return RefFrame(epoch, datum, name=name)
293RefFrames = RefFrames(RefFrame) # PYCHOK singleton
294'''Some pre-defined L{RefFrame}s, all I{lazily} instantiated.'''
295# <https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js>
296RefFrames._assert(
297 ETRF88 = _lazy(_ETRF88_, _E(1988)), # epoch, datum?
298 ETRF89 = _lazy(_ETRF89_, _E(1989)), # epoch, datum?
299 ETRF90 = _lazy(_ETRF90_, _E(1990)), # epoch, datum?
300 ETRF91 = _lazy(_ETRF91_, _E(1991)), # epoch, datum?
301 ETRF92 = _lazy(_ETRF92_, _E(1992)), # epoch, datum?
302 ETRF93 = _lazy(_ETRF93_, _E(1993)), # epoch, datum?
303 ETRF94 = _lazy(_ETRF94_, _E(1994)), # epoch, datum?
304 ETRF96 = _lazy(_ETRF96_, _E(1996)), # epoch, datum?
305 ETRF97 = _lazy(_ETRF97_, _E(1997)), # epoch, datum?
306 ETRF2000 = _lazy(_ETRF2000_, _E(2005)),
307 ETRF2005 = _lazy(_ETRF2005_, _E(2005)), # epoch, datum?
308 ETRF2008 = _lazy(_ETRF2008_, _E(2008)), # epoch, datum?
309 ETRF2014 = _lazy(_ETRF2014_, _E(2014)), # epoch, datum?
310 ETRF2020 = _lazy(_ETRF2020_, _E(2020)), # epoch, datum?
311 GDA94 = _lazy(_GDA94_, _E(1994)), # Australia
312 GDA2020 = _lazy(_GDA2020_, _E(2020)), # Australia
313 ITRF88 = _lazy(_ITRF88_, _E(1988)),
314 ITRF89 = _lazy(_ITRF89_, _E(1989)),
315 ITRF90 = _lazy(_ITRF90_, _E(1988)),
316 ITRF91 = _lazy(_ITRF91_, _E(1988)),
317 ITRF92 = _lazy(_ITRF92_, _E(1988)),
318 ITRF93 = _lazy(_ITRF93_, _E(1988)),
319 ITRF94 = _lazy(_ITRF94_, _E(1993)),
320 ITRF96 = _lazy(_ITRF96_, _E(1997)),
321 ITRF97 = _lazy(_ITRF97_, _E(1997)),
322 ITRF2000 = _lazy(_ITRF2000_, _E(1997)), # aka ITRF00
323 ITRF2005 = _lazy(_ITRF2005_, _E(2000)),
324 ITRF2008 = _lazy(_ITRF2008_, _E(2005)), # aka ITRF08
325 ITRF2014 = _lazy(_ITRF2014_, _E(2010)),
326 ITRF2020 = _lazy(_ITRF2020_, _E(2015)),
327 NAD83 = _lazy(_NAD83_, _E(1997)),
328 NAD83cors96 = _lazy(_NAD83cors96_, _E(1997)),
329 WGS84 = _lazy(_WGS84_, _E(1984), _WGS84),
330 WGS84g1150 = _lazy(_WGS84g1150_, _E(2001), _WGS84),
331 WGS84g1674 = _lazy(_WGS84g1674_, _E(2005), _WGS84),
332 WGS84g1762 = _lazy(_WGS84g1762_, _E(2005), _WGS84)) # same epoch
335class TransformXform(Transform):
336 '''Helmert transformation, extended with an C{Xform} converter.
338 @see: L{Transform<datums.Transform>} and L{Xform<TRFXform>}.
339 '''
340 _Xform = None
342 def __init__(self, name=NN, **tx_ty_tz_s_sx_sy_sz): # PYCHOK signature
343 '''New L{TransformXform}.
345 @kwarg name: Optional name (C{str}), I{not registered}.
347 @see: L{Transform<datums.Transform>} for details.
349 @note: This L{TransformXform}'s name starts with C{"-"} iff
350 I{inversed}.
351 '''
352 Transform.__init__(self, **tx_ty_tz_s_sx_sy_sz)
353 if name:
354 self.name = name
356 def __eq__(self, other):
357 return isinstance(other, TransformXform) and Transform.__eq__(self, other)
359 def rename(self, name=NN):
360 '''Change this transform's name.
362 @arg name: New name (C{str}), overriding this transform's Xform's name.
364 @return: The previous name (C{str}).
365 '''
366 X = self.Xform
367 n = name or (X.toStr() if X else NN)
368 return Transform.rename(self, n)
370 def toRefFrame(self, point, name=NN): # PYCHOK signature
371 '''Convert an ellipsoidal point using this transform and Xform.
373 @arg point: The point to convert (C{Cartesian} or C{LatLon}).
375 @return: A copy of the B{C{point}}, converted I{directly} to
376 this transform's Xform's C{refName2} and C{epoch}.
378 @note: The B{C{point}}'s original C{reframe} and C{epoch} are
379 I{ignored}, its C{datum} and C{height} are preserved
380 but I{not} taken into account.
381 '''
382 _ = _xellipsoidall(point)
383 p = point.dup() if self.isunity else point.toTransform(self)
384 X = self.Xform
385 if X: # see _toRefFrame below
386 p._reframe = X.reframe2
387 p._epoch = X.epoch
388 p.rename(name or self.name)
389 return p
391 def toTransform(self, epoch1, **epoch2_inverse):
392 '''Return this transform observed at B{C{epoch1}} as a Helmert
393 L{TransformXform}, optionally at B{C{epoch2 or epoch1}}.
395 @arg epoch1: Epoch to observe I{from} (C{scalar}).
396 @kwarg epoch2_inverse: Optional C{B{epoch2}=None} to observe
397 I{to} and C{B{inverse}=False}, see method
398 L{toTransform<TRFXform.toTransform>} from
399 L{TRFXform}.
401 @return: The Helmert transform (L{TransformXform}).
403 @raise TRFError: Invalid B{C{epoch1}}, B{C{epoch2}} or
404 missing Xform.
405 '''
406 X = self.Xform
407 if X is None:
408 raise TRFError(Xform=X, txt=MISSING)
409 return X.toTransform(epoch1, **epoch2_inverse)
411 def velocities(self, factor=_MM2M, **Vector_and_kwds):
412 '''Compute the X, Y and Z I{velocities} of this transform.
414 @kwarg factor: Factor to scale this Xform's C{rates} (C{scalar}),
415 default from C{milli-meter-} to C{meter-per-year}.
416 @kwarg Vector_and_kwds: An optional, (3-D) C{B{Vector}=None} or
417 cartesian class and additional C{B{Vector}}
418 keyword arguments to return the I{velocities}.
420 @return: A L{Vector3Tuple}C{(x, y, z)} unless some B{C{Vector_and_kwds}}
421 is specified or C{None} if this transform's Xform is missing.
423 @raise TypeError: Non-scalar B{C{factor}}.
425 @see: Altamimi, Z. "EUREF-TN-1-Jan-31-2024", U{Appendix A, equation (3)
426 <http://ETRS89.ENSG.IGN.FR/pub/EUREF-TN-1-Jan-31-2024.pdf>}.
427 '''
428 v = X = self.Xform
429 if X is not None:
430 r = X.rates * factor # eq (3) ...
431 H = Transform(tx=r.sx, ty=r.sy, tz=r.sz, # Xyy-dot
432 s=_S_S1, name=NN(self.name, _v_))
433 H.s1, H.rx, H.ry, H.rz = 0, self.rx, self.ry, self.rz
434 v = H.transform(r.tx, r.ty, r.tz, inverse=False, # Xyy
435 **Vector_and_kwds)
436 return v
438 @property_doc_(''' the Xform (L{TRFXform}).''')
439 def Xform(self):
440 '''Get this Helmert transform's Xform (L{TRFXform} or C{None}).
441 '''
442 return self._Xform
444 @Xform.setter # PYCHOK setter!
445 def Xform(self, Xform):
446 '''Set this Helmert transform's Xform (L{TRFXform}).
448 @raise TypeError: Invalid B{C{Xform}}.
449 '''
450 _xinstanceof(TRFXform, Xform=Xform)
451 self._Xform = Xform
454class TRFXform7Tuple(_NamedTuple):
455 '''7-Tuple C{(tx, ty, tz, s, sx, sy, sz)} of conversion parameters with
456 translations C{tx}, C{ty} and C{tz} in C{milli-meter}, scale C{s} in
457 C{ppb} and rates C{sx}, C{sy} and C{sz} in C{milli-arc-seconds-per-year}.
459 @note: The parameters are also named as C{(Tx, Ty, Tz, D, Rx, Ry, Rz)}
460 or C{(T1, T2, T3, D, R1, R2, R3)}.
462 @see: Class L{TransformXform}'s matching keyword argument names.
463 '''
464 _Names_ = _Names7 # ('tx', 'ty', 'tz', _s_, 'sx', 'sy', 'sz') == Transform.__init__
465 _Units_ = (_MM, _MM, _MM, _PPB, _MAS, _MAS, _MAS)
467 def __add__(self, other):
468 _xinstanceof(TRFXform7Tuple, other=other)
469 return type(self)(((a + b) for a, b in _zip(self, other)), name=_PLUS_) # .fsums._add_op
471 def __eq__(self, other):
472 return isinstance(other, TRFXform7Tuple) and all(a == b for a, b in _zip(self, other))
473 # PYCHOK and self.name == other.name
475 def __hash__(self):
476 return self._hash # memoized
478 def __mul__(self, factor):
479 _xisscalar(factor=factor)
480 return type(self)((s * factor for s in self), name=_STAR_) # .fsums._mul_op
482 def __neg__(self):
483 return self.inverse()
485 def __sub__(self, other):
486 _xinstanceof(TRFXform7Tuple, other=other)
487 return type(self)(((a - b) for a, b in _zip(self, other)), name=_MINUS_) # .fsums._sub_op
489 @Property_RO
490 def _hash(self):
491 return hash(s for s in self)
493 def inverse(self, name=NN):
494 '''Return the inverse of this transform.
496 @kwarg name: Optional name (C{str}).
498 @return: Inverse (L{TransformXform}).
499 '''
500 n = name or _minus(self.name)
501 return type(self)(map(neg, self), name=n)
503 @Property_RO
504 def isunity(self):
505 '''Is this a C{unity, identidy} transform (C{bool}).
506 '''
507 return not any(self)
510class TRFXform(_Named):
511 '''A Terrestrial Reference Frame (TRF) converter between two
512 reference frames observed at an C{epoch}.
513 '''
514 _epoch = _EP0CH
515 _epoch_d = _0_0
516 _indir_d = NN # refName
517 _inver_d = False
518 refName1 = \
519 refName2 = NN
520 rates = \
521 xform = None
523 def __init__(self, refName1, refName2, epoch=None, xform=None,
524 rates=None, name=NN):
525 '''New L{trfXform}.
527 @arg refName1: Source reframe (C{str}), converting I{from}.
528 @arg refName2: Destination reframe (C{str}), converting I{to}.
529 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str}).
530 @kwarg xform: I{Transform} parameters (L{TRFXform7Tuple}).
531 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), like B{C{xform}},
532 but in C{units-per-year}.
533 @kwarg name: Optional name (C{str}), overriding the default from
534 method L{toStr<TRFXform.toStr>}.
536 @return: The TRF converter (L{TRFXform}).
538 @raise TRFError: Invalid B{C{epoch}}, B{C{xform}} or B{C{rates}}.
539 '''
540 self.refName1 = str(refName1)
541 self.refName2 = str(refName2)
542 _xinstanceof(TRFXform7Tuple, xform=xform, rates=rates)
543 self.epoch = epoch
544 self.xform = xform
545 self.rates = rates
546 self.rename(name or self.toStr())
548 def __eq__(self, other):
549 return isinstance(other, TRFXform) and self.epoch == other.epoch and \
550 self.xform == other.xform and self.rates == other.rates
552 def __lt__(self, other): # for sorting
553 return isinstance(other, TRFXform) and (self.refName1 < other.refName1
554 or self.refName2 < other.refName2
555 or self.epoch < other.epoch)
557 def __neg__(self):
558 return self.inverse()
560 def __repr__(self):
561 return self.toRepr()
563 def __str__(self):
564 return self.toStr()
566 def _at(self, epoch):
567 '''(INTERNAL) Return C{"self.nameB{@}epoch"}.
568 '''
569 n = self.name
570 if epoch != self.epoch:
571 _e = _AT_(NN, epoch)
572 if not n.endswith(_e):
573 n = NN(n, _e)
574 return n
576 @property_doc_(''' the epoch, fractional year (L{Epoch}).''')
577 def epoch(self):
578 '''Get the epoch (L{Epoch}).
579 '''
580 return self._epoch
582 @epoch.setter # PYCHOK setter!
583 def epoch(self, epoch):
584 '''Set the epoch (L{Epoch}, C{scalar} or C{str}).
586 @raise TRFError: Invalid B{C{epoch}}.
587 '''
588 e = _Epoch(epoch)
589 if self._epoch != e:
590 self.rename(self._at(e))
591 self._epoch = e
593 @property_RO
594 def epoched(self):
595 '''Get this Xform's I{epoch} deltas (C{float}).
596 '''
597 return self._epoch_d
599 @property_RO
600 def indirected(self):
601 '''Is this an I{indirected} Xform? (C{str}) or C{NN}.
602 '''
603 return self._indir_d
605 def inverse(self, name=NN):
606 '''Get an I{inverse} of this Xform, C{refName1} and C{-2} swapped.
608 @return: Inverse (L{TRFXform}).
609 '''
610 return self.dup(refName1=self.refName2, xform=-self.xform,
611 refName2=self.refName1, rates=-self.rates,
612 name=name or _minus(self.name),
613 _inver_d=not self.inversed)
615 @property_RO
616 def inversed(self):
617 '''Is this an I{inversed} Xform? (C{bool}).
618 '''
619 return self._inver_d
621 def _reframe(self, name, datum=_GRS80):
622 '''(INTERNAL) Get an un-/registered frame.
623 '''
624 r = RefFrames.get(name)
625 if r is None or r.datum != datum:
626 r = RefFrame(self.epoch, datum)
627 r.name = name # unregistered
628 return r
630 @property_RO
631 def reframe1(self):
632 '''Get the un-/registered I{from} frame (C{RefFrame}).
633 '''
634 return self._reframe(self.refName1)
636 @property_RO
637 def reframe2(self):
638 '''Get the un-/registered I{to} frame (C{RefFrame}).
639 '''
640 return self._reframe(self.refName2)
642 def rename(self, name=NN):
643 '''Change this Xform's name.
645 @arg name: New name (C{str}), overriding the base
646 name C{"refName1B{@}epochB{x}refName2"}.
648 @return: The old name (C{str}).
649 '''
650 return _Named.rename(self, name or self.toStr())
652 def toEpoch(self, epoch):
653 '''Convert this Xform to B{C{epoch}}, if needed.
655 @arg epoch: Epoch, fractional year (C{Epoch}, C{scalar}
656 or C{str}).
658 @return: This Xform or a copy converted to B{C{epoch}}.
660 @raise TRFError: Invalid B{C{epoch}}.
661 '''
662 e = _Epoch(epoch)
663 X, d = self, e - self.epoch
664 if d:
665 t = X.xform + X.rates * d
666 X = X.dup(epoch=e, xform=t, name=X._at(e))
667 X._epoch_d += d # abs(d)?
668 return X
670 def toHelmert(self, factor=_MM2M):
671 '''Return the Helmert transform from this Xform scaled accordingly.
673 @kwarg factor: Scale to convert C{milli-meter} (C{scalar}).
675 @return: The Helmert transform (L{TransformXform}).
677 @note: By defaut, Translations are converted from C{milli-meter} to
678 C{meter}, rates from C{milli-arc-seconds} to C{arc-seconds}
679 and scale from C{ppb} to C{ppM}.
680 '''
681 h = self.xform * factor
682 H = TransformXform(name=self.name, **dict(h.items()))
683 H.Xform = self
684 return H
686 def toRefFrame(self, point, epoch=None, datum=_GRS80, **epoch2_name):
687 '''Convert an ellipsoidal point from this Xform's C{refName1} and
688 C{epoch} to this Xform's C{refName2} and C{epoch2 or epoch}.
690 @arg point: The point to convert (C{Cartesian} or C{LatLon}).
691 @kwarg epoch: Optional epoch ((L{Epoch}, C{scalar} or C{str})),
692 overriding this Xform's C{epoch}.
693 @kwarg datum: Optional datum to define a temporary L{RefFrame} from
694 this Xform's C{refName1} or C{refName2} (C{datum}).
695 @kwarg epoch2_name: Optional keyword arguments B{C{epoch2}=None}
696 and C{B{name}=refName1}.
698 @return: A copy of the B{C{point}}, converted or renamed.
700 @see: Method L{RefFrame.toRefFrame} for more details.
701 '''
702 def _r(name):
703 r = RefFrames.get(name)
704 if r is None or r.datum != datum:
705 r = RefFrame(epoch or self.epoch, datum)
706 r.name = name # unregistered
707 return r
709 return _r(self.refName1).toRefFrame(point,
710 _r(self.refName2), epoch=epoch, **epoch2_name)
712 def toRepr(self, **unused): # PYCHOK signature
713 '''Return the represention of this Xform (C{str}).
714 '''
715 return unstr(self.classname, name=self.name, epoch=self.epoch)
717 def toStr(self, epoch=None, **unused): # PYCHOK signature
718 '''Return this Xform as C{"refName1B{@}epochB{x}refName2"} (C{str}).
720 @kwarg epoch: Epoch (C{Epoch}, C{scalar} or C{str}), overriding
721 this Xform's epoch.
722 '''
723 e = self.epoch if epoch is None else _Epoch(epoch)
724 return NN(_AT_(self.refName1, e), _x_, self.refName2)
726 def toTransform(self, epoch, epoch2=None, inverse=False):
727 '''Combine this Xform observed at B{C{epoch}} into a Helmert
728 L{TransformXform}, optionally at B{C{epoch2 or epoch}}.
730 @arg epoch: Epoch to observe I{from} (C{scalar}).
731 @kwarg epoch2: Optional epoch to observe I{to} (C{scalar}).
732 @kwarg inverse: Use the Xform's inverse (C{bool}).
734 @return: The Helmert transform (L{TransformXform}).
736 @raise TRFError: Invalid B{C{epoch}} or B{C{epoch2}}.
738 @see: Method L{toHelmert}.
739 '''
740 # X=self.toEpoch(epoch); if epoch2: X=X.toEpoch(epoch2)
741 e = epoch if epoch2 is None else Epoch(epoch2=epoch2)
742 X = self.toEpoch(e)
743 if inverse:
744 X = X.inverse()
745 return X.toHelmert()
748def date2epoch(year, month, day):
749 '''Return the C{epoch} for a calendar day.
751 @arg year: Year of the date (C{scalar}).
752 @arg month: Month in the B{C{year}} (C{scalar}, 1..12).
753 @arg day: Day in the B{C{month}} (C{scalar}, 1..31).
755 @return: Epoch, the fractional year (C{float}).
757 @raise TRFError: Invalid B{C{year}}, B{C{month}} or B{C{day}}.
759 @note: Any B{C{year}} is considered a leap year, i.e. having
760 29 days in February.
761 '''
762 try:
763 y, m, d = map1(int, year, month, day)
764 if y > 0 and 1 <= m <= 12 and 1 <= d <= _mDays[m]:
765 e = y + float(sum(_mDays[:m]) + d) / _366_0
766 return Epoch(e, low=0)
768 raise ValueError # _invalid_
769 except (TRFError, TypeError, ValueError) as x:
770 raise TRFError(year=year, month=month, day=day, cause=x)
773def _direct(n1, n2):
774 '''(INTERNAL) Get the C{n1} to C{n2} Xform or C{None}.
775 '''
776 r = RefFrames.get(n1)
777 return r._Xto.get(n2, None) if r else None
780def _Epoch(e, **kwds):
781 '''(INTERNAL) Get the C{Epoch(B{e})}.
782 '''
783 return e if isinstance(e, Epoch) and not kwds else Epoch(e, **kwds)
786def epoch2date(epoch):
787 '''Return the date for a reference frame C{epoch}.
789 @arg epoch: Fractional year (C{scalar}).
791 @return: 3-Tuple C{(year, month, day)}.
793 @raise TRFError: Invalid B{C{epoch}}.
795 @note: Any B{C{year}} is considered a leap year, i.e. having
796 29 days in February.
797 '''
798 e = Epoch(epoch, low=0)
799 y = int(e)
800 d = int(_ceil((e - y) * _366_0))
801 for m, n in enumerate(_mDays[1:]):
802 if d > n:
803 d -= n
804 else:
805 break
806 return y, (m + 1), max(1, d)
809def _indirects(n1, n2):
810 '''(INTERNAL) Yield all Xforms between C{n1} and C{n2} via C{n}.
811 '''
812 def _X4(_Xto, n2):
813 _d = _direct
814 for n, X1 in _Xto.items():
815 X2 = _d(n, n2)
816 if X2:
817 yield X1, X2, n, True # +
818 X2 = _d(n2, n)
819 if X2:
820 yield X1, X2, n, False # -
822 r1 = RefFrames.get(n1)
823 if r1:
824 for X1, X2, n, f in _X4(r1._Xto, n2):
825 e1, e2 = X1.epoch, X2.epoch
826 if e1 < e2: # X1 to e2
827 X1 = X1.toEpoch(e2)
828 e1 = e2
829 elif e1 > e2: # X2 to e1
830 X2 = X2.toEpoch(e1)
831 # U{Appendix, Table 7, last column "Sum of the previous ..."
832 # <https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf">}
833 X = TRFXform(n1, n2, epoch=e1,
834 xform=X1.xform + (X2.xform if f else -X2.xform),
835 rates=X1.rates + (X2.rates if f else -X2.rates),
836 name=NN(X1._at(e1), _PLUS_ if f else _MINUS_,
837 X2._at(e1)))
838 X._epoch_d = X1.epoched + X2.epoched # max, abs?
839 X._indir_d = n # reframe?
840 yield X
843def _reframe(**name_reframe):
844 '''(INTERNAL) Get a C{reframe}.
845 '''
846 if len(name_reframe) == 1:
847 for r in name_reframe.values():
848 break
849 if isstr(r) and r: # not NN
850 r = RefFrames.get(r)
851 if r and isinstance(r, RefFrame):
852 return r
853 raise TRFError(**name_reframe) # _invalid_
856def _toRefFrame(point, reframe2, reframe=None, epoch=None,
857 epoch2=None, name=NN, **LatLon_kwds):
858 '''(INTERNAL) Convert an ellipsoidal point to C{reframe2}
859 and C{epoch2 or epoch or pont.epoch or reframe.epoch}.
860 '''
861 ll = _xellipsoidall(point)
862 r1 = reframe or point.reframe
863 if not r1:
864 t = _SPACE_(_DOT_(repr(point), _reframe_), MISSING)
865 raise TRFError(_no_(_conversion_), txt=t)
867 _xinstanceof(RefFrame, reframe2=reframe2, reframe=r1)
869 e1 = _Epoch(epoch or point.epoch or r1.epoch)
870 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2)
871 t0 = _toTransform0(r1.name, e1, reframe2.name, e2)
872 if t0 is None:
873 t = _SPACE_(RefFrame.__name__, _AT_(r1.name, e1),
874 _to_, _AT_(reframe2.name, e2))
875 raise TRFError(_no_(_conversion_), txt=t)
877 if t0: # is not ()
878 if t0.isunity:
879 p = point.dup()
880 elif point.datum:
881 p = point.toCartesian() if ll else point
882 p = p.toDatum( r1.datum).toTransform(t0) \
883 .toDatum(reframe2.datum).toDatum(point.datum)
884 if ll:
885 p = p.toLatLon(LatLon=point.classof, **LatLon_kwds)
886 elif ll: # and LatLon_kwds
887 p = point.toTransform(t0, **LatLon_kwds)
888 else:
889 p = point.toTransform(t0)
890 p._reframe = reframe2 # see TRFXform.toRefFrame above
891 p._epoch = _xattr(t0.Xform, epoch=e2)
892 p.rename(name or reframe2.name)
893 else:
894 p = point.dup(name=name) if name else point
895 return p
898def _toTransform0(n1, e1, n2, e2, **indirect_inverse):
899 '''(INTERNAL) Return a L{TransformXform}, 0-tuple or C{None}.
900 '''
901 if n1 == n2 and e1 == e2:
902 return () # unity?
904 for X in _toTransforms(n1, e1, n2, e2, **indirect_inverse):
905 return X # first OK?
907 if (n1.startswith(_ITRF_) and n2.startswith(_WGS84_)) or \
908 (n2.startswith(_ITRF_) and n1.startswith(_WGS84_)):
909 return () # unity?
911 return None
914def _toTransforms(n1, e1, n2, e2, indirect=True, inverse=True):
915 '''(INTERNAL) Yield all possible Helmert transforms, if any.
916 '''
917 def _k(X):
918 return -X.epoch
920 X = _direct(n1, n2)
921 if X:
922 yield X.toTransform(e1, epoch2=e2)
924 if inverse:
925 X = _direct(n2, n1)
926 if X:
927 yield X.toTransform(e1, epoch2=e2, inverse=True)
929 if indirect:
930 for X in sorted(_indirects(n1, n2), key=_k):
931 yield X.toTransform(e1, epoch2=e2)
933 if inverse:
934 for X in sorted(_indirects(n2, n1), key=_k):
935 yield X.toTransform(e1, epoch2=e2, inverse=True)
938def trfTransform0(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True):
939 '''Get a Helmert transform to convert one C{reframe} observed at C{epoch}
940 to an other C{reframe2} at observed at C{epoch2 or epoch}.
942 @return: A L{TransformXform} instance, a C{0-tuple} for I{unity, identity} or
943 C{None} if no conversion exists.
945 @see: Function L{trfTransforms} for futher details.
946 '''
947 return _trfT0s(_toTransform0, reframe, reframe2, epoch, epoch2,
948 indirect=indirect, inverse=inverse)
951def trfTransforms(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True):
952 '''Yield all Helmert transform to convert one C{reframe} observed at C{epoch}
953 to an other C{reframe2} at observed at C{epoch2 or epoch}.
955 @arg reframe: The frame to convert I{from} (L{RefFrame} or C{str}).
956 @arg reframe2: The frame to convert I{to} (L{RefFrame} or C{str}).
957 @arg epoch: Epoch to observe I{from} (L{Epoch}, C{scalar} or C{str}),
958 otherwise C{B{reframe}}'s C{epoch}.
959 @kwarg epoch2: Optional epoch to observe to observe I{to} (L{Epoch}, C{scalar}
960 or C{str}), otherwise B{C{epoch}} or C{B{reframe}}'s C{epoch}.
961 @kwarg indirect: If C{True}, include transforms via I{one} intermediate reframe,
962 otherwise only I{direct} B{C{reframe}} to B{C{reframe2}}
963 transforms (C{bool}).
964 @kwarg inverse: If C{True}, include inverse, otherwise only forward transforms
965 (C{bool}).
967 @return: A L{TransformXform} instance for each available conversion.
969 @raise TRFError: Invalid B{C{reframe}}, B{C{epoch}}, B{C{reframe2}} or
970 B{C{epoch2}}.
972 @raise TypeError: Invalid B{C{reframe}} or B{C{reframe2}}.
973 '''
974 return _trfT0s(_toTransforms, reframe, reframe2, epoch, epoch2,
975 indirect=indirect, inverse=inverse)
978def _trfT0s(_toT0s, reframe, reframe2, epoch, epoch2, **indirect_inverse):
979 '''(INTERNAL) Handle C{trfTransforms0} and C{trfTransforms} calls.
980 '''
981 r1 = _reframe(reframe=reframe)
982 e1 = r1.epoch if epoch is None else _Epoch(epoch)
983 r2 = _reframe(reframe2=reframe2)
984 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2)
985 return _toT0s(r1.name, e1, r2.name, e2, **indirect_inverse)
988def trfXform(reframe1, reframe2, epoch=None, xform=None, rates=None, raiser=True):
989 '''Define a new Terrestrial Reference Frame (TRF) converter or get an
990 existing one.
992 @arg reframe1: Source frame (L{RefFrame} or C{str}), converting I{from}.
993 @arg reframe2: Destination frame (L{RefFrame} or C{str}), converting I{to}.
994 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str})
995 or C{None} for C{B{reframe2}}'s epoch.
996 @kwarg xform: I{Transform} parameters (L{TRFXform7Tuple}).
997 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), as B{C{xform}},
998 but in C{units-per-year}.
999 @kwarg raiser: If C{False}, do not raise an error if the converter
1000 exists, replace it (C{bool}).
1002 @return: The new TRF converter (L{TRFXform}) or if no B{C{epoch}},
1003 B{C{xform}} and B{C{rates}} are given, return the existing
1004 one (L{TRFXform}) or C{None} if not available.
1006 @raise TRFError: Invalid B{C{reframe1}}, B{C{reframe2}}, B{C{epoch}},
1007 B{C{xform}} or B{C{rates}} or the TRF converter
1008 already exists.
1009 '''
1010 try:
1011 r1 = _reframe(reframe1=reframe1)
1012 r2 = _reframe(reframe2=reframe2)
1013 if epoch is None:
1014 if xform is rates is None:
1015 return r1._Xto.get(r2.name, None)
1016 e = r2.epoch
1017 else:
1018 e = _Epoch(epoch)
1019 return _trfX(r1.name, r2.name, raiser=raiser, epoch=e,
1020 xform=xform, rates=rates)
1021 except (TypeError, ValueError) as x:
1022 t = unstr(trfXform, reframe1, reframe2, epoch=epoch)
1023 raise TRFError(t, cause=x)
1026def _trfX(n1, n2, raiser=True, **epoch_xform_rates):
1027 '''(INTERNAL) New, I{unique} L{TRFXform} converter.
1028 '''
1029 r1 = RefFrames.get(n1)
1030 if r1 is None:
1031 raise ValueError(_invalid_)
1032 r2 = RefFrames.get(n2)
1033 if r2 is None:
1034 raise ValueError(_invalid_)
1035 if raiser:
1036 if n2 in r1._Xto:
1037 raise ValueError(_exists_)
1038 if n1 in r2._Xto:
1039 raise ValueError(_SPACE_(_inverse_, _exists_))
1040 r1._Xto[n2] = X = TRFXform(n1, n2, **epoch_xform_rates)
1041 return X
1044def _X(*ps): # deleted below
1045 return _P(ps, _xform_, _Xs) # PYCHOK del
1048def _R(*ps): # deleted below
1049 return _P(ps, _rates_, _Rs) # PYCHOK del
1052_P_0_0s = TRFXform7Tuple(_0_0s(len(_Names7)), name='unity')
1054# TRF conversions specified as an epoch and 2 sets of 7 parameters. Most from Altamimi, Z. U{"EUREF Technical
1055# Note 1: Relationship and Transformation between the International and the European Terrestrial Reference
1056# Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Appendix A, more at U{Quinsy QPS <https://
1057# confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ITRF_Transformation_Parameters.xlsx>}.
1058# See also U{Quinsy International Terrestrial Reference Frame 2014 (ITRF2014)<https://confluence.QPS.NL/qinsy/latest/
1059# en/international-terrestrial-reference-frame-2014-itrf2014-182618383.html>}.
1060_trfX(_ITRF2020_, _ITRF2014_, epoch=_E(2015), # <https://ITRF.IGN.Fr/docs/solutions/itrf2020/Transfo-ITRF2020_TRFs.txt>
1061 xform=_X( -1.4, -0.9, 1.4, -0.42, _0_0, _0_0, _0_0),
1062 rates=_R( _0_0, -0.1, 0.2, _0_0, _0_0, _0_0, _0_0))
1063_trfX(_ITRF2020_, _ITRF2008_, epoch=_E(2015),
1064 xform=_X( 0.2, 1.0, 3.3, -0.29, _0_0, _0_0, _0_0),
1065 rates=_R( _0_0, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0))
1066_trfX(_ITRF2020_, _ITRF2005_, epoch=_E(2015),
1067 xform=_X( 2.7, 0.1, -1.4, 0.65, _0_0, _0_0, _0_0),
1068 rates=_R( 0.3, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0))
1069_trfX(_ITRF2020_, _ITRF2000_, epoch=_E(2015),
1070 xform=_X( -0.2, 0.8, -34.2, 2.25, _0_0, _0_0, _0_0),
1071 rates=_R( 0.1, _0_0, -1.7, 0.11, _0_0, _0_0, _0_0))
1072_trfX(_ITRF2020_, _ITRF97_, epoch=_E(2015),
1073 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
1074 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1075_trfX(_ITRF2020_, _ITRF96_, epoch=_E(2015),
1076 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
1077 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1078_trfX(_ITRF2020_, _ITRF94_, epoch=_E(2015),
1079 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
1080 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1081_trfX(_ITRF2020_, _ITRF93_, epoch=_E(2015),
1082 xform=_X( -65.8, 1.9, -71.3, 4.47, -3.36, -4.33, 0.75),
1083 rates=_R( -2.8, -0.2, -2.3, 0.12, -0.11, -0.19, 0.07))
1084_trfX(_ITRF2020_, _ITRF92_, epoch=_E(2015),
1085 xform=_X( 14.5, -1.9, -85.9, 3.27, _0_0, _0_0, 0.36),
1086 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1087_trfX(_ITRF2020_, _ITRF91_, epoch=_E(2015),
1088 xform=_X( 26.5, 12.1, -91.9, 4.67, _0_0, _0_0, 0.36),
1089 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1090_trfX(_ITRF2020_, _ITRF90_, epoch=_E(2015),
1091 xform=_X( 24.5, 8.1, -107.9, 4.97, _0_0, _0_0, 0.36),
1092 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1093_trfX(_ITRF2020_, _ITRF89_, epoch=_E(2015),
1094 xform=_X( 29.5, 32.1, -145.9, 8.37, _0_0, _0_0, 0.36),
1095 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1096_trfX(_ITRF2020_, _ITRF88_, epoch=_E(2015),
1097 xform=_X( 24.5, -3.9, -169.9, 11.47, 0.1, _0_0, 0.36),
1098 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1100# see U{Transformation Parameters ITRF2014<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2014_ITRFs.txt>} and
1101# Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1102# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1.pdf>} Appendix A.
1103_trfX(_ITRF2014_, _ITRF2008_, epoch=(2010), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2014/tp_14-08.php>
1104 xform=_X( 1.6, 1.9, 2.4, -0.02, _0_0, _0_0, _0_0),
1105 rates=_R( _0_0, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0))
1106_trfX(_ITRF2014_, _ITRF2005_, epoch=_E(2010),
1107 xform=_X( 2.6, _1_0, -2.3, 0.92, _0_0, _0_0, _0_0),
1108 rates=_R( 0.3, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0))
1109_trfX(_ITRF2014_, _ITRF2000_, epoch=_E(2010),
1110 xform=_X( 0.7, 1.2, -26.1, 2.12, _0_0, _0_0, _0_0),
1111 rates=_R( 0.1, 0.1, -1.9, 0.11, _0_0, _0_0, _0_0))
1112_trfX(_ITRF2014_, _ITRF97_, epoch=_E(2010),
1113 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1114 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1115_trfX(_ITRF2014_, _ITRF96_, epoch=_E(2010),
1116 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1117 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1118_trfX(_ITRF2014_, _ITRF94_, epoch=_E(2010),
1119 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1120 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1121_trfX(_ITRF2014_, _ITRF93_, epoch=_E(2010),
1122 xform=_X( -50.4, 3.3, -60.2, 4.29, -2.81, -3.38, 0.4),
1123 rates=_R( -2.8, -0.1, -2.5, 0.12, -0.11, -0.19, 0.07))
1124_trfX(_ITRF2014_, _ITRF92_, epoch=_E(2010),
1125 xform=_X( 15.4, 1.5, -70.8, 3.09, _0_0, _0_0, 0.26),
1126 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1127_trfX(_ITRF2014_, _ITRF91_, epoch=_E(2010),
1128 xform=_X( 27.4, 15.5, -76.8, 4.49, _0_0, _0_0, 0.26),
1129 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1130_trfX(_ITRF2014_, _ITRF90_, epoch=_E(2010),
1131 xform=_X( 25.4, 11.5, -92.8, 4.79, _0_0, _0_0, 0.26),
1132 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1133_trfX(_ITRF2014_, _ITRF89_, epoch=_E(2010),
1134 xform=_X( 30.4, 35.5, -130.8, 8.19, _0_0, _0_0, 0.26),
1135 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1136_trfX(_ITRF2014_, _ITRF88_, epoch=_E(2010),
1137 xform=_X( 25.4, -0.5, -154.8, 11.29, 0.1, _0_0, 0.26),
1138 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1140# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1141# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 1st and 2nd column
1142_trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2005),
1143 xform=_X( -0.5, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1144 rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1145# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(1997),
1146# xform=_X( -2.9, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1147# rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1148# see U{Transformation Parameters ITRF2008<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2008_ITRFs.txt>}
1149# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2008/tp_08-05.php>
1150# xform=_X( -2.0, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1151# rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1152_trfX(_ITRF2008_, _ITRF2000_, epoch=_E(2000),
1153 xform=_X( -1.9, -1.7, -10.5, 1.34, _0_0, _0_0, _0_0),
1154 rates=_R( 0.1, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1155_trfX(_ITRF2008_, _ITRF97_, epoch=_E(2000),
1156 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1157 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1158_trfX(_ITRF2008_, _ITRF96_, epoch=_E(2000),
1159 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1160 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1161_trfX(_ITRF2008_, _ITRF94_, epoch=_E(2000),
1162 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1163 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1164_trfX(_ITRF2008_, _ITRF93_, epoch=_E(2000),
1165 xform=_X( -24.0, 2.4, -38.6, 3.41, -1.71, -1.48, -0.3),
1166 rates=_R( -2.8, -0.1, -2.4, 0.09, -0.11, -0.19, 0.07))
1167_trfX(_ITRF2008_, _ITRF92_, epoch=_E(2000),
1168 xform=_X( 12.8, 4.6, -41.2, 2.21, _0_0, _0_0, 0.06),
1169 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1170_trfX(_ITRF2008_, _ITRF91_, epoch=_E(2000),
1171 xform=_X( 24.8, 18.6, -47.2, 3.61, _0_0, _0_0, 0.06),
1172 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1173_trfX(_ITRF2008_, _ITRF90_, epoch=_E(2000),
1174 xform=_X( 22.8, 14.6, -63.2, 3.91, _0_0, _0_0, 0.06),
1175 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1176_trfX(_ITRF2008_, _ITRF89_, epoch=_E(2000),
1177 xform=_X( 27.8, 38.6, -101.2, 7.31, _0_0, _0_0, 0.06),
1178 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1179_trfX(_ITRF2008_, _ITRF88_, epoch=_E(2000),
1180 xform=_X( 22.8, 2.6, -125.2, 10.41, 0.1, _0_0, 0.06),
1181 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1183# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1184# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 3rd column
1185# _trfX(_ITRF2005_, _ITRF2000_, epoch=_E(1997),
1186# xform=_X( 0.7, -1.1, -0.4, 0.16, -0.2, 0.1 -1.8),
1187# rates=_R( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1188_trfX(_ITRF2005_, _ITRF2000_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2005/tp_05-00.php>
1189 xform=_X( 0.1, -0.8, -5.8, 0.4, _0_0, _0_0, _0_0),
1190 rates=_R( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1192_trfX(_ITRF2000_, _ITRF97_, epoch=_E(1997),
1193 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1194 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, -0.02)) # 0.02?
1195_trfX(_ITRF2000_, _ITRF96_, epoch=_E(1997),
1196 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1197 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1198_trfX(_ITRF2000_, _ITRF94_, epoch=_E(1997),
1199 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1200 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1201_trfX(_ITRF2000_, _ITRF93_, epoch=_E(1988),
1202 xform=_X( 12.7, 6.5, -20.9, 1.95, -0.39, 0.8, -1.14),
1203 rates=_R( -2.9, -0.2, -0.6, 0.01, -0.11, -0.19, 0.07))
1204_trfX(_ITRF2000_, _ITRF92_, epoch=_E(1988),
1205 xform=_X( 1.47, 1.35, -1.39, 0.75, _0_0, _0_0, -0.18),
1206 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1207_trfX(_ITRF2000_, _ITRF91_, epoch=_E(1988),
1208 xform=_X( 26.7, 27.5, -19.9, 2.15, _0_0, _0_0, -0.18),
1209 rates=_R( _0_0, -0.6, -1.4, 0.01, _0_0, _0_0, 0.02))
1210_trfX(_ITRF2000_, _ITRF90_, epoch=_E(1988),
1211 xform=_X( 2.47, 2.35, -3.59, 2.45, _0_0, _0_0, -0.18),
1212 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1213_trfX(_ITRF2000_, _ITRF89_, epoch=_E(1988),
1214 xform=_X( 2.97, 4.75, -7.39, 5.85, _0_0, _0_0, -0.18),
1215 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1216_trfX(_ITRF2000_, _ITRF88_, epoch=_E(1988),
1217 xform=_X( 2.47, 1.15, -9.79, 8.95, 0.1, _0_0, -0.18),
1218 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1220# Soler, T .& Snay R.A. U{"Transforming Positions and Velocities between the International Terrestrial
1221# Reference Frame of 2000 and North American Datum of 1983"<https://www.ResearchGate.net/publication/245291390>},
1222# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1223# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 5th and 6th column
1224_trfX(_ITRF97_, _ITRF96_, epoch=_E(1997),
1225 xform=_X( -2.07, -0.21, 9.95, -0.93496, 0.1267, -0.22355, -0.06065,),
1226 rates=_R( 0.69, -0.1, 1.86, -0.19201, 0.01347, -0.01514, 0.00027))
1227_trfX(_ITRF96_, _NAD83_, epoch=_E(1997),
1228 xform=_X( 991.0, -190.72, -512.9, _0_0, 25.79, 9.65, 11.66,),
1229 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.0532, -0.7423, -0.0316,))
1231# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1232# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 1.
1233# _trfX(_ITRF2020_, _ETRF2020_, epoch=_E(1989), # see Table 2 below
1234# xform=_P_0_0s,
1235# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753))
1236# _trfX(_ITRF2014_, _ETRF2014_, epoch=_E(1989), # see Table 3 below
1237# xform=_P_0_0s,
1238# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77))
1239_trfX(_ITRF2005_, _ETRF2005_, epoch=_E(1989),
1240 xform=_X( 56.0, 48.0, -37.0, _0_0, _0_0, _0_0, _0_0),
1241 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.054, 0.518, -0.781))
1242# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(1989), # see Table 4 below
1243# xform=_X( 54.0, 51.0, -48.0, _0_0, _0_0, _0_0, _0_0),
1244# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1245_trfX(_ITRF97_, _ETRF97_, epoch=_E(1989),
1246 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1247 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1248_trfX(_ITRF96_, _ETRF96_, epoch=_E(1989),
1249 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1250 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1251_trfX(_ITRF94_, _ETRF94_, epoch=_E(1989),
1252 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1253 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1254_trfX(_ITRF93_, _ETRF93_, epoch=_E(1989),
1255 xform=_X( 19.0, 53.0, -21.0, _0_0, _0_0, _0_0, _0_0),
1256 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.32, 0.78, -0.67))
1257_trfX(_ITRF92_, _ETRF92_, epoch=_E(1989),
1258 xform=_X( 38.0, 40.0, -37.0, 0.0, 0.0, 0.0, 0.0),
1259 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68))
1260_trfX(_ITRF91_, _ETRF91_, epoch=_E(1989),
1261 xform=_X( 21.0, 25.0, -37.0, _0_0, _0_0, _0_0, _0_0),
1262 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68))
1263_trfX(_ITRF90_, _ETRF90_, epoch=_E(1989),
1264 xform=_X( 19.0, 28.0, -23.0, _0_0, _0_0, _0_0, _0_0),
1265 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71))
1266_trfX(_ITRF89_, _ETRF89_, epoch=_E(1989),
1267 xform=_P_0_0s,
1268 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71))
1270# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1271# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 2.
1272_trfX(_ITRF2020_, _ETRF2020_, epoch=_E(2015),
1273 xform=_X( _0_0, _0_0, _0_0, _0_0, 2.236, 13.494, -19.578),
1274 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753))
1275_trfX(_ITRF2014_, _ETRF2020_, epoch=_E(2015),
1276 xform=_X( 1.4, 0.9, -1.4, 0.42, 2.236, 13.494, -19.578),
1277 rates=_R( _0_0, 0.1, -0.2, _0_0, 0.086, 0.519, -0.753))
1278_trfX(_ITRF2008_, _ETRF2020_, epoch=_E(2015),
1279 xform=_X( 3.0, 2.8, 0.5, 0.55, 2.236, 13.494, -19.578),
1280 rates=_R( _0_0, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753))
1281_trfX(_ITRF2005_, _ETRF2020_, epoch=_E(2015),
1282 xform=_X( 5.5, 1.9, -4.2, 1.49, 2.236, 13.494, -19.578),
1283 rates=_R( 0.3, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753))
1284_trfX(_ITRF2000_, _ETRF2020_, epoch=_E(2015),
1285 xform=_X( 2.6, 2.6, -37.0, 3.09, 2.236, 13.494, -19.578),
1286 rates=_R( 0.1, 0.2, -2.1, 0.11, 0.086, 0.519, -0.753))
1287_trfX(_ITRF97_, _ETRF2020_, epoch=_E(2015),
1288 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1289 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1290_trfX(_ITRF96_, _ETRF2020_, epoch=_E(2015),
1291 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1292 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1293_trfX(_ITRF94_, _ETRF2020_, epoch=_E(2015),
1294 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1295 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1296_trfX(_ITRF93_, _ETRF2020_, epoch=_E(2015),
1297 xform=_X( -63.0, 3.7, -74.1, 5.31, -1.124, 9.164, -18.828),
1298 rates=_R( -2.8, _0_0, -2.7, 0.12, -0.024, 0.329, -0.683))
1299_trfX(_ITRF92_, _ETRF2020_, epoch=_E(2015),
1300 xform=_X( 17.3, -0.1, -88.7, 4.11, 2.236, 13.494, -19.218),
1301 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1302_trfX(_ITRF91_, _ETRF2020_, epoch=_E(2015),
1303 xform=_X( 29.3, 13.9, -94.7, 5.51, 2.236, 13.494, -19.218),
1304 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1305_trfX(_ITRF90_, _ETRF2020_, epoch=_E(2015),
1306 xform=_X( 27.3, 9.9, -110.7, 5.81, 2.236, 13.494, -19.218),
1307 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1308_trfX(_ITRF89_, _ETRF2020_, epoch=_E(2015),
1309 xform=_X( 32.3, 33.9, -148.7, 9.21, 2.236, 13.494, -19.218),
1310 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1311_trfX(_ITRF88_, _ETRF2020_, epoch=_E(2015),
1312 xform=_X( 27.3, -2.1, -172.7, 12.31, 2.336, 13.494, -19.218),
1313 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1315# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1316# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 3.
1317_trfX(_ITRF2020_, _ETRF2014_, epoch=_E(2015),
1318 xform=_X( -1.4, -0.9, 1.4, 0.42, 2.21, 13.806, -20.02),
1319 rates=_R( _0_0, -0.1, 0.2, _0_0, 0.085, 0.531, -0.77))
1320_trfX(_ITRF2014_, _ETRF2014_, epoch=_E(2015),
1321 xform=_X( _0_0, _0_0, _0_0, _0_0, 2.21, 13.806, -20.02),
1322 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77))
1323_trfX(_ITRF2008_, _ETRF2014_, epoch=_E(2015),
1324 xform=_X( -1.6, -1.9, -1.9, -0.13, 2.21, 13.806, -20.02),
1325 rates=_R( _0_0, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77))
1326_trfX(_ITRF2005_, _ETRF2014_, epoch=_E(2015),
1327 xform=_X( -4.1, -1.0, 2.8, -1.07, 2.21, 13.806, -20.02),
1328 rates=_R( -0.3, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77))
1329_trfX(_ITRF2000_, _ETRF2014_, epoch=_E(2015),
1330 xform=_X( -1.2, -1.7, 35.6, -2.67, 2.21, 13.806, -20.02),
1331 rates=_R( -0.1, -0.1, 1.9, -0.11, 0.085, 0.531, -0.77))
1332_trfX(_ITRF97_, _ETRF2014_, epoch=_E(2015),
1333 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1334 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1335_trfX(_ITRF96_, _ETRF2014_, epoch=_E(2015),
1336 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1337 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1338_trfX(_ITRF94_, _ETRF2014_, epoch=_E(2015),
1339 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1340 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1341_trfX(_ITRF93_, _ETRF2014_, epoch=_E(2015),
1342 xform=_X( 64.4, -2.8, 72.7, -4.89, 5.570, 18.136, -20.77),
1343 rates=_R( 2.8, 0.1, 2.5, -0.12, 0.195, 0.721, -0.84))
1344_trfX(_ITRF92_, _ETRF2014_, epoch=_E(2015),
1345 xform=_X( -15.9, 1.0, 87.3, -3.69, 2.21, 13.806, -20.38),
1346 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1347_trfX(_ITRF91_, _ETRF2014_, epoch=_E(2015),
1348 xform=_X( -27.9, -13.0, 93.3, -5.09, 2.21, 13.806, -20.38),
1349 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1350_trfX(_ITRF90_, _ETRF2014_, epoch=_E(2015),
1351 xform=_X( -25.9, -9.0, 109.3, -5.39, 2.21, 13.806, -20.38),
1352 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1353_trfX(_ITRF89_, _ETRF2014_, epoch=_E(2015),
1354 xform=_X( -30.9, -33.0, 147.3, -8.79, 2.21, 13.806, -20.38),
1355 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1356_trfX(_ITRF88_, _ETRF2014_, epoch=_E(2015),
1357 xform=_X( -25.9, 3.0, 171.3, -11.89, 2.11, 13.806, -20.38),
1358 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1360# see U{Altamimi, Z. "EUREF Technical Note 1: Relationship and Transformation between the International and
1361# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 4,
1362# U{Boucher, C. & Altamimi, Z. "Memo: Specifications for reference frame fixing in the analysis of a EUREF GPS
1363# campaign" (2011) <https://ETRS89.ENSG.IGN.Fr/memo-V8.pdf>} and U{Altamimi, Z. "Key results of ITRF2014 and
1364# implication to ETRS89 realization", EUREF2016<https://www.EUREF.EU/symposia/2016SanSebastian/01-02-Altamimi.pdf>}.
1365_trfX(_ITRF2020_, _ETRF2000_, epoch=_E(2015),
1366 xform=_X( 53.8, 51.8, -82.2, 2.25, 2.106, 12.74, -20.592),
1367 rates=_R( 0.1, _0_0, -1.7, 0.11, 0.081, 0.49, -0.792))
1368# _trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2000),
1369# xform=_X( 53.7, 51.2, -55.1, 1.02, 0.891, 5.39, -8.712),
1370# rates=_R( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792))
1371_trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2015),
1372 xform=_X( 55.2, 52.7, -83.6, 2.67, 2.106, 12.74, -20.592),
1373 rates=_R( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792))
1374# _trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2000),
1375# xform=_X( 52.1, 49.3, -58.5, 1.34, 0.891, 5.39, -8.712),
1376# rates=_R( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1377_trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2015),
1378 xform=_X( 53.6, 50.8, -85.5, 2.54, 2.106, 12.74, -20.592),
1379 rates=_R( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1380# _trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2000),
1381# xform=_X( 54.1, 50.2, -53.8, 0.4, 0.891, 5.39, -8.712),
1382# rates=_R( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1383_trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2015),
1384 xform=_X( 51.1, 51.7, -80.8, 1.6, 2.106, 12.74, -20.592),
1385 rates=_R( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1386# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2000),
1387# xform=_X( 54.0, 51.0, -48.0, _0_0, 0.891, 5.39, -8.712),
1388# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1389_trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2015),
1390 xform=_X( 54.0, 51.0, -48.0, _0_0, 2.106, 12.74, -20.592),
1391 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1392_trfX(_ITRF97_, _ETRF2000_, epoch=_E(2015),
1393 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1394 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1395_trfX(_ITRF96_, _ETRF2000_, epoch=_E(2015),
1396 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1397 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1398_trfX(_ITRF94_, _ETRF2000_, epoch=_E(2015),
1399 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1400 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1401_trfX(_ITRF93_, _ETRF2000_, epoch=_E(2015),
1402 xform=_X( 119.6, 49.9, -10.9, -2.22, 5.466, 17.07, -21.342),
1403 rates=_R( 2.9, 0.2, 0.6, -0.01, 0.191, 0.68, -0.862))
1404_trfX(_ITRF92_, _ETRF2000_, epoch=_E(2015),
1405 xform=_X( 39.3, 53.7, 3.7, -1.02, 2.106, 12.74, -20.952),
1406 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1407_trfX(_ITRF91_, _ETRF2000_, epoch=_E(2015),
1408 xform=_X( 27.3, 39.7, 9.7, -2.42, 2.106, 12.74, -20.952),
1409 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1410_trfX(_ITRF90_, _ETRF2000_, epoch=_E(2015),
1411 xform=_X( 29.3, 43.7, 25.7, -2.72, 2.106, 12.74, -20.952),
1412 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1413_trfX(_ITRF89_, _ETRF2000_, epoch=_E(2015),
1414 xform=_X( 24.3, 19.7, 63.7, -6.12, 2.106, 12.74, -20.952),
1415 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1416_trfX(_ITRF88_, _ETRF2000_, epoch=_E(2015),
1417 xform=_X( 29.3, 55.7, 87.7, -9.22, 2.006, 12.74, -20.952),
1418 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1420# GDA2020 "Geocentric Datum of Australia 2020 Technical Manual", v1.5, 2020-12-09, Table 3.3 and 3.4
1421# <https://www.ICSM.gov.AU/sites/default/files/2020-12/GDA2020%20Technical%20Manual%20V1.5_4.pdf>
1422# (the GDA2020 xforms are different but the rates are the same as GDA94, further below)
1423_trfX(_ITRF2014_, _GDA2020_, epoch=_E(2020),
1424 xform=_P_0_0s,
1425 rates=_R( _0_0, _0_0, _0_0, _0_0, 1.50379, 1.18346, 1.20716))
1426_trfX(_ITRF2008_, _GDA2020_, epoch=_E(2020),
1427 xform=_X( 13.79, 4.55, 15.22, 2.5, 0.2808, 0.2677, -0.4638),
1428 rates=_R( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))
1429_trfX(_ITRF2005_, _GDA2020_, epoch=_E(2020),
1430 xform=_X( 40.32, -33.85, -16.72, 4.286, -1.2893, -0.8492, -0.3342),
1431 rates=_R( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))
1432_trfX(_ITRF2000_, _GDA2020_, epoch=_E(2020),
1433 xform=_X(-105.52, 51.58, 231.68, 3.55, 4.2175, 6.3941, 0.8617),
1434 rates=_R( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))
1436# see Table 2 in U{Dawson, J. & Woods, A. "ITRF to GDA94 coordinate transformations", Journal of Applied
1437# Geodesy 4 (2010), 189-199<https://www.ResearchGate.net/publication/258401581_ITRF_to_GDA94_coordinate_transformations>}
1438# (note, sign of rotations for GDA94 reversed as "Australia assumes rotation to be of coordinate axes",
1439# rather than the more conventional "position around the coordinate axes")
1440_trfX(_ITRF2008_, _GDA94_, epoch=_E(1994),
1441 xform=_X( -84.68, -19.42, 32.01, 9.71, -0.4254, 2.2578, 2.4015),
1442 rates=_R( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))
1443_trfX(_ITRF2005_, _GDA94_, epoch=_E(1994),
1444 xform=_X( -79.73, -6.86, 38.03, 6.636, 0.0351, -2.1211, -2.1411),
1445 rates=_R( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))
1446_trfX(_ITRF2000_, _GDA94_, epoch=_E(1994),
1447 xform=_X( -45.91, -29.85, -20.37, 7.07, -1.6705, 0.4594, 1.9356),
1448 rates=_R( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))
1450# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
1451# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 and Pearson, C. & Snay, R. U{"Introducing
1452# HTDP 3.1 to transform coordinates across time and spatial reference frames"<https://Geodesy.NOAA.gov/
1453# TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 7th column
1454_trfX(_ITRF2008_, _NAD83_, epoch=_E(1997),
1455 xform=_X( 993.43, -1903.31, -526.55, 1.71504, -25.91467, -9.42645, -11.59935),
1456 rates=_R( 0.79, -0.6, -1.34, -0.10201, -0.06667, 0.75744, 0.05133))
1457# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
1458# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83
1459_trfX(_ITRF2005_, _NAD83_, epoch=_E(1997),
1460 xform=_X( 996.3, -1902.4, -521.9, 0.775, -25.915, -9.426, -11.599),
1461 rates=_R( 0.5, -0.6, -1.3, -0.10201, -0.06667, 0.75744, 0.05133))
1462# see U{Solar, T. & Snay, R.A. "Transforming Positions and Velocities between the International Terrestrial Reference
1463# Frame of 2000 and North American Datum of 1983" (2004)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>}
1464_trfX(_ITRF2000_, _NAD83_, epoch=_E(1997), # note NAD83(CORS96)
1465 xform=_X( 995.6, -1901.3, -521.5, 0.615, -25.915, -9.426, -11.599),
1466 rates=_R( 0.7, -0.7, _0_5, -0.182, -0.06667, 0.75744, 0.05133))
1467_trfX(_ITRF90_, _NAD83_, epoch=_E(1997),
1468 xform=_X( 973.0, -1919.2, -482.9, -0.9, -25.79, -9.65, -11.66),
1469 rates=_R( _0_0, _0_0, _0_0, _0_0, -0.053, 0.742, 0.032))
1470_trfX(_ITRF90_, _WGS84_, epoch=_E(1984), # coverage
1471 xform=_X( 60.0, -517.0, -223.0, -11.0, 18.3, -0.3, 7.0),
1472 rates=_P_0_0s)
1474# equivalents U{"Transformations Between NAD83 and WGS84"<https://www.NGS.NOAA.gov/CORS/Articles/WGS84NAD83.pdf>}
1475trfXform(_NAD83cors96_, _NAD83_, epoch=_E(1997), xform=_P_0_0s, rates=_P_0_0s)
1476trfXform(_WGS84g1150_, _ITRF2000_, epoch=_E(2004), xform=_P_0_0s, rates=_P_0_0s)
1478del _E, _Es, _i, _P, _P_0_0s, _R, _Rs, _X, _Xs
1480if __name__ == '__main__':
1482 def _main():
1483 from pygeodesy.interns import _COLONSPACE_,_COMMA_, _NL_, _NLATvar_, _vs_
1484 from pygeodesy.lazily import printf
1485 from time import localtime
1487 D = date2epoch.__name__
1488 E = epoch2date.__name__
1489 y = localtime()[0]
1490 for m in range(1, 13):
1491 for d in (1, 15, _mDays[m] - 1, _mDays[m]):
1492 f = '%s(%d,%3d,%3d)' % (D, y, m, d)
1493 e = date2epoch(y, m, d)
1494 t = epoch2date(e)
1495 x = NN if t == (y, m, d) else _STAR_
1496 e = '%.3f' % (e,)
1497 e = '%s, %s(%s)' % (e, E, e)
1498 t = '%d,%3d,%3d' % t
1499 printf('# %s = %s = %s %s', f, e, t, x)
1501 # __doc__ of this file, force all into registery
1502 def _RFs():
1503 yield NN
1504 for t in RefFrames.toRepr(all=True).split(_NL_):
1505 t = t.strip(_COMMA_)
1506 n = t.split(_COLONSPACE_)[0].split(_DOT_)[1]
1507 r = RefFrames.get(n)
1508 x = len(r.Xforms()), -len(r.Xforms(inverse=True))
1509 yield '%s .Xforms=%s' % (t, x)
1511 printf(_NLATvar_.join(sorted(_RFs())), nt=1)
1513 X, t = (), 0 # all form
1514 for r in RefFrames.values():
1515 X += tuple(r._Xto.values())
1516 for X in sorted(X):
1517 t += 1
1518 printf('#%4d %-24s xform=%r', t, X.name, X.xform)
1519 printf('#%29s rates=%r', _SPACE_, X.rates)
1521 t = _MODS.basics._args_kwds_names(Transform.__init__)
1522 for n in TRFXform7Tuple._Names_:
1523 if n not in t:
1524 raise AssertionError(_SPACE_(n, _vs_, t))
1526 _main()
1527 del _main
1529# **) MIT License
1530#
1531# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1532#
1533# Permission is hereby granted, free of charge, to any person obtaining a
1534# copy of this software and associated documentation files (the "Software"),
1535# to deal in the Software without restriction, including without limitation
1536# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1537# and/or sell copies of the Software, and to permit persons to whom the
1538# Software is furnished to do so, subject to the following conditions:
1539#
1540# The above copyright notice and this permission notice shall be included
1541# in all copies or substantial portions of the Software.
1542#
1543# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1544# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1545# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1546# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1547# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1548# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1549# OTHER DEALINGS IN THE SOFTWARE.
1551# % python -m pygeodesy.trf
1552#
1553# date2epoch(2024, 1, 1) = 2024.003, epoch2date(2024.003) = 2024, 1, 1
1554# date2epoch(2024, 1, 15) = 2024.041, epoch2date(2024.041) = 2024, 1, 15
1555# date2epoch(2024, 1, 30) = 2024.082, epoch2date(2024.082) = 2024, 1, 30
1556# date2epoch(2024, 1, 31) = 2024.085, epoch2date(2024.085) = 2024, 1, 31
1557# date2epoch(2024, 2, 1) = 2024.087, epoch2date(2024.087) = 2024, 2, 2 *
1558# date2epoch(2024, 2, 15) = 2024.126, epoch2date(2024.126) = 2024, 2, 16 *
1559# date2epoch(2024, 2, 28) = 2024.161, epoch2date(2024.161) = 2024, 2, 28
1560# date2epoch(2024, 2, 29) = 2024.164, epoch2date(2024.164) = 2024, 3, 1 *
1561# date2epoch(2024, 3, 1) = 2024.167, epoch2date(2024.167) = 2024, 3, 2 *
1562# date2epoch(2024, 3, 15) = 2024.205, epoch2date(2024.205) = 2024, 3, 16 *
1563# date2epoch(2024, 3, 30) = 2024.246, epoch2date(2024.246) = 2024, 3, 31 *
1564# date2epoch(2024, 3, 31) = 2024.249, epoch2date(2024.249) = 2024, 4, 1 *
1565# date2epoch(2024, 4, 1) = 2024.251, epoch2date(2024.251) = 2024, 4, 1
1566# date2epoch(2024, 4, 15) = 2024.290, epoch2date(2024.290) = 2024, 4, 15
1567# date2epoch(2024, 4, 29) = 2024.328, epoch2date(2024.328) = 2024, 4, 29
1568# date2epoch(2024, 4, 30) = 2024.331, epoch2date(2024.331) = 2024, 4, 30
1569# date2epoch(2024, 5, 1) = 2024.333, epoch2date(2024.333) = 2024, 5, 1
1570# date2epoch(2024, 5, 15) = 2024.372, epoch2date(2024.372) = 2024, 5, 15
1571# date2epoch(2024, 5, 30) = 2024.413, epoch2date(2024.413) = 2024, 5, 30
1572# date2epoch(2024, 5, 31) = 2024.415, epoch2date(2024.415) = 2024, 6, 1 *
1573# date2epoch(2024, 6, 1) = 2024.418, epoch2date(2024.418) = 2024, 6, 2 *
1574# date2epoch(2024, 6, 15) = 2024.456, epoch2date(2024.456) = 2024, 6, 16 *
1575# date2epoch(2024, 6, 29) = 2024.495, epoch2date(2024.495) = 2024, 6, 30 *
1576# date2epoch(2024, 6, 30) = 2024.497, epoch2date(2024.497) = 2024, 7, 1 *
1577# date2epoch(2024, 7, 1) = 2024.500, epoch2date(2024.500) = 2024, 7, 1
1578# date2epoch(2024, 7, 15) = 2024.538, epoch2date(2024.538) = 2024, 7, 16 *
1579# date2epoch(2024, 7, 30) = 2024.579, epoch2date(2024.579) = 2024, 7, 30
1580# date2epoch(2024, 7, 31) = 2024.582, epoch2date(2024.582) = 2024, 7, 31
1581# date2epoch(2024, 8, 1) = 2024.585, epoch2date(2024.585) = 2024, 8, 1
1582# date2epoch(2024, 8, 15) = 2024.623, epoch2date(2024.623) = 2024, 8, 15
1583# date2epoch(2024, 8, 30) = 2024.664, epoch2date(2024.664) = 2024, 8, 31 *
1584# date2epoch(2024, 8, 31) = 2024.667, epoch2date(2024.667) = 2024, 9, 1 *
1585# date2epoch(2024, 9, 1) = 2024.669, epoch2date(2024.669) = 2024, 9, 2 *
1586# date2epoch(2024, 9, 15) = 2024.708, epoch2date(2024.708) = 2024, 9, 16 *
1587# date2epoch(2024, 9, 29) = 2024.746, epoch2date(2024.746) = 2024, 9, 30 *
1588# date2epoch(2024, 9, 30) = 2024.749, epoch2date(2024.749) = 2024, 10, 1 *
1589# date2epoch(2024, 10, 1) = 2024.751, epoch2date(2024.751) = 2024, 10, 1
1590# date2epoch(2024, 10, 15) = 2024.790, epoch2date(2024.790) = 2024, 10, 15
1591# date2epoch(2024, 10, 30) = 2024.831, epoch2date(2024.831) = 2024, 10, 30
1592# date2epoch(2024, 10, 31) = 2024.833, epoch2date(2024.833) = 2024, 10, 31
1593# date2epoch(2024, 11, 1) = 2024.836, epoch2date(2024.836) = 2024, 11, 1
1594# date2epoch(2024, 11, 15) = 2024.874, epoch2date(2024.874) = 2024, 11, 15
1595# date2epoch(2024, 11, 29) = 2024.913, epoch2date(2024.913) = 2024, 11, 29
1596# date2epoch(2024, 11, 30) = 2024.915, epoch2date(2024.915) = 2024, 12, 1 *
1597# date2epoch(2024, 12, 1) = 2024.918, epoch2date(2024.918) = 2024, 12, 2 *
1598# date2epoch(2024, 12, 15) = 2024.956, epoch2date(2024.956) = 2024, 12, 16 *
1599# date2epoch(2024, 12, 30) = 2024.997, epoch2date(2024.997) = 2024, 12, 31 *
1600# date2epoch(2024, 12, 31) = 2025.000, epoch2date(2025.000) = 2025, 1, 1 *
1602# 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)
1603# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1604# 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)
1605# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1606# 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)
1607# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1608# 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)
1609# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1610# 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)
1611# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1612# 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)
1613# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1614# 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)
1615# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
1616# 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)
1617# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1618# 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)
1619# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1620# 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)
1621# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
1622# 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)
1623# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=-0.053, sy=0.742, sz=0.032)
1624# 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)
1625# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1626# 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)
1627# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
1628# 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)
1629# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1630# 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)
1631# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1632# 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)
1633# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1634# 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)
1635# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
1636# 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)
1637# rates=rates(tx=2.9, ty=0.2, tz=0.6, s=-0.01, sx=0.191, sy=0.68, sz=-0.862)
1638# 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)
1639# rates=rates(tx=2.8, ty=0.1, tz=2.5, s=-0.12, sx=0.195, sy=0.721, sz=-0.84)
1640# 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)
1641# rates=rates(tx=-2.8, ty=0.0, tz=-2.7, s=0.12, sx=-0.024, sy=0.329, sz=-0.683)
1642# 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)
1643# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.32, sy=0.78, sz=-0.67)
1644# 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)
1645# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1646# 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)
1647# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1648# 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)
1649# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1650# 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)
1651# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1652# 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)
1653# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1654# 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)
1655# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1656# 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)
1657# rates=rates(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
1658# 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)
1659# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.081, sy=0.49, sz=-0.792)
1660# 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)
1661# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1662# 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)
1663# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1664# 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)
1665# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1666# 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)
1667# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1668# 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)
1669# rates=rates(tx=-0.1, ty=-0.1, tz=1.9, s=-0.11, sx=0.085, sy=0.531, sz=-0.77)
1670# 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)
1671# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1672# 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)
1673# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1674# 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)
1675# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1676# 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)
1677# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1678# 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)
1679# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1680# 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)
1681# rates=rates(tx=0.1, ty=0.2, tz=-2.1, s=0.11, sx=0.086, sy=0.519, sz=-0.753)
1682# 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)
1683# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1684# 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)
1685# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1686# 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)
1687# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1688# 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)
1689# rates=rates(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
1690# 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)
1691# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1692# 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)
1693# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1694# 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)
1695# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1696# 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)
1697# rates=rates(tx=0.0, ty=-0.6, tz=-1.4, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1698# 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)
1699# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1700# 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)
1701# rates=rates(tx=-2.9, ty=-0.2, tz=-0.6, s=0.01, sx=-0.11, sy=-0.19, sz=0.07)
1702# 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)
1703# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1704# 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)
1705# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1706# 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)
1707# rates=rates(tx=0.69, ty=-0.1, tz=1.86, s=-0.19201, sx=0.01347, sy=-0.01514, sz=0.00027)
1708# 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)
1709# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=-0.02)
1710# 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)
1711# rates=rates(tx=0.7, ty=-0.7, tz=0.5, s=-0.182, sx=-0.06667, sy=0.75744, sz=0.05133)
1712# 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)
1713# rates=rates(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
1714# 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)
1715# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.054, sy=0.518, sz=-0.781)
1716# 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)
1717# rates=rates(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
1718# 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)
1719# rates=rates(tx=0.5, ty=-0.6, tz=-1.3, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
1720# 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)
1721# rates=rates(tx=-0.3, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
1722# 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)
1723# rates=rates(tx=0.3, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
1724# 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)
1725# rates=rates(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
1726# 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)
1727# rates=rates(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
1728# 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)
1729# rates=rates(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
1730# 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)
1731# rates=rates(tx=0.79, ty=-0.6, tz=-1.34, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
1732# 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)
1733# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0532, sy=-0.7423, sz=-0.0316)
1734# 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)
1735# rates=rates(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
1736# 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)
1737# rates=rates(tx=0.0, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
1738# 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)
1739# rates=rates(tx=0.0, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
1740# 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)
1741# rates=rates(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
1742# 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)
1743# rates=rates(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
1744# 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)
1745# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1746# 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)
1747# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1748# 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)
1749# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1750# 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)
1751# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1752# 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)
1753# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1754# 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)
1755# rates=rates(tx=-2.8, ty=-0.1, tz=-2.4, s=0.09, sx=-0.11, sy=-0.19, sz=0.07)
1756# 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)
1757# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1758# 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)
1759# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1760# 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)
1761# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1762# 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)
1763# rates=rates(tx=0.3, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1764# 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)
1765# rates=rates(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
1766# 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)
1767# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
1768# 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)
1769# rates=rates(tx=0.0, ty=0.1, tz=-0.2, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
1770# 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)
1771# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=1.50379, sy=1.18346, sz=1.20716)
1772# 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)
1773# rates=rates(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.0, sy=0.0, sz=0.0)
1774# 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)
1775# rates=rates(tx=0.3, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1776# 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)
1777# rates=rates(tx=0.0, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1778# 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)
1779# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1780# 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)
1781# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1782# 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)
1783# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1784# 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)
1785# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1786# 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)
1787# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1788# 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)
1789# rates=rates(tx=-2.8, ty=-0.1, tz=-2.5, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
1790# 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)
1791# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1792# 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)
1793# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1794# 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)
1795# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1796# 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)
1797# rates=rates(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
1798# 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)
1799# rates=rates(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
1800# 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)
1801# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
1802# 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)
1803# rates=rates(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.0, sy=0.0, sz=0.0)
1804# 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)
1805# rates=rates(tx=0.3, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1806# 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)
1807# rates=rates(tx=0.0, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1808# 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)
1809# rates=rates(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1810# 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)
1811# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1812# 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)
1813# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1814# 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)
1815# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1816# 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)
1817# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1818# 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)
1819# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1820# 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)
1821# rates=rates(tx=-2.8, ty=-0.2, tz=-2.3, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
1822# 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)
1823# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1824# 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)
1825# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1826# 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)
1827# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)