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# -*- coding: utf-8 -*- 

 

u'''Terrestrial Reference Frame (TRF) classes L{RefFrame}, registry L{RefFrames} and L{TRFError}. 

 

Transcribed from I{Chris Veness'} (C) 2006-2019 JavaScript originals 

U{latlon-ellipsoidal-referenceframe.js<https://GitHub.com/chrisveness/geodesy/blob/master/ 

latlon-ellipsoidal-referenceframe.js>} and U{latlon-ellipsoidal-referenceframe-txparams.js 

<https://GitHub.com/chrisveness/geodesy/blob/master/latlon-ellipsoidal-referenceframe-txparams.js>}. 

 

Modern geodetic reference frames: a latitude/longitude point defines a geographic location on, 

above or below the earth’s surface, measured in degrees from the equator and the U{International 

Reference Meridian<https://WikiPedia.org/wiki/IERS_Reference_Meridian>} (IRM) and metres above 

the ellipsoid within a given I{Terrestrial Reference Frame} at a given I{epoch}. 

 

This is scratching the surface of complexities involved in high precision geodesy, but may 

be of interest and/or value to those with less demanding requirements. More information U{here 

<https://www.Movable-Type.co.UK/scripts/geodesy-library.html>} and U{here 

<https://www.Movable-Type.co.UK/scripts/geodesy-library.html#latlon-ellipsoidal-referenceframe>}. 

 

Note that I{ITRF solutions} do not directly use an ellipsoid, but are specified by Cartesian 

coordinates. The GRS80 ellipsoid is recommended for transformations to geographical coordinates. 

 

Note WGS84(G730/G873/G1150) are coincident with ITRF at 10-centimetre level, see also U{here 

<ftp://ITRF.ENSG.IGN.FR/pub/itrf/WGS84.TXT>}. WGS84(G1674) and ITRF20014 / ITRF2008 ‘are likely 

to agree at the centimeter level’, see also U{QPS/QINSy<https://Confluence.QPS.NL/qinsy/ 

en/how-to-deal-with-etrs89-datum-and-time-dependent-transformation-parameters-45353274.html>}. 

 

@var RefFrames.ETRF2000: RefFrame(name='ETRF2000', epoch=2005.0, ellipsoid=Ellipsoid(name='GRS80') 

@var RefFrames.GDA94: RefFrame(name='GDA94', epoch=1994.0, ellipsoid=Ellipsoid(name='GRS80') 

@var RefFrames.ITRF2000: RefFrame(name='ITRF2000', epoch=1997.0, ellipsoid=Ellipsoid(name='GRS80') 

@var RefFrames.ITRF2005: RefFrame(name='ITRF2005', epoch=2000.0, ellipsoid=Ellipsoid(name='GRS80') 

@var RefFrames.ITRF2008: RefFrame(name='ITRF2008', epoch=2005.0, ellipsoid=Ellipsoid(name='GRS80') 

@var RefFrames.ITRF2014: RefFrame(name='ITRF2014', epoch=2010.0, ellipsoid=Ellipsoid(name='GRS80') 

@var RefFrames.ITRF91: RefFrame(name='ITRF91', epoch=1988.0, ellipsoid=Ellipsoid(name='GRS80') 

@var RefFrames.ITRF93: RefFrame(name='ITRF93', epoch=1988.0, ellipsoid=Ellipsoid(name='GRS80') 

@var RefFrames.NAD83: RefFrame(name='NAD83', epoch=1997.0, ellipsoid=Ellipsoid(name='GRS80') 

@var RefFrames.WGS84g1150: RefFrame(name='WGS84g1150', epoch=2001.0, ellipsoid=Ellipsoid(name='WGS84') 

@var RefFrames.WGS84g1674: RefFrame(name='WGS84g1674', epoch=2005.0, ellipsoid=Ellipsoid(name='WGS84') 

@var RefFrames.WGS84g1762: RefFrame(name='WGS84g1762', epoch=2005.0, ellipsoid=Ellipsoid(name='WGS84') 

''' 

 

from pygeodesy.basics import map1, property_RO 

from pygeodesy.datums import _ellipsoid, Transform 

from pygeodesy.ellipsoids import Ellipsoids 

from pygeodesy.errors import TRFError 

from pygeodesy.interns import NN, _COMMA_SPACE_, _ellipsoid_, \ 

_epoch_, _float as _F, _floatuple as _T, \ 

_name_, _no_conversion_, _0_0 

from pygeodesy.lazily import _ALL_LAZY 

from pygeodesy.named import classname, _NamedDict as _D, \ 

_NamedEnum, _NamedEnumItem 

from pygeodesy.units import Epoch 

 

from math import ceil 

 

__all__ = _ALL_LAZY.trf 

__version__ = '20.09.27' 

 

_366_0 = _F(366) 

_mDays = (0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 0) 

 

 

class _S(object): 

'''Single-instance strings. 

''' 

ETRF2000 = 'ETRF2000' 

GDA94 = 'GDA94' 

ITRF = 'ITRF' 

ITRF88 = 'ITRF88' 

ITRF89 = 'ITRF89' 

ITRF90 = 'ITRF90' 

ITRF91 = 'ITRF91' 

ITRF92 = 'ITRF92' 

ITRF93 = 'ITRF93' 

ITRF94 = 'ITRF94' 

ITRF96 = 'ITRF96' 

ITRF97 = 'ITRF97' 

ITRF2000 = 'ITRF2000' 

ITRF2005 = 'ITRF2005' 

ITRF2008 = 'ITRF2008' 

ITRF2014 = 'ITRF2014' 

ITRF2014AU = 'ITRF2014AU' 

NAD83 = 'NAD83' 

WGS84 = 'WGS84' 

WGS84g1150 = 'WGS84g1150' 

WGS84g1674 = 'WGS84g1674' 

WGS84g1762 = 'WGS84g1762' 

 

_S = _S() # PYCHOK freeze 

 

 

class RefFrame(_NamedEnumItem): 

'''Terrestrial Reference Frame (TRF) parameters. 

''' 

_ellipsoid = None # ellipsoid GRS80 or WGS84 (L{Ellipsoid} or L{Ellipsoid2}) 

_epoch = _0_0 # epoch, calendar year (L{Epoch} or C{float}) 

 

def __init__(self, epoch, ellipsoid, name=NN): 

'''New L{RefFrame}. 

 

@arg epoch: Epoch, a fractional calendar year (C{scalar} or C{str}). 

@arg ellipsoid: The ellipsoid (L{Ellipsoid}, L{Ellipsoid2}, 

L{datum} or L{a_f2Tuple}). 

@kwarg name: Optional, unique name (C{str}). 

 

@raise NameError: A L{RefFrame} with that B{C{name}} 

already exists. 

 

@raise TRFError: Invalid B{C{epoch}}. 

 

@raise TypeError: Invalid B{C{ellipsoid}}. 

''' 

self._ellipsoid = _ellipsoid(ellipsoid, name=name) 

self._epoch = Epoch(epoch) 

self._register(RefFrames, name) 

 

@property_RO 

def ellipsoid(self): 

'''Get this reference frame's ellipsoid (L{Ellipsoid} or L{Ellipsoid2}). 

''' 

return self._ellipsoid 

 

@property_RO 

def epoch(self): 

'''Get this reference frame's epoch (C{Epoch}). 

''' 

return self._epoch 

 

def toStr(self): # PYCHOK expected 

'''Return this reference frame as a text string. 

 

@return: This L{RefFrame}'s attributes (C{str}). 

''' 

e = self.ellipsoid 

t = ('%s=%r' % (_name_, self.name), 

'%s=%s' % (_epoch_, self.epoch), 

'%s=%s(%s=%r)' % (_ellipsoid_, classname(e), _name_, e.name)) 

return _COMMA_SPACE_.join(t) 

 

 

RefFrames = _NamedEnum('RefFrames', RefFrame) # registered reference frames 

# <https://GitHub.com/chrisveness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js> 

RefFrames._assert( 

# ITRF2014AU = RefFrame(_F(2020), Ellipsoids.GRS80, _S.ITRF2014AU), 

ITRF2014 = RefFrame(_F(2010), Ellipsoids.GRS80, _S.ITRF2014), 

ITRF2008 = RefFrame(_F(2005), Ellipsoids.GRS80, _S.ITRF2008), 

ITRF2005 = RefFrame(_F(2000), Ellipsoids.GRS80, _S.ITRF2005), 

ITRF2000 = RefFrame(_F(1997), Ellipsoids.GRS80, _S.ITRF2000), 

ITRF93 = RefFrame(_F(1988), Ellipsoids.GRS80, _S.ITRF93), 

ITRF91 = RefFrame(_F(1988), Ellipsoids.GRS80, _S.ITRF91), 

WGS84g1762 = RefFrame(_F(2005), Ellipsoids.WGS84, _S.WGS84g1762), 

WGS84g1674 = RefFrame(_F(2005), Ellipsoids.WGS84, _S.WGS84g1674), 

WGS84g1150 = RefFrame(_F(2001), Ellipsoids.WGS84, _S.WGS84g1150), 

ETRF2000 = RefFrame(_F(2005), Ellipsoids.GRS80, _S.ETRF2000), # ETRF2000(R08) 

NAD83 = RefFrame(_F(1997), Ellipsoids.GRS80, _S.NAD83), # CORS96 

GDA94 = RefFrame(_F(1994), Ellipsoids.GRS80, _S.GDA94)) 

 

 

def date2epoch(year, month, day): 

'''Return the reference frame C{epoch} for a calendar day. 

 

@arg year: Year of the date (C{scalar}). 

@arg month: Month in the B{C{year}} (C{scalar}, 1..12). 

@arg day: Day in the B{C{month}} (C{scalar}, 1..31). 

 

@return: Epoch, the fractional year (C{float}). 

 

@raise TRFError: Invalid B{C{year}}, B{C{month}} or B{C{day}}. 

 

@note: Any B{C{year}} is considered a leap year, i.e. having 

29 days in February. 

''' 

try: 

y, m, d = map1(int, year, month, day) 

if y > 0 and 1 <= m <= 12 and 1 <= d <= _mDays[m]: 

return Epoch(y + float(sum(_mDays[:m]) + d) / _366_0, low=0) 

 

t = NN # _invalid_ 

except (TRFError, TypeError, ValueError) as x: 

t = str(x) 

raise TRFError(year=year, month=month, day=day, txt=t) 

 

 

def epoch2date(epoch): 

'''Return the date for a reference frame C{epoch}. 

 

@arg epoch: Fractional year (C{scalar}). 

 

@return: 3-Tuple C{(year, month, day)}. 

 

@raise TRFError: Invalid B{C{epoch}}. 

 

@note: Any B{C{year}} is considered a leap year, i.e. having 

29 days in February. 

''' 

e = Epoch(epoch, Error=TRFError, low=0) 

y = int(e) 

d = int(ceil(_366_0 * (e - y))) 

for m, n in enumerate(_mDays[1:]): 

if d > n: 

d -= n 

else: 

break 

return y, (m + 1), max(1, d) 

 

 

# TRF conversions specified as 7-parameter Helmert transforms and an epoch. Most 

# from U{Transformation Parameters<http://ITRF.IGN.FR/trans_para.php>}, more at U{QPS 

# <https://Confluence.QPS.NL/qinsy/files/en/29856813/45482834/2/1453459502000/ITRF_Transformation_Parameters.xlsx>}. 

_trfNs = ('tx', 'ty', 'tz', 's', 'sx', 'sy', 'sz') 

_trfXs = { # (from_TRF, to_TRF): mm mm mm ppb mas mas mas 

# see U{Transformation Parameters ITRF2014<http://ITRF.IGN.FR/doc_ITRF/Transfo-ITRF2014_ITRFs.txt>} 

(_S.ITRF2014, _S.ITRF2008): _D(epoch=_F(2010), # <http://ITRF.ENSG.IGN.FR/ITRF_solutions/2014/tp_14-08.php> 

xform=_T( 1.6, 1.9, 2.4, -0.02, 0.0, 0.0, 0.0), 

rates=_T( 0.0, 0.0, -0.1, 0.03, 0.0, 0.0, 0.0)), 

(_S.ITRF2014, _S.ITRF2005): _D(epoch=_F(2010), 

xform=_T( 2.6, 1.0, -2.3, 0.92, 0.0, 0.0, 0.0), 

rates=_T( 0.3, 0.0, -0.1, 0.03, 0.0, 0.0, 0.0)), 

(_S.ITRF2014, _S.ITRF2000): _D(epoch=_F(2010), 

xform=_T( 0.7, 1.2, -26.1, 2.12, 0.0, 0.0, 0.0), 

rates=_T( 0.1, 0.1, -1.9, 0.11, 0.0, 0.0, 0.0)), 

(_S.ITRF2014, _S.ITRF97): _D(epoch=_F(2010), 

xform=_T( 7.4, -0.5, -62.8, 3.8, 0.0, 0.0, 0.26), 

rates=_T( 0.1, -0.5, -3.3, 0.12, 0.0, 0.0, 0.02)), 

(_S.ITRF2014, _S.ITRF96): _D(epoch=_F(2010), 

xform=_T( 7.4, -0.5, -62.8, 3.8, 0.0, 0.0, 0.26), 

rates=_T( 0.1, -0.5, -3.3, 0.12, 0.0, 0.0, 0.02)), 

(_S.ITRF2014, _S.ITRF94): _D(epoch=_F(2010), 

xform=_T( 7.4, -0.5, -62.8, 3.8, 0.0, 0.0, 0.26), 

rates=_T( 0.1, -0.5, -3.3, 0.12, 0.0, 0.0, 0.02)), 

(_S.ITRF2014, _S.ITRF93): _D(epoch=_F(2010), 

xform=_T(-50.4, 3.3, -60.2, 4.29, -2.81, -3.38, 0.4), 

rates=_T( -2.8, -0.1, -2.5, 0.12, -0.11, -0.19, 0.07)), 

(_S.ITRF2014, _S.ITRF92): _D(epoch=_F(2010), 

xform=_T( 15.4, 1.5, -70.8, 3.09, 0.0, 0.0, 0.26), 

rates=_T( 0.1, -0.5, -3.3, 0.12, 0.0, 0.0, 0.02)), 

(_S.ITRF2014, _S.ITRF91): _D(epoch=_F(2010), 

xform=_T( 27.4, 15.5, -76.8, 4.49, 0.0, 0.0, 0.26), 

rates=_T( 0.1, -0.5, -3.3, 0.12, 0.0, 0.0, 0.02)), 

(_S.ITRF2014, _S.ITRF90): _D(epoch=_F(2010), 

xform=_T( 25.4, 11.5, -92.8, 4.79, 0.0, 0.0, 0.26), 

rates=_T( 0.1, -0.5, -3.3, 0.12, 0.0, 0.0, 0.02)), 

(_S.ITRF2014, _S.ITRF89): _D(epoch=_F(2010), 

xform=_T( 30.4, 35.5, -130.8, 8.19, 0.0, 0.0, 0.26), 

rates=_T( 0.1, -0.5, -3.3, 0.12, 0.0, 0.0, 0.02)), 

(_S.ITRF2014, _S.ITRF88): _D(epoch=_F(2010), 

xform=_T( 25.4, -0.5, -154.8, 11.29, 0.1, 0.0, 0.26), 

rates=_T( 0.1, -0.5, -3.3, 0.12, 0.0, 0.0, 0.02)), 

 

# see U{Transformation Parameters ITRF2008<http://ITRF.IGN.FR/doc_ITRF/Transfo-ITRF2008_ITRFs.txt>} 

# (_S.ITRF2008, _S.ITRF2005): _D(epoch=_F(2005), # <http://ITRF.ENSG.IGN.FR/ITRF_solutions/2008/tp_08-05.php> 

# xform=_T( -0.5, -0.9, -4.7, 0.94, 0.0, 0.0, 0.0), 

# rates=_T( 0.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)), 

(_S.ITRF2008, _S.ITRF2005): _D(epoch=_F(2000), 

xform=_T( -2.0, -0.9, -4.7, 0.94, 0.0, 0.0, 0.0), 

rates=_T( 0.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)), 

(_S.ITRF2008, _S.ITRF2000): _D(epoch=_F(2000), 

xform=_T( -1.9, -1.7, -10.5, 1.34, 0.0, 0.0, 0.0), 

rates=_T( 0.1, 0.1, -1.8, 0.08, 0.0, 0.0, 0.0)), 

(_S.ITRF2008, _S.ITRF97): _D(epoch=_F(2000), 

xform=_T( 4.8, 2.6, -33.2, 2.92, 0.0, 0.0, 0.06), 

rates=_T( 0.1, -0.5, -3.2, 0.09, 0.0, 0.0, 0.02)), 

(_S.ITRF2008, _S.ITRF96): _D(epoch=_F(2000), 

xform=_T( 4.8, 2.6, -33.2, 2.92, 0.0, 0.0, 0.06), 

rates=_T( 0.1, -0.5, -3.2, 0.09, 0.0, 0.0, 0.02)), 

(_S.ITRF2008, _S.ITRF94): _D(epoch=_F(2000), 

xform=_T( 4.8, 2.6, -33.2, 2.92, 0.0, 0.0, 0.06), 

rates=_T( 0.1, -0.5, -3.2, 0.09, 0.0, 0.0, 0.02)), 

(_S.ITRF2008, _S.ITRF93): _D(epoch=_F(2000), 

xform=_T(-24.0, 2.4, -38.6, 3.41, -1.71, -1.48, -0.3), 

rates=_T( -2.8, -0.1, -2.4, 0.09, -0.11, -0.19, 0.07)), 

(_S.ITRF2008, _S.ITRF92): _D(epoch=_F(2000), 

xform=_T( 12.8, 4.6, -41.2, 2.21, 0.0, 0.0, 0.06), 

rates=_T( 0.1, -0.5, -3.2, 0.09, 0.0, 0.0, 0.02)), 

(_S.ITRF2008, _S.ITRF91): _D(epoch=_F(2000), 

xform=_T( 24.8, 18.6, -47.2, 3.61, 0.0, 0.0, 0.06), 

rates=_T( 0.1, -0.5, -3.2, 0.09, 0.0, 0.0, 0.02)), 

(_S.ITRF2008, _S.ITRF90): _D(epoch=_F(2000), 

xform=_T( 22.8, 14.6, -63.2, 3.91, 0.0, 0.0, 0.06), 

rates=_T( 0.1, -0.5, -3.2, 0.09, 0.0, 0.0, 0.02)), 

(_S.ITRF2008, _S.ITRF89): _D(epoch=_F(2000), 

xform=_T( 27.8, 38.6, -101.2, 7.31, 0.0, 0.0, 0.06), 

rates=_T( 0.1, -0.5, -3.2, 0.09, 0.0, 0.0, 0.02)), 

(_S.ITRF2008, _S.ITRF88): _D(epoch=_F(2000), 

xform=_T( 22.8, 2.6, -125.2, 10.41, 0.1, 0.0, 0.06), 

rates=_T( 0.1, -0.5, -3.2, 0.09, 0.0, 0.0, 0.02)), 

 

(_S.ITRF2005, _S.ITRF2000): _D(epoch=_F(2000), # <http://ITRF.ENSG.IGN.FR/ITRF_solutions/2005/tp_05-00.php> 

xform=_T( 0.1, -0.8, -5.8, 0.4, 0.0, 0.0, 0.0), 

rates=_T( -0.2, 0.1, -1.8, 0.08, 0.0, 0.0, 0.0)), 

 

(_S.ITRF2000, _S.ITRF97): _D(epoch=_F(1997), 

xform=_T( 0.67, 0.61, -1.85, 1.55, 0.0, 0.0, 0.0), 

rates=_T( 0.0, -0.06, -0.14, 0.01, 0.0, 0.0, 0.02)), 

(_S.ITRF2000, _S.ITRF96): _D(epoch=_F(1997), 

xform=_T( 0.67, 0.61, -1.85, 1.55, 0.0, 0.0, 0.0), 

rates=_T( 0.0, -0.06, -0.14, 0.01, 0.0, 0.0, 0.02)), 

(_S.ITRF2000, _S.ITRF94): _D(epoch=_F(1997), 

xform=_T( 0.67, 0.61, -1.85, 1.55, 0.0, 0.0, 0.0), 

rates=_T( 0.0, -0.06, -0.14, 0.01, 0.0, 0.0, 0.02)), 

(_S.ITRF2000, _S.ITRF93): _D(epoch=_F(1988), 

xform=_T( 12.7, 6.5, -20.9, 1.95, -0.39, 0.8, -1.14), 

rates=_T( -2.9, -0.2, -0.6, 0.01, -0.11, -0.19, 0.07)), 

(_S.ITRF2000, _S.ITRF92): _D(epoch=_F(1988), 

xform=_T( 1.47, 1.35, -1.39, 0.75, 0.0, 0.0, -0.18), 

rates=_T( 0.0, -0.06, -0.14, 0.01, 0.0, 0.0, 0.02)), 

(_S.ITRF2000, _S.ITRF91): _D(epoch=_F(1988), 

xform=_T( 26.7, 27.5, -19.9, 2.15, 0.0, 0.0, -0.18), 

rates=_T( 0.0, -0.6, -1.4, 0.01, 0.0, 0.0, 0.02)), 

(_S.ITRF2000, _S.ITRF90): _D(epoch=_F(1988), 

xform=_T( 2.47, 2.35, -3.59, 2.45, 0.0, 0.0, -0.18), 

rates=_T( 0.0, -0.06, -0.14, 0.01, 0.0, 0.0, 0.02)), 

(_S.ITRF2000, _S.ITRF89): _D(epoch=_F(1988), 

xform=_T( 2.97, 4.75, -7.39, 5.85, 0.0, 0.0, -0.18), 

rates=_T( 0.0, -0.06, -0.14, 0.01, 0.0, 0.0, 0.02)), 

(_S.ITRF2000, _S.ITRF88): _D(epoch=_F(1988), 

xform=_T( 2.47, 1.15, -9.79, 8.95, 0.1, 0.0, -0.18), 

rates=_T( 0.0, -0.06, -0.14, 0.01, 0.0, 0.0, 0.02)), 

 

# see U{Boucher, C. & Altamimi, Z. "Memo: Specifications for reference frame fixing in the 

# analysis of a EUREF GPS campaign" (2011) <https://ETRS89.ENSG.IGN.FR/memo-V8.pdf>} and 

# Altamimi, Z. U{"Key results of ITRF2014 and implication to ETRS89 realization", EUREF2016 

# <https://www.EUREF.EU/symposia/2016SanSebastian/01-02-Altamimi.pdf>}. 

(_S.ITRF2014, _S.ETRF2000): _D(epoch=_F(2000), 

xform=_T( 53.7, 51.2, -55.1, 1.02, 0.891, 5.39, -8.712), 

rates=_T( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792)), 

(_S.ITRF2008, _S.ETRF2000): _D(epoch=_F(2000), 

xform=_T( 52.1, 49.3, -58.5, 1.34, 0.891, 5.39, -8.712), 

rates=_T( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)), 

(_S.ITRF2005, _S.ETRF2000): _D(epoch=_F(2000), 

xform=_T( 54.1, 50.2, -53.8, 0.4, 0.891, 5.39, -8.712), 

rates=_T( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)), 

(_S.ITRF2000, _S.ETRF2000): _D(epoch=_F(2000), 

xform=_T( 54.0, 51.0, -48.0, 0.0, 0.891, 5.39, -8.712), 

rates=_T( 0.0, 0.0, 0.0, 0.0, 0.081, 0.49, -0.792)), 

 

# see U{Solar, T. & Snay, R.A. "Transforming Positions and Velocities between the 

# International Terrestrial Reference Frame of 2000 and North American Datum of 1983" 

# (2004)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>} 

(_S.ITRF2000, _S.NAD83): _D(epoch=_F(1997), # note NAD83(CORS96) 

xform=_T(995.6, -1901.3, -521.5, 0.62, 25.915, 9.426, 11.599), 

rates=_T( 0.7, -0.7, 0.5, -0.18, 0.067, -0.757, -0.051)), 

 

# see Table 2 in U{Dawson, J. & Woods, A. "ITRF to GDA94 coordinate transformations", Journal of 

# Applied Geodesy 4 (2010), 189-199<https://www.ResearchGate.net/publication/258401581_ITRF_to_GDA94_coordinate_transformations>} 

# (note, sign of rotations for GDA94 reversed as "Australia assumes rotation to be of coordinate 

# axes" rather than the more conventional "position around the coordinate axes") 

(_S.ITRF2008, _S.GDA94): _D(epoch=_F(1994), 

xform=_T(-84.68, -19.42, 32.01, 9.71, -0.4254, 2.2578, 2.4015), 

rates=_T( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551)), 

(_S.ITRF2005, _S.GDA94): _D(epoch=_F(1994), 

xform=_T(-79.73, -6.86, 38.03, 6.636, 0.0351, -2.1211, -2.1411), 

rates=_T( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701)), 

(_S.ITRF2000, _S.GDA94): _D(epoch=_F(1994), 

xform=_T(-45.91, -29.85, -20.37, 7.07, -1.6705, 0.4594, 1.9356), 

rates=_T( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224)), 

} 

 

_Forward = _F( 1.0e-3) # mm2m, ppb2ppM, mas2as 

_Reverse = _F(-1.0e-3) # same, inverse transforms 

 

 

def _intermediate(n1, n2): 

'''(INTERNAL) Find a trf* "in between" C{n1} and C{n2}. 

''' 

f1 = set(m for n, m in _trfXs.keys() if n == n1) # from trf1 

t2 = set(n for n, m in _trfXs.keys() if m == n2) # to trf2 

n = f1.intersection(t2) 

return n.pop() if n else NN 

 

 

def _reframeTransforms(rf2, rf, epoch): 

'''(INTERNAL) Get 0, 1 or 2 Helmert C{Transforms} to convert 

reference frame C{rf} observed at C{epoch} into C{rf2}. 

''' 

n2 = rf2.name # .upper() 

n1 = rf.name # .upper() 

if n1 == n2 or (n1.startswith(_S.ITRF) and n2.startswith(_S.WGS84)) \ 

or (n2.startswith(_S.ITRF) and n1.startswith(_S.WGS84)): 

return () # PYCHOK returns 

 

if (n1, n2) in _trfXs: 

return (_2Transform((n1, n2), epoch, _Forward),) # PYCHOK returns 

 

if (n2, n1) in _trfXs: 

return (_2Transform((n2, n1), epoch, _Reverse),) # PYCHOK returns 

 

n = _intermediate(n1, n2) 

if n: 

return (_2Transform((n1, n), epoch, _Forward), # PYCHOK returns 

_2Transform((n, n2), epoch, _Forward)) 

 

n = _intermediate(n2, n1) 

if n: 

return (_2Transform((n, n1), epoch, _Reverse), # PYCHOK returns 

_2Transform((n2, n), epoch, _Reverse)) 

 

t = '%s %r to %r' % (RefFrame.__name__, n1, n2) 

raise TRFError(_no_conversion_, txt=t) 

 

 

def _2Transform(n1_n2, epoch, _Forward_Reverse): 

'''(INTERNAL) Combine a 14-element Helmert C{trfX} and 

C{d_epoch} into a single 7-element C{Transform}. 

''' 

X = _trfXs[n1_n2] 

e = epoch - X.epoch # fractional delta years 

d = dict((n, (x + r * e) * _Forward_Reverse) for 

n, x, r in zip(_trfNs, X.xform, X.rates)) 

t = Transform(**d) 

return t 

 

 

if __name__ == '__main__': 

 

for m in range(1, 13): 

y, d = 2020, _mDays[m] 

e = date2epoch(y, m, d) 

print('%s(%d, %d, %d) %.3F' % (date2epoch.__name__, y, m, d, e)) 

 

# __doc__ of this file 

t = [''] + repr(RefFrames).split('\n') 

print('\n@var '.join(i.strip(',') for i in t)) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. 

# 

# Permission is hereby granted, free of charge, to any person obtaining a 

# copy of this software and associated documentation files (the "Software"), 

# to deal in the Software without restriction, including without limitation 

# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

# and/or sell copies of the Software, and to permit persons to whom the 

# Software is furnished to do so, subject to the following conditions: 

# 

# The above copyright notice and this permission notice shall be included 

# in all copies or substantial portions of the Software. 

# 

# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

# OTHER DEALINGS IN THE SOFTWARE. 

 

# % python -m pygeodesy.trf 

# len(_trfFs) 216 / len(_trfXs) 627: 34.4% 

# 

# date2epoch(2020, 1, 31) 2020.085 

# date2epoch(2020, 2, 29) 2020.164 

# date2epoch(2020, 3, 31) 2020.249 

# date2epoch(2020, 4, 30) 2020.331 

# date2epoch(2020, 5, 31) 2020.415 

# date2epoch(2020, 6, 30) 2020.497 

# date2epoch(2020, 7, 31) 2020.582 

# date2epoch(2020, 8, 31) 2020.667 

# date2epoch(2020, 9, 30) 2020.749 

# date2epoch(2020, 10, 31) 2020.833 

# date2epoch(2020, 11, 30) 2020.915 

# date2epoch(2020, 12, 31) 2021.000