# Coverage for pygeodesy/osgr.py : 97%

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Classes L{Osgr} and L{OSGRError} and functions L{parseOSGR} and L{toOsgr}. A pure Python implementation, transcoded from I{Chris Veness}' JavaScript originals U{OS National Grid <https://www.Movable-Type.co.UK/scripts/latlong-os-gridref.html>} and U{Module osgridref <https://www.Movable-Type.co.UK/scripts/geodesy/docs/module-osgridref.html>} and I{Charles Karney}'s C++ class U{OSGB<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1OSGB.html>}. OSGR provides geocoordinate references for UK mapping purposes, converted in 2015 to work with the C{WGS84} or the original C{OSGB36} datum. In addition, this implementation includes both the OS recommended and the Krüger-based method to convert between OSGR and geodetic coordinates (with keyword argument C{kTM} of function L{toOsgr}, method L{Osgr.toLatLon} and method C{toOsgr} of any ellipsoidal C{LatLon} class). See U{Transverse Mercator: Redfearn series<https://WikiPedia.org/wiki/Transverse_Mercator:_Redfearn_series>}, Karney's U{"Transverse Mercator with an accuracy of a few nanometers", 2011<https://Arxiv.org/pdf/1002.1417v3.pdf>} (building on U{"Konforme Abbildung des Erdellipsoids in der Ebene", 1912<https://bib.GFZ-Potsdam.DE/pub/digi/krueger2.pdf>}, U{"Die Mathematik der Gauß-Krueger-Abbildung", 2006<https://DE.WikiPedia.org/wiki/Gauß-Krüger-Koordinatensystem>}, U{A Guide<https://www.OrdnanceSurvey.co.UK/documents/resources/guide-coordinate-systems-great-britain.pdf>} and U{Ordnance Survey National Grid<https://WikiPedia.org/wiki/Ordnance_Survey_National_Grid>}. ''' # make sure int/int division yields float quotient, see .basics from __future__ import division as _; del _ # PYCHOK semicolon from pygeodesy.basics import halfs2, isbool, isfloat, map1, _xsubclassof from pygeodesy.datums import Datums, _ellipsoidal_datum, _WGS84 # from pygeodesy.dms import parseDMS2 # _MODS from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB from pygeodesy.errors import _parseX, _TypeError, _ValueError, \ _xkwds, _xkwds_get from pygeodesy.fmath import Fdot, fpowers, Fsum # from pygeodesy.fsums import Fsum # from .fmath from pygeodesy.interns import MISSING, NN, _A_, _COLON_, _COMMA_, \ _COMMASPACE_, _DOT_, _convergence_, \ _ellipsoidal_, _latlon_, _no_, _not_, \ _SPACE_, _splituple, _1_0, _10_0 from pygeodesy.interns import _N_2_0 # PYCHOK used! from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS from pygeodesy.named import _NamedBase, nameof, _xnamed from pygeodesy.namedTuples import EasNor2Tuple, LatLon2Tuple, \ LatLonDatum3Tuple from pygeodesy.props import Property_RO, property_RO from pygeodesy.streprs import _EN_WIDE, enstr2, _enstr2m3, Fmt, \ _resolution10, unstr, _xzipairs from pygeodesy.units import Easting, Lam_, Lat, Lon, Northing, \ Phi_, Scalar, _10um, _100km from pygeodesy.utily import degrees90, degrees180, sincostan3, truncate from math import cos, radians, sin, sqrt __all__ = _ALL_LAZY.osgr __version__ = '22.08.18' _equivalent_ = 'equivalent' _OSGR_ = 'OSGR' _ord_A = ord(_A_) _TRIPS = 33 # .toLatLon convergence class _NG(object): '''Ordnance Survey National Grid parameters. ''' @Property_RO def a0(self): # equatoradius, scaled return self.ellipsoid.a * self.k0 @Property_RO def b0(self): # polaradius, scaled return self.ellipsoid.b * self.k0 @Property_RO def datum(self): # datum, Airy130 ellipsoid return Datums.OSGB36 @Property_RO def eas0(self): # False origin easting (C{meter}) return Easting(4 * _100km) @Property_RO def easX(self): # easting [0..extent] (C{meter}) return Easting(7 * _100km) @Property_RO def ellipsoid(self): # ellipsoid, Airy130 return self.datum.ellipsoid def forward2(self, latlon): # convert C{latlon} to (easting, norting), as I{Karney}'s # U{Forward<https://GeographicLib.SourceForge.io/C++/doc/OSGB_8hpp_source.html>} t = self.kTM.forward(latlon.lat, latlon.lon, lon0=self.lon0) e = t.easting + self.eas0 n = t.northing + self.nor0ffset return e, n @Property_RO def k0(self): # central scale (C{float}), like I{Karney}'s CentralScale # <https://GeographicLib.SourceForge.io/C++/doc/OSGB_8hpp_source.html> _0_9998268 = (9998268 - 10000000) / 10000000 return Scalar(_10_0**_0_9998268) # 0.9996012717... @Property_RO def kTM(self): # the L{KTransverseMercator} instance, like I{Karney}'s OSGBTM # <https://GeographicLib.SourceForge.io/C++/doc/OSGB_8cpp_source.html> return _MODS.ktm.KTransverseMercator(self.datum, lon0=0, k0=self.k0) @Property_RO def lam0(self): # True origin longitude C{radians} return Lam_(self.lon0) @Property_RO def lat0(self): # True origin latitude, 49°N return Lat(49.0) @Property_RO def lon0(self): # True origin longitude, 2°W return Lon(_N_2_0) @Property_RO def Mabcd(self): # meridional coefficients (a, b, c, d) n, n2, n3 = fpowers(self.ellipsoid.n, 3) M = (Fsum(4, 4 * n, 5 * n2, 5 * n3) / 4, Fsum( 24 * n, 24 * n2, 21 * n3) / 8, Fsum( 15 * n2, 15 * n3) / 8, (35 * n3 / 24)) return M def Mabcd0(self, a): # meridional arc, scaled c = a + self.phi0 s = a - self.phi0 R = Fdot(self.Mabcd, s, -sin(s) * cos(c), sin(s * 2) * cos(c * 2), -sin(s * 3) * cos(c * 3)) return float(R * self.b0) @Property_RO def nor0(self): # False origin northing (C{meter}) return Northing(-_100km) @Property_RO def nor0ffset(self): # like I{Karney}'s computenorthoffset # <https://GeographicLib.SourceForge.io/C++/doc/OSGB_8cpp_source.html> return self.nor0 - self.kTM.forward(self.lat0, 0).northing @Property_RO def norX(self): # northing [0..extent] (C{meter}) return Northing(13 * _100km) def nu_rho_eta3(self, sa): # 3-tuple (nu, nu / rho, eta2) E = self.ellipsoid # rho, nu = E.roc2_(sa) # .k0? s = E.e2s2(sa) # == 1 - E.e2 * sa**2 v = self.a0 / sqrt(s) # == nu, transverse roc # rho = .a0 * E.e21 / s**1.5 == v * E.e21 / s # r = v * E.e21 / s # == rho, meridional roc # nu / rho == v / (v * E.e21 / s) == s / E.e21 == ... s *= E._1_e21 # ... s * E._1_e21 == s * E.a2_b2 return v, s, (s - _1_0) # η2 = nu / rho - 1 @Property_RO def phi0(self): # True origin latitude C{radians} return Phi_(self.lat0) def reverse(self, osgr): # convert C{osgr} to (ellipsoidal} LatLon, as I{Karney}'s # U{Reverse<https://GeographicLib.SourceForge.io/C++/doc/OSGB_8hpp_source.html>} r = osgr._latlonTM if r is None: x = osgr.easting - self.eas0 y = osgr.northing - self.nor0ffset t = self.kTM.reverse(x, y, lon0=self.lon0) r = _LLEB(t.lat, t.lon, datum=self.datum, name=osgr.name) osgr._latlonTM = r return r _NG = _NG() # PYCHOK singleton class OSGRError(_ValueError): '''Error raised for a L{parseOSGR}, L{Osgr} or other OSGR issue. ''' pass class Osgr(_NamedBase): '''Ordnance Survey Grid References (OSGR) coordinates on the U{National Grid<https://www.OrdnanceSurvey.co.UK/ documents/resources/guide-to-nationalgrid.pdf>}. ''' _datum = _NG.datum # default datum (L{Datums.OSGB36}) _easting = 0 # Easting (C{meter}) _latlon = None # cached B{C{_toLatlon}} _latlonTM = None # cached B{C{_toLatlon kTM}} _northing = 0 # Nothing (C{meter}) _resolution = 0 # from L{parseOSGR} (C{meter}) def __init__(self, easting, northing, datum=None, name=NN, resolution=0): '''New L{Osgr} coordinate. @arg easting: Easting from the OS C{National Grid} origin (C{meter}). @arg northing: Northing from the OS C{National Grid} origin (C{meter}). @kwarg datum: Override default datum (C{Datums.OSGB36}). @kwarg name: Optional name (C{str}). @kwarg resolution: Optional resolution (C{meter}), C{0} for default. @raise OSGRError: Invalid or negative B{C{easting}} or B{C{northing}} or B{C{datum}} not an C{Datums.OSGB36} equivalent. ''' if datum: # PYCHOK no cover try: self._datum = _ellipsoidal_datum(datum) if self.datum != _NG.datum: raise ValueError(_not_(_NG.datum.name, _equivalent_)) except (TypeError, ValueError) as x: raise OSGRError(datum=datum, txt=str(x)) self._easting = Easting( easting, Error=OSGRError, high=_NG.easX) self._northing = Northing(northing, Error=OSGRError, high=_NG.norX) if name: self.name = name if resolution: self._resolution = _resolution10(resolution, Error=OSGRError) def __str__(self): return self.toStr(GD=True, sep=_SPACE_) @Property_RO def datum(self): '''Get the datum (L{Datum}). ''' return self._datum @Property_RO def easting(self): '''Get the easting (C{meter}). ''' return self._easting @Property_RO def falsing0(self): '''Get the C{OS National Grid} falsing (L{EasNor2Tuple}). ''' return EasNor2Tuple(_NG.eas0, _NG.nor0, name=_OSGR_) @property_RO def iteration(self): '''Get the most recent C{Osgr.toLatLon} iteration number (C{int}) or C{None} if not available/applicable. ''' return self._iteration @Property_RO def latlon0(self): '''Get the C{OS National Grid} origin (L{LatLon2Tuple}). ''' return LatLon2Tuple(_NG.lat, _NG.lon0, name=_OSGR_) @Property_RO def northing(self): '''Get the northing (C{meter}). ''' return self._northing def parse(self, strOSGR, name=NN): '''Parse an OSGR reference to a similar L{Osgr} instance. @arg strOSGR: The OSGR reference (C{str}), see function L{parseOSGR}. @kwarg name: Optional instance name (C{str}), overriding this name. @return: The similar instance (L{Osgr}) @raise OSGRError: Invalid B{C{strOSGR}}. ''' return parseOSGR(strOSGR, Osgr=self.classof, name=name or self.name) @property_RO def resolution(self): '''Get the OSGR resolution (C{meter}, power of 10) or C{0} if undefined. ''' return self._resolution def toLatLon(self, LatLon=None, datum=_WGS84, kTM=False, eps=_10um, **LatLon_kwds): '''Convert this L{Osgr} coordinate to an (ellipsoidal) geodetic point. @kwarg LatLon: Optional ellipsoidal class to return the geodetic point (C{LatLon}) or C{None}. @kwarg datum: Optional datum to convert to (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg kTM: If C{True} use I{Karney}'s Krüger method from module L{ktm}, otherwise use the Ordnance Survey formulation (C{bool}). @kwarg eps: Tolerance for OS convergence (C{meter}). @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon} is None}. @return: A B{C{LatLon}} instance or if B{C{LatLon}} is C{None} a L{LatLonDatum3Tuple}C{(lat, lon, datum)}. @note: While OS grid references are based on the OSGB36 datum, the Ordnance Survey have deprecated the use of OSGB36 for lat-/longitude coordinates (in favour of WGS84). Hence, this method returns WGS84 by default with OSGB36 as an option, U{see<https://www.OrdnanceSurvey.co.UK/blog/2014/12/2>}. @note: The formulation implemented here due to Thomas, Redfearn, etc. is as published by the Ordnance Survey, but is inferior to Krüger as used by e.g. Karney 2011. @raise OSGRError: No convergence. @raise TypeError: If B{C{LatLon}} is not ellipsoidal or B{C{datum}} is invalid or conversion to B{C{datum}} failed. @example: >>> from pygeodesy import Datums, ellipsoidalVincenty as eV, Osgr >>> g = Osgr(651409.903, 313177.270) >>> p = g.toLatLon(eV.LatLon) # 52°39′28.723″N, 001°42′57.787″E >>> p = g.toLatLon(eV.LatLon, kTM=True) # 52°39′28.723″N, 001°42′57.787″E >>> # to obtain (historical) OSGB36 lat-/longitude point >>> p = g.toLatLon(eV.LatLon, datum=Datums.OSGB36) # 52°39′27.253″N, 001°43′04.518″E ''' NG = _NG if kTM: r = NG.reverse(self) elif self._latlon is None: e0 = self.easting - NG.eas0 n0 = m = self.northing - NG.nor0 _M = NG.Mabcd0 a0 = NG.a0 a = NG.phi0 _A = Fsum(a).fsum_ for self._iteration in range(1, _TRIPS): a = _A(m / a0) m = n0 - _M(a) # meridional arc if abs(m) < eps: break else: # PYCHOK no cover t = str(self) t = Fmt.PAREN(self.classname, repr(t)) t = _DOT_(t, self.toLatLon.__name__) t = unstr(t, eps=eps, kTM=kTM) raise OSGRError(_no_(_convergence_), abs(m), txt=t) sa, ca, ta = sincostan3(a) v, v_r, n2 = NG.nu_rho_eta3(sa) ta2 = ta**2 ta4 = ta2**2 ta *= v_r / 2 d = e0 / v d2 = d**2 a = (d2 * ta * (-1 + # Horner-like d2 / 12 * (Fsum( 5, 3 * ta2, -9 * ta2 * n2, n2) - d2 / 30 * Fsum(61, 90 * ta2, 45 * ta4)))).fsum_(a) b = (d / ca * (1 - # Horner-like d2 / 6 * (Fsum(v_r, 2 * ta2) - d2 / 20 * (Fsum( 5, 28 * ta2, 24 * ta4) + d2 / 42 * Fsum(61, 662 * ta2, 1320 * ta4, 720 * ta2 * ta4))))).fsum_(NG.lam0) r = _LLEB(degrees90(a), degrees180(b), datum=self.datum, name=self.name) r._iteration = self._iteration # only ellipsoidal LatLon self._latlon = r else: r = self._latlon return _ll2LatLon3(r, LatLon, datum, LatLon_kwds) @Property_RO def scale0(self): '''Get the C{OS National Grid} central scale (C{scalar}). ''' return _NG.k0 def toRepr(self, GD=None, fmt=Fmt.SQUARE, sep=_COMMASPACE_, **prec): # PYCHOK expected '''Return a string representation of this L{Osgr} coordinate. @kwarg GD: If C{bool}, in- or exclude the 2-letter grid designation and get the new B{C{prec}} behavior, otherwise if C{None}, default to the DEPRECATED definition C{B{prec}=5} I{for backward compatibility}. @kwarg fmt: Enclosing backets format (C{str}). @kwarg sep: Separator to join (C{str}) or C{None} to return an unjoined 2- or 3-C{tuple} of C{str}s. @kwarg prec: Precison C{B{prec}=0}, the number of I{decimal} digits (C{int}) or if negative, the number of I{units to drop}, like MGRS U{PRECISION <https://GeographicLib.SourceForge.io/C++/doc/GeoConvert.1.html#PRECISION>}. @return: This OSGR as (C{str}), C{"[G:GD, E:meter, N:meter]"} or if C{B{GD}=False} C{"[OSGR:easting,northing]"} or C{B{GD}=False} and C{B{prec} > 0} if C{"[OSGR:easting.d,northing.d]"}. @note: OSGR easting and northing values are truncated, not rounded. @raise OSGRError: If C{B{GD} not in (None, True, False)} or if C{B{prec} < -4} and C{B{GD}=False}. @raise ValueError: Invalid B{C{prec}}. ''' GD, prec = _GD_prec2(GD, fmt=fmt, sep=sep, **prec) if GD: t = self.toStr(GD=True, prec=prec, sep=None) t = _xzipairs('GEN', t, sep=sep, fmt=fmt) else: t = _COLON_(_OSGR_, self.toStr(GD=False, prec=prec)) if fmt: t = fmt % (t,) return t def toStr(self, GD=None, sep=NN, **prec): # PYCHOK expected '''Return this L{Osgr} coordinate as a string. @kwarg GD: If C{bool}, in- or exclude the 2-letter grid designation and get the new B{C{prec}} behavior, otherwise if C{None}, default to the DEPRECATED definition C{B{prec}=5} I{for backward compatibility}. @kwarg sep: Separator to join (C{str}) or C{None} to return an unjoined 2- or 3-C{tuple} of C{str}s. @kwarg prec: Precison C{B{prec}=0}, the number of I{decimal} digits (C{int}) or if negative, the number of I{units to drop}, like MGRS U{PRECISION <https://GeographicLib.SourceForge.io/C++/doc/GeoConvert.1.html#PRECISION>}. @return: This OSGR as (C{str}), C{"GD meter meter"} or if C{B{GD}=False} C{"easting,northing"} or if C{B{GD}=False} and C{B{prec} > 0} C{"easting.d,northing.d"} @note: OSGR easting and northing values are truncated, not rounded. @raise OSGRError: If C{B{GD} not in (None, True, False)} or if C{B{prec} < -4} and C{B{GD}=False}. @raise ValueError: Invalid B{C{prec}}. @example: >>> r = Osgr(651409, 313177) >>> str(r) # 'TG 5140 1317' >>> r.toStr() # 'TG5140913177' >>> r.toStr(GD=False) # '651409,313177' ''' def _i2c(i): if i > 7: i += 1 return chr(_ord_A + i) GD, prec = _GD_prec2(GD, sep=sep, **prec) if GD: E, e = divmod(self.easting, _100km) N, n = divmod(self.northing, _100km) E, N = int(E), int(N) if 0 > E or E > 6 or \ 0 > N or N > 12: raise OSGRError(E=E, e=e, N=N, n=n, prec=prec, sep=sep) N = 19 - N EN = _i2c( N - (N % 5) + (E + 10) // 5) + \ _i2c((N * 5) % 25 + (E % 5)) t = enstr2(e, n, prec, EN) s = sep elif prec <= -_EN_WIDE: raise OSGRError(GD=GD, prec=prec, sep=sep) else: t = enstr2(self.easting, self.northing, prec, dot=True, wide=_EN_WIDE + 1) s = sep if sep is None else (sep or _COMMA_) return t if s is None else s.join(t) def _GD_prec2(GD, **prec_et_al): '''(INTERNAL) Handle C{prec} backward compatibility. ''' if GD is None: # old C{prec} 5+ or neg prec = _xkwds_get(prec_et_al, prec=_EN_WIDE) GD = prec > 0 prec = (prec - _EN_WIDE) if GD else -prec elif isbool(GD): prec = _xkwds_get(prec_et_al, prec=0) else: raise OSGRError(GD=GD, **prec_et_al) return GD, prec def _ll2datum(ll, datum, name): '''(INTERNAL) Convert datum if needed. ''' if datum: try: if ll.datum != datum: ll = ll.toDatum(datum) except (AttributeError, TypeError, ValueError) as x: raise _TypeError(txt=str(x), datum=datum.name, **{name: ll}) return ll def _ll2LatLon3(ll, LatLon, datum, LatLon_kwds): '''(INTERNAL) Convert C{ll} to C{LatLon} ''' if LatLon is None: r = _ll2datum(ll, datum, LatLonDatum3Tuple.__name__) r = LatLonDatum3Tuple(r.lat, r.lon, r.datum) else: # must be ellipsoidal _xsubclassof(_LLEB, LatLon=LatLon) r = _ll2datum(ll, datum, LatLon.__name__) r = LatLon(r.lat, r.lon, datum=r.datum, **LatLon_kwds) if r._iteration != ll._iteration: r._iteration = ll._iteration return _xnamed(r, nameof(ll)) def parseOSGR(strOSGR, Osgr=Osgr, name=NN, **Osgr_kwds): '''Parse a string representing an OS Grid Reference, consisting of C{"[GD] easting northing"}. Accepts standard OS Grid References like "SU 387 148", with or without whitespace separators, from 2- up to 22-digit references, or all-numeric, comma-separated references in meters, for example "438700,114800". @arg strOSGR: An OSGR coordinate (C{str}). @kwarg Osgr: Optional class to return the OSGR coordinate (L{Osgr}) or C{None}. @kwarg name: Optional B{C{Osgr}} name (C{str}). @kwarg Osgr_kwds: Optional, additional B{C{Osgr}} keyword arguments, ignored if C{B{Osgr} is None}. @return: An (B{C{Osgr}}) instance or if B{C{Osgr}} is C{None} an L{EasNor2Tuple}C{(easting, northing)}. @raise OSGRError: Invalid B{C{strOSGR}}. @example: >>> r = parseOSGR('TG5140913177') >>> str(r) # 'TG 51409 13177' >>> r = parseOSGR('TG 51409 13177') >>> r.toStr() # 'TG5140913177' >>> r = parseOSGR('651409,313177') >>> r.toStr(sep=' ') # 'TG 51409 13177' >>> r.toStr(GD=False) # '651409,313177' ''' def _c2i(G): g = ord(G.upper()) - _ord_A if g > 7: g -= 1 if g < 0 or g > 25: raise ValueError return g def _OSGR(strOSGR, Osgr, name): s = _splituple(strOSGR.strip()) p = len(s) if not p: raise ValueError g = s[0] if p == 2 and isfloat(g): # "easting,northing" e, n, m = _enstr2m3(*s, wide=_EN_WIDE + 1) else: if p == 1: # "GReastingnorthing" s = halfs2(g[2:]) g = g[:2] elif p == 2: # "GReasting northing" s = g[2:], s[1] # for backward ... g = g[:2] # ... compatibility elif p != 3: raise ValueError else: # "GR easting northing" s = s[1:] e, n = map(_c2i, g) n, m = divmod(n, 5) E = ((e - 2) % 5) * 5 + m N = 19 - (e // 5) * 5 - n if 0 > E or E > 6 or \ 0 > N or N > 12: raise ValueError e, n, m = _enstr2m3(*s, wide=_EN_WIDE) e += E * _100km n += N * _100km if Osgr is None: _ = _MODS.osgr.Osgr(e, n, resolution=m) # validate r = EasNor2Tuple(e, n, name=name) else: r = Osgr(e, n, name=name, **_xkwds(Osgr_kwds, resolution=m)) return r return _parseX(_OSGR, strOSGR, Osgr, name, strOSGR=strOSGR, Error=OSGRError) def toOsgr(latlon, lon=None, kTM=False, datum=_WGS84, Osgr=Osgr, name=NN, # MCCABE 14 **prec_Osgr_kwds): '''Convert a lat-/longitude point to an OSGR coordinate. @arg latlon: Latitude (C{degrees}) or an (ellipsoidal) geodetic C{LatLon} point. @kwarg lon: Optional longitude in degrees (scalar or C{None}). @kwarg kTM: If C{True} use I{Karney}'s Krüger method from module L{ktm}, otherwise use the Ordnance Survey formulation (C{bool}). @kwarg datum: Optional datum to convert B{C{lat, lon}} from (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg Osgr: Optional class to return the OSGR coordinate (L{Osgr}) or C{None}. @kwarg name: Optional B{C{Osgr}} name (C{str}). @kwarg prec_Osgr_kwds: Optional L{truncate} precision C{B{prec}=ndigits} and/or additional B{C{Osgr}} keyword arguments, ignored if C{B{Osgr} is None}. @return: An (B{C{Osgr}}) instance or if B{C{Osgr}} is C{None} an L{EasNor2Tuple}C{(easting, northing)}. @note: If L{isint{C{(B{prec})} both easting and northing are L{truncate}d to the given number of digits. @raise OSGRError: Invalid B{C{latlon}} or B{C{lon}}. @raise TypeError: Non-ellipsoidal B{C{latlon}} or invalid B{C{datum}}, B{C{Osgr}}, B{C{Osgr_kwds}} or conversion to C{Datums.OSGB36} failed. @example: >>> p = LatLon(52.65798, 1.71605) >>> r = toOsgr(p) # [G:TG, E:51409, N:13177] >>> # for conversion of (historical) OSGB36 lat-/longitude: >>> r = toOsgr(52.65757, 1.71791, datum=Datums.OSGB36) >>> # alternatively and using Krüger >>> r = p.toOsgr(kTM=True) # [G:TG, E:51409, N:13177] ''' def _prec_kwds2(prec=MISSING, **kwds): return prec, kwds if lon is not None: try: lat, lon = _MODS.dms.parseDMS2(latlon, lon) latlon = _LLEB(lat, lon, datum=datum) except Exception as x: raise OSGRError(latlon=latlon, lon=lon, datum=datum, txt=str(x)) elif not isinstance(latlon, _LLEB): raise _TypeError(latlon=latlon, txt=_not_(_ellipsoidal_)) elif not name: # use latlon.name name = nameof(latlon) NG = _NG # convert latlon to OSGB36 first ll = _ll2datum(latlon, NG.datum, _latlon_) if kTM: e, n = NG.forward2(ll) else: try: a, b = ll.philam except AttributeError: a, b = map1(radians, ll.lat, ll.lon) sa, ca, ta = sincostan3(a) v, v_r, n2 = NG.nu_rho_eta3(sa) m0 = NG.Mabcd0(a) b -= NG.lam0 t = b * sa * v / 2 d = b * ca d2 = d**2 ta2 = -(ta**2) ta4 = ta2**2 e = (d * v * (1 + # Horner-like d2 / 6 * (Fsum(v_r, ta2) + d2 / 20 * Fsum(5, 18 * ta2, ta4, 14 * n2, 58 * n2 * ta2)))).fsum_(NG.eas0) n = (d * t * (1 + # Horner-like d2 / 12 * (Fsum( 5, ta2, 9 * n2) + d2 / 30 * Fsum(61, ta4, 58 * ta2)))).fsum_(m0, NG.nor0) p, kwds = _prec_kwds2(**prec_Osgr_kwds) if p is not MISSING: e = truncate(e, p) n = truncate(n, p) if Osgr is None: _ = _MODS.osgr.Osgr(e, n) # validate r = EasNor2Tuple(e, n) else: r = Osgr(e, n, **kwds) # datum=NG.datum if lon is None and isinstance(latlon, _LLEB): if kTM: r._latlonTM = latlon # XXX weakref(latlon)? else: r._latlon = latlon # XXX weakref(latlon)? return _xnamed(r, name or nameof(latlon)) if __name__ == '__main__': from pygeodesy.lazily import printf from random import random, seed from time import localtime seed(localtime().tm_yday) def _rnd(X, n): X -= 2 d = set() while len(d) < n: r = 1 + int(random() * X) if r not in d: d.add(r) yield r D = _NG.datum i = t = 0 t1 = t2 = 0, 0, 0, 0 for e in _rnd(_NG.easX, 256): for n in _rnd(_NG.norX, 512): p = False t += 1 g = Osgr(e, n) v = g.toLatLon(kTM=False, datum=D) k = g.toLatLon(kTM=True, datum=D) d = max(abs(v.lat - k.lat), abs(v.lon - k.lon)) if d > t1[2]: t1 = e, n, d, t p = True ll = _LLEB((v.lat + k.lat) / 2, (v.lon + k.lon) / 2, datum=D) v = ll.toOsgr(kTM=False) k = ll.toOsgr(kTM=True) d = max(abs(v.easting - k.easting), abs(v.northing - k.northing)) if d > t2[2]: t2 = ll.lat, ll.lon, d, t p = True if p: i += 1 printf('%5d: %s %s', i, 'll(%.2f, %.2f) %.3e %d' % t2, 'en(%d, %d) %.3e %d' % t1) printf('%d total %s', t, D.name) # **) MIT License # # Copyright (C) 2016-2022 -- 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. # % python3 -m pygeodesy.osgr # 1: ll(53.42, -0.59) 4.672e-07 1 en(493496, 392519) 2.796e-11 1 # 2: ll(60.86, -0.28) 2.760e-05 2 en(493496, 1220986) 2.509e-10 2 # 3: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1281644) 2.774e-10 13 # 4: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1192797) 3.038e-10 20 # 5: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1192249) 3.073e-10 120 # 6: ll(61.55, -0.24) 3.120e-05 160 en(493496, 1192249) 3.073e-10 120 # 7: ll(61.55, -0.24) 3.122e-05 435 en(493496, 1192249) 3.073e-10 120 # 8: ll(61.57, -0.24) 3.130e-05 473 en(493496, 1192249) 3.073e-10 120 # 9: ll(58.66, -8.56) 8.084e-04 513 en(19711, 993800) 3.020e-06 513 # 10: ll(52.83, -7.65) 8.156e-04 518 en(19711, 993800) 3.020e-06 513 # 11: ll(51.55, -7.49) 8.755e-04 519 en(19711, 993800) 3.020e-06 513 # 12: ll(60.20, -8.87) 9.439e-04 521 en(19711, 1165686) 4.318e-06 521 # 13: ll(60.45, -8.92) 9.668e-04 532 en(19711, 1194002) 4.588e-06 532 # 14: ll(61.17, -9.08) 1.371e-03 535 en(19711, 1274463) 5.465e-06 535 # 15: ll(61.31, -9.11) 1.463e-03 642 en(19711, 1290590) 5.663e-06 642 # 16: ll(61.35, -9.12) 1.488e-03 807 en(19711, 1294976) 5.718e-06 807 # 17: ll(61.38, -9.13) 1.510e-03 929 en(19711, 1298667) 5.765e-06 929 # 18: ll(61.11, -9.24) 1.584e-03 11270 en(10307, 1268759) 6.404e-06 11270 # 19: ll(61.20, -9.26) 1.650e-03 11319 en(10307, 1278686) 6.545e-06 11319 # 20: ll(61.23, -9.27) 1.676e-03 11383 en(10307, 1282514) 6.600e-06 11383 # 21: ll(61.36, -9.30) 1.776e-03 11437 en(10307, 1297037) 6.816e-06 11437 # 22: ll(61.38, -9.30) 1.789e-03 11472 en(10307, 1298889) 6.844e-06 11472 # 23: ll(61.25, -9.39) 1.885e-03 91137 en(4367, 1285831) 7.392e-06 91137 # 24: ll(61.32, -9.40) 1.944e-03 91207 en(4367, 1293568) 7.519e-06 91207 # 25: ll(61.34, -9.41) 1.963e-03 91376 en(4367, 1296061) 7.561e-06 91376 # 26: ll(61.37, -9.41) 1.986e-03 91595 en(4367, 1298908) 7.608e-06 91595 # 131072 total OSGB36