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# -*- coding: utf-8 -*- 

 

u'''Ordnance Survey Grid References (OSGR) references on the UK U{National Grid 

<https://www.OrdnanceSurvey.co.UK/documents/resources/guide-to-nationalgrid.pdf>}. 

 

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.constants import _1_0, _10_0, _N_2_0 # PYCHOK used! 

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_, _ellipsoidal_, \ 

_latlon_, _not_, _SPACE_, _splituple 

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__ = '22.09.12' 

 

_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(Fmt.no_convergence(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