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# -*- coding: utf-8 -*- 

 

u'''Ordinance Survey Grid References (OSGR) references. 

 

Classes L{Osgr} and L{OSGRError} and functions L{parseOSGR} and L{toOsgr}. 

 

Pure Python implementation of OS Grid Reference functions using an 

ellipsoidal earth model, transcoded from JavaScript originals by 

I{(C) Chris Veness 2005-2016} published under the same MIT Licence**, see 

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>}. 

 

OSGR provides geocoordinate references for UK mapping purposes, converted 

in 2015 to work with WGS84 datum by default or OSGB36 as option. 

 

See U{Guide<https://www.OrdnanceSurvey.co.UK/docs/support/guide-coordinate-systems-great-britain.pdf>}, 

U{Proposed Changes<https://www.OrdnanceSurvey.co.UK/blog/2014/09/proposed-changes-to-latitude-and-longitude-representation-on-paper-maps-tell-us-your-thoughts>}, 

U{Confirmation<https://www.OrdnanceSurvey.co.UK/blog/2014/12/confirmation-on-changes-to-latitude-and-longitude>} 

and U{Ordnance Survey National Grid<https://WikiPedia.org/wiki/Ordnance_Survey_National_Grid>}. 

 

See also Karney U{'Transverse Mercator with an accuracy of a few nanometers' 

<https://Arxiv.org/pdf/1002.1417v3.pdf>}, 2011 (building on Krüger 

U{'Konforme Abbildung des Erdellipsoids in der Ebene' 

<https://bib.GFZ-Potsdam.DE/pub/digi/krueger2.pdf>}, 1912), Seidel 

U{'Die Mathematik der Gauß-Krueger-Abbildung' 

<https://DE.WikiPedia.org/wiki/Gauß-Krüger-Koordinatensystem>}, 2006 and 

U{Transverse Mercator: Redfearn series 

<https://WikiPedia.org/wiki/Transverse_Mercator:_Redfearn_series>}. 

''' 

# make sure int/int division yields float quotient, see .basics 

from __future__ import division as _; del _ # PYCHOK semicolon 

 

from pygeodesy.basics import halfs2, map1, _xsubclassof 

from pygeodesy.datums import Datums, _ellipsoidal_datum, _WGS84 

from pygeodesy.dms import parseDMS2 

from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB 

from pygeodesy.errors import _parseX, _TypeError, _ValueError 

from pygeodesy.fmath import fdot, fpowers 

from pygeodesy.fsums import Fsum, fsum_ 

from pygeodesy.interns import NN, _A_, _COMMA_, _COMMASPACE_, _DOT_, \ 

_convergence_, _float, _latlon_, _no_, \ 

_not_, _SPACE_, _1_0, _2_0, _6_0, \ 

_24_0, _120_0, _720_0 

from pygeodesy.interns import _COLON_ # PYCHOK used! 

from pygeodesy.lazily import _ALL_LAZY 

from pygeodesy.named import _NamedBase, nameof, _xnamed 

from pygeodesy.namedTuples import EasNor2Tuple, LatLonDatum3Tuple 

from pygeodesy.props import Property_RO, property_RO 

from pygeodesy.streprs import enstr2, Fmt, _xzipairs, _0wd, _0wpF 

from pygeodesy.units import Easting, Lam_, Northing, Phi_, Scalar, \ 

_10um, _100km 

from pygeodesy.utily import degrees90, degrees180, sincos2 

 

from math import cos, radians, sin, sqrt, tan 

 

__all__ = _ALL_LAZY.osgr 

__version__ = '22.04.27' 

 

_100_000 = int(_100km) # 100 km (int C{meter}) 

_5040_0 = _float(5040) 

 

_A0 = Phi_(49) # NatGrid true origin latitude, 49°N 

_B0 = Lam_(-2) # NatGrid true origin longitude, 2°W 

_E0 = Easting(400e3) # Easting of true origin (C{meter}) 

_N0 = Northing(-_100km) # Northing of true origin (C{meter}) 

_F0 = Scalar(0.9996012717) # NatGrid scale of central meridian (C{float}) 

 

_OSGB36 = Datums.OSGB36 # Airy130 ellipsoid 

_no_toDatum_ = 'no .toDatum' 

_ord_A = ord(_A_) 

_TRIPS = 33 # .toLatLon convergence 

 

 

def _ll2datum(ll, datum, name): 

'''(INTERNAL) Convert datum if needed. 

''' 

if datum not in (None, ll.datum): 

try: 

ll = ll.toDatum(datum) 

except AttributeError: 

raise _TypeError(name, ll, txt=Fmt.PAREN(_no_toDatum_, datum.name)) 

return ll 

 

 

def _M(Mabcd, a): 

'''(INTERNAL) Compute meridional arc. 

''' 

a_ = a - _A0 

_a = a + _A0 

return fdot(Mabcd, a_, -sin(a_) * cos(_a), 

sin(a_ * 2) * cos(_a * 2), 

-sin(a_ * 3) * cos(_a * 3)) 

 

 

class OSGRError(_ValueError): 

'''Ordinance Survey Grid References (OSGR) parse or other L{Osgr} issue. 

''' 

pass 

 

 

class Osgr(_NamedBase): 

'''Ordinance Survey Grid References (OSGR) coordinate. 

''' 

_datum = _OSGB36 # default datum (L{Datum}) 

_easting = 0 # Easting (C{meter}) 

_latlon = None # cached B{C{_toLatlon}} 

_northing = 0 # Nothing (C{meter}) 

 

def __init__(self, easting, northing, datum=None, name=NN): 

'''New L{Osgr} National Grid Reference. 

 

@arg easting: Easting from OS false easting (C{meter}). 

@arg northing: Northing from from OS false northing (C{meter}). 

@kwarg datum: Default datum (C{Datums.OSGB36}). 

@kwarg name: Optional name (C{str}). 

 

@raise OSGRError: Invalid or negative B{C{easting}} or 

B{C{northing}} or B{C{datum}} not 

C{Datums.OSBG36}. 

 

@example: 

 

>>> from pygeodesy import Osgr 

>>> r = Osgr(651409, 313177) 

''' 

self._easting = Easting( easting, Error=OSGRError, osgr=True) 

self._northing = Northing(northing, Error=OSGRError, osgr=True) 

 

if datum not in (None, _OSGB36): 

try: 

if _ellipsoidal_datum(datum) != _OSGB36: 

raise ValueError 

except (TypeError, ValueError): 

raise OSGRError(datum=datum) 

if name: 

self.name = name 

 

@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 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 northing(self): 

'''Get the northing (C{meter}). 

''' 

return self._northing 

 

def parse(self, strOSGR, name=NN): 

'''Parse a string 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) 

 

def toLatLon(self, LatLon=None, datum=_WGS84): 

'''Convert this OSGR coordinate to an (ellipsoidal) geodetic 

point. 

 

While OS grid references are based on the OSGB36 datum, the 

I{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>}. 

 

I{Note formulation implemented here due to Thomas, Redfearn, 

etc. is as published by OS, but is inferior to Krüger as 

used by e.g. Karney 2011.} 

 

@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}). 

 

@return: The geodetic point (B{C{LatLon}}) or a 

L{LatLonDatum3Tuple}C{(lat, lon, datum)} 

if B{C{LatLon}} is C{None}. 

 

@raise OSGRError: No convergence. 

 

@raise TypeError: If B{C{LatLon}} is not ellipsoidal or 

B{C{datum}} is invalid or conversion failed. 

 

@example: 

 

>>> from pygeodesy import ellipsoidalVincenty as eV 

>>> g = Osgr(651409.903, 313177.270) 

>>> p = g.toLatLon(eV.LatLon) # 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 

''' 

if self._latlon: 

return self._latlon3(LatLon, datum) 

 

E = self.datum.ellipsoid # _Datums_OSGB36.ellipsoid, Airy130 

a_F0 = E.a * _F0 

b_F0 = E.b * _F0 

 

e, n = self.easting, self.northing 

n_N0 = n - _N0 

 

a, m = _A0, n_N0 

A = Fsum(a) 

for self._iteration in range(1, _TRIPS): 

a = A.fsum_(m / a_F0) 

m = n_N0 - b_F0 * _M(E.Mabcd, a) # meridional arc 

if abs(m) < _10um: 

break 

else: 

t = _DOT_(Fmt.PAREN(self.classname, self.toStr(prec=-3)), 

self.toLatLon.__name__) 

raise OSGRError(_no_(_convergence_), txt=t) 

sa, ca = sincos2(a) 

 

s = E.e2s2(sa) # r, v = E.roc2_(sa, _F0) 

v = a_F0 / sqrt(s) # nu 

r = v * E.e12 / s # rho = a_F0 * E.e12 / pow(s, 1.5) == a_F0 * E.e12 / (s * sqrt(s)) 

 

vr = v / r # == s / E.e12 == s * E._1_e12 

x2 = vr - _1_0 # η2 

ta = tan(a) 

 

v3, v5, v7 = fpowers(v, 7, alts=3) # PYCHOK false! 

ta2, ta4, ta6 = fpowers(ta**2, 3) # PYCHOK false! 

 

d1, d2, d3, d4, d5, d6, d7 = fpowers(e - _E0, 7) # PYCHOK false! 

 

t = ta / r 

a = fsum_(a, 

-d2 * t / ( _2_0 * v), 

d4 * t / ( _24_0 * v3) * fsum_(5, x2, 3 * ta2, -9 * ta2 * x2), 

-d6 * t / (_720_0 * v5) * fsum_(61, 90 * ta2, 45 * ta4)) 

 

t = _1_0 / ca 

b = fsum_(_B0, 

d1 * t / v, 

-d3 * t / ( _6_0 * v3) * fsum_(vr, ta2, ta2), 

d5 * t / ( _120_0 * v5) * fsum_(5, 28 * ta2, 24 * ta4), 

-d7 * t / (_5040_0 * v7) * fsum_(61, 662 * ta2, 1320 * ta4, 720 * ta6)) 

 

r = _LLEB(degrees90(a), degrees180(b), datum=self.datum, name=self.name) 

r._iteration = self._iteration # only ellipsoidal LatLon 

self._latlon = r 

return self._latlon3(LatLon, datum) 

 

def _latlon3(self, LatLon, datum): 

'''(INTERNAL) Convert cached latlon to C{LatLon} 

''' 

ll = self._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) 

r._iteration = ll._iteration 

return _xnamed(r, nameof(ll)) 

 

def toRepr(self, prec=10, fmt=Fmt.SQUARE, sep=_COMMASPACE_): # PYCHOK expected 

'''Return a string representation of this OSGR coordinate. 

 

@kwarg prec: Number of digits (C{int}). 

@kwarg fmt: Enclosing backets format (C{str}). 

@kwarg sep: Separator to join (C{str}). 

 

@return: This OSGR (C{str}) "[G:00B, E:meter, N:meter]" or 

"[OSGR:meter,meter]" if B{C{prec}} is non-positive. 

''' 

t = self.toStr(prec=prec, sep=None) 

if prec > 0: 

t = _xzipairs('GEN', t, sep=sep, fmt=fmt) 

else: 

t = _COLON_(Osgr.__name__.upper(), t) 

if fmt: 

t = fmt % (t,) 

return t 

 

def toStr(self, prec=10, sep=_SPACE_): # PYCHOK expected 

'''Return a string representation of this OSGR coordinate. 

 

Note that OSGR coordinates are truncated, not rounded 

(unlike UTM grid references). 

 

@kwarg prec: Optional number of digits (C{int}). 

@kwarg sep: Optional separator to join (C{str}) or C{None} 

to return an unjoined C{tuple} of C{str}s. 

 

@return: This OSGR as C{"EN easting northing"} or as 

C{"easting,northing"} if B{C{prec}} is non-positive 

(C{str}). 

 

@raise ValueError: Invalid B{C{prec}}. 

 

@example: 

 

>>> r = Osgr(651409, 313177) 

>>> str(r) # TG 5140 1317 

>>> r.toStr(prec=0) # 651409,313177 

''' 

def _i2c(i): 

if i > 7: 

i += 1 

return chr(_ord_A + i) 

 

e, n, s = self._easting, self._northing, _COMMA_ 

if prec > 0: 

E, e = divmod(e, _100_000) 

N, n = divmod(n, _100_000) 

E, N = int(E), int(N) 

if 0 > E or E > 6 or \ 

0 > N or N > 12: 

return NN 

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 -6 < prec < 0: 

w = 6 + 1 - prec 

t = [_0wpF(w, -prec, t) for t in (e, n)] 

else: 

t = [_0wd(6, int(t)) for t in (e, n)] 

 

return tuple(t) if s is None else s.join(t) 

 

 

def parseOSGR(strOSGR, Osgr=Osgr, name=NN): 

'''Parse a string representing an OSGR grid reference, 

consisting of C{"[grid] easting northing"}. 

 

Accepts standard OS Grid References like 'SU 387 148', 

with or without whitespace separators, from 2- up to 

10-digit references (1 m × 1 m square), 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}). 

 

@return: The OSGR coordinate (B{C{Osgr}}) or an 

L{EasNor2Tuple}C{(easting, northing)} if 

B{C{Osgr}} is C{None}. 

 

@raise OSGRError: Invalid B{C{strOSGR}}. 

 

@example: 

 

>>> g = parseOSGR('TG 51409 13177') 

>>> str(g) # TG 51409 13177 

>>> g = parseOSGR('TG5140913177') 

>>> str(g) # TG 51409 13177 

>>> g = parseOSGR('TG51409 13177') 

>>> str(g) # TG 51409 13177 

>>> g = parseOSGR('651409,313177') 

>>> str(g) # TG 51409 13177 

>>> g.toStr(prec=0) # 651409,313177 

''' 

def _c2i(G): 

g = ord(G.upper()) - _ord_A 

if g > 7: 

g -= 1 

return g 

 

def _s2f(g): 

return float(g.strip()) 

 

def _s2i(G, g): 

m = g + '00000' # std to meter 

return int(str(G) + m[:5]) 

 

def _OSGR(strOSGR, Osgr, name): 

s = strOSGR.strip() 

g = s.split(_COMMA_) 

if len(g) == 2: # "easting,northing" 

if len(s) < 13: 

raise ValueError 

e, n = map(_s2f, g) 

 

else: # "GR easting northing" 

g, s = s[:2], s[2:].strip() 

 

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 

 

g = s.split() 

if len(g) == 1: # no whitespace 

e, n = halfs2(s) 

elif len(g) == 2: 

e, n = g 

else: 

raise ValueError 

 

e = _s2i(E, e) 

n = _s2i(N, n) 

 

return EasNor2Tuple(e, n, name=name) if Osgr is None else \ 

_xnamed(Osgr(e, n), name) 

 

return _parseX(_OSGR, strOSGR, Osgr, name, 

strOSGR=strOSGR, Error=OSGRError) 

 

 

def toOsgr(latlon, lon=None, datum=_WGS84, Osgr=Osgr, name=NN, 

**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 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 Osgr_kwds: Optional, additional B{C{Osgr}} keyword 

arguments, ignored if C{B{Osgr} is None}. 

 

@return: The OSGR coordinate (B{C{Osgr}}) or an 

L{EasNor2Tuple}C{(easting, northing)} if B{C{Osgr}} 

is C{None}. 

 

@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}} 

argument or conversion failed. 

 

@example: 

 

>>> p = LatLon(52.65798, 1.71605) 

>>> r = toOsgr(p) # TG 51409 13177 

>>> # for conversion of (historical) OSGB36 lat-/longitude: 

>>> r = toOsgr(52.65757, 1.71791, datum=Datums.OSGB36) 

''' 

if not isinstance(latlon, _LLEB): 

# XXX fix failing _LLEB.toDatum() 

latlon = _LLEB(*parseDMS2(latlon, lon), datum=datum) 

elif lon is not None: 

raise OSGRError(lon=lon, txt=_not_(None)) 

elif not name: # use latlon.name 

name = nameof(latlon) 

 

# if necessary, convert to OSGB36 first 

ll = _ll2datum(latlon, _OSGB36, _latlon_) 

try: 

a, b = ll.philam 

except AttributeError: 

a, b = map1(radians, ll.lat, ll.lon) 

sa, ca = sincos2(a) 

 

E = _OSGB36.ellipsoid 

 

s = E.e2s2(sa) # r, v = E.roc2_(sa, _F0); r = v / r 

v = E.a * _F0 / sqrt(s) # nu 

r = s * E._1_e12 # nu / rho == v / (v * E.e12 / s) == s / E.e12 == s * E._1_e12 

 

x2 = r - _1_0 # η2 

ta = tan(a) 

 

ca3, ca5 = fpowers(ca, 5, alts=3) # PYCHOK false! 

ta2, ta4 = fpowers(ta, 4, alts=2) # PYCHOK false! 

 

d1, d2, d3, d4, d5, d6 = fpowers(b - _B0, 6) # PYCHOK false! 

 

t = fsum_(-18 * ta2, 5, ta4, 14 * x2, -58 * ta2 * x2) 

e = fsum_(_E0, 

d1 * v * ca, 

d3 * v / _6_0 * ca3 * (r - ta2), 

d5 * v / _120_0 * ca5 * t) 

 

t = v * sa 

n = fsum_(_N0, 

_F0 * E.b * _M(E.Mabcd, a), 

d2 * t / _2_0 * ca, 

d4 * t / _24_0 * ca3 * fsum_(5, -ta2, 9 * x2), 

d6 * t / _720_0 * ca5 * fsum_(61, ta4, -58 * ta2)) 

 

if Osgr is None: 

r = EasNor2Tuple(e, n) 

else: 

r = Osgr(e, n, datum=_OSGB36, **Osgr_kwds) 

if lon is None and isinstance(latlon, _LLEB): 

r._latlon = latlon # XXX weakref(latlon)? 

return _xnamed(r, name or nameof(latlon)) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2022 -- mrJean1 at Gmail -- All Rights Reserved. 

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# 

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