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# -*- coding: utf-8 -*- 

 

u'''Ordinance Survey Grid References (OSGR) classes L{Osgr} an L{OSGRError} 

and functions L{parseOSGR} and L{toOsgr}. 

 

Pure Python implementation of OS Grid Reference functions using an 

ellipsoidal earth model, transcribed 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://Henrik-Seidel.GMXhome.DE/gausskrueger.pdf>}, 2006 and 

U{Transverse Mercator: Redfearn series 

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

 

@newfield example: Example, Examples 

''' 

 

from pygeodesy.datum import Datums 

from pygeodesy.dms import parseDMS2 

from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB 

from pygeodesy.fmath import fdot, fpowers, Fsum, fsum_, _IsNotError, map1 

from pygeodesy.lazily import _ALL_LAZY 

from pygeodesy.named import EasNor2Tuple, LatLonDatum3Tuple, \ 

_NamedBase, nameof, _xattrs, _xnamed 

from pygeodesy.utily import degrees90, degrees180, enStr2, false2f, \ 

halfs2, issubclassof, property_RO, sincos2 

 

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

 

# all public contants, classes and functions 

__all__ = _ALL_LAZY.osgr 

__version__ = '19.10.24' 

 

_10um = 1e-5 #: (INTERNAL) 0.01 millimeter (C{meter}) 

_100km = 100000 #: (INTERNAL) 100 km (int meter) 

 

_A0, _B0 = radians(49), radians(-2) #: (INTERNAL) NatGrid true origin, 49°N,2°W. 

_E0, _N0 = 400e3, -100e3 #: (INTERNAL) East-/northing of true origin (C{meter}). 

_F0 = 0.9996012717 #: (INTERNAL) NatGrid scale of central meridian (C{float}). 

 

_OSGB36 = Datums.OSGB36 #: (INTERNAL) Airy130 ellipsoid 

 

 

def _ll2datum(ll, datum, name): 

'''(INTERNAL) Convert datum if needed. 

''' 

if datum and ll.datum != datum: 

try: 

ll = ll.convertDatum(datum) 

except AttributeError: 

raise TypeError('no %s.convertDatum: %r' % (name, ll)) 

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 #: (INTERNAL) Datum (L{Datum}) 

_easting = 0 #: (INTERNAL) Easting (C{meter}). 

_latlon = None #: (INTERNAL) Cache B{C{_toLatlon}}. 

_northing = 0 #: (INTERNAL) Nothing (C{meter}). 

 

def __init__(self, easting, northing, name=''): 

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

 

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

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

@keyword name: Optional name (C{str}). 

 

@raise OSGRError: Invalid B{C{easting}} or B{C{northing}}. 

 

@example: 

 

>>> from pygeodesy import Osgr 

>>> r = Osgr(651409, 313177) 

''' 

if name: 

self.name = name 

 

self._easting = false2f(easting, 'easting', Error=OSGRError) 

self._northing = false2f(northing, 'northing', Error=OSGRError) 

 

def _xcopy(self, *attrs): 

'''(INTERNAL) Make copy with add'l, subclass attributes. 

''' 

return _xattrs(self.classof(self.easting, self.northing), 

self, *attrs) 

 

def copy(self): 

'''Copy this OSGR reference. 

 

@return: The copy (L{Osgr} or subclass thereof). 

''' 

return self._xcopy() 

 

@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 northing(self): 

'''Get the northing (C{meter}). 

''' 

return self._northing 

 

def parse(self, strOSGR): 

'''Parse a string to an Osgr instance. 

 

For more details, see function L{parseOSGR} in this module L{osgr}. 

''' 

return parseOSGR(strOSGR) 

 

def toLatLon(self, LatLon=None, datum=Datums.WGS84): 

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

point. 

 

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.} 

 

@keyword LatLon: Optional ellipsoidal (sub-)class to return 

the point (C{LatLon}) or C{None}. 

@keyword datum: Optional datum to use (C{Datum}). 

 

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

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

if B{C{LatLon}} is C{None}. 

 

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

B{C{datum}} 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 = _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, 0 

sa = Fsum(a) 

while True: 

t = n_N0 - M 

if t < _10um: 

break 

a = sa.fsum_(t / a_F0) 

M = b_F0 * _M(E.Mabcd, a) 

 

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 

 

vr = v / r # == s / E.e12 

x2 = vr - 1 # η2 

ta = tan(a) 

 

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

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

 

tar = ta / r 

V4 = (a, 

tar / ( 2 * v), 

tar / ( 24 * v3) * fdot((1, 3, -9), 5 + x2, ta2, ta2 * x2), 

tar / (720 * v5) * fdot((61, 90, 45), 1, ta2, ta4)) 

 

csa = 1.0 / ca 

X5 = (_B0, 

csa / v, 

csa / ( 6 * v3) * fsum_(vr, ta, ta), 

csa / ( 120 * v5) * fdot((5, 28, 24), 1, ta2, ta4), 

csa / (5040 * v7) * fdot((61, 662, 1320, 720), ta, ta2, ta4, ta6)) 

 

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

a = fdot(V4, 1, -d2, d4, -d6) 

b = fdot(X5, 1, d, -d3, d5, -d7) 

 

self._latlon = _LLEB(degrees90(a), degrees180(b), datum=_OSGB36, name=self.name) 

return self._latlon3(LatLon, datum) 

 

def _latlon3(self, LatLon, datum): 

'''(INTERNAL) Convert cached LatLon 

''' 

ll = self._latlon 

if LatLon is None: 

if datum and datum != ll.datum: 

raise TypeError('no %s.convertDatum: %r' % (LatLon, ll)) 

return _xnamed(LatLonDatum3Tuple(ll.lat, ll.lon, ll.datum), ll.name) 

elif issubclassof(LatLon, _LLEB): 

ll = _xnamed(LatLon(ll.lat, ll.lon, datum=ll.datum), ll.name) 

return _ll2datum(ll, datum, 'LatLon') 

raise _IsNotError(_LLEB.__name__, LatLon=LatLon) 

 

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

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

 

Note that OSGR coordinates are truncated, not rounded 

(unlike UTM grid references). 

 

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

@keyword sep: Optional C{join} separator (C{str}). 

 

@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, ',' 

if prec > 0: 

E, e = divmod(e, _100km) 

N, n = divmod(n, _100km) 

E, N = int(E), int(N) 

if 0 > E or E > 6 or \ 

0 > N or N > 12: 

return '' 

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 = ['%0*.*f' % (w, -prec, t) for t in (e, n)] 

else: 

t = ['%06d' % int(t) for t in (e, n)] 

return s.join(t) 

 

def toStr2(self, prec=10, fmt='[%s]', sep=', '): # PYCHOK expected 

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

 

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

@keyword fmt: Optional enclosing backets format (C{str}). 

@keyword sep: Optional 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=' ') 

if prec > 0: 

t = sep.join('%s:%s' % t for t in zip('GEN', t.split())) 

else: 

t = 'OSGR:' + t 

return fmt % (t,) 

 

 

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

'''Parse an OSGR coordinate string to an Osgr instance. 

 

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 fully 

numeric, comma-separated references in metres, for 

example '438700,114800'. 

 

@param strOSGR: An OSGR coordinate (C{str}). 

@keyword Osgr: Optional (sub-)class to return the OSGR 

coordinate (L{Osgr}) or C{None}. 

@keyword 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]) 

 

s = strOSGR.strip() 

try: 

g = s.split(',') 

if len(g) == 2: # "easting,northing" 

if len(s) < 13: 

raise ValueError # caught below 

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 # caught below 

 

g = s.split() 

if len(g) == 1: # no whitespace 

e, n = halfs2(s) 

elif len(g) == 2: 

e, n = g 

else: 

raise ValueError # caught below 

 

e = _s2i(E, e) 

n = _s2i(N, n) 

 

except ValueError: 

raise OSGRError('%s invalid: %r' % ('strOSGR', strOSGR)) 

 

r = EasNor2Tuple(e, n) if Osgr is None else Osgr(e, n) 

return _xnamed(r, name) 

 

 

def toOsgr(latlon, lon=None, datum=Datums.WGS84, Osgr=Osgr, name=''): 

'''Convert a lat-/longitude point to an OSGR coordinate. 

 

@param latlon: Latitude (C{degrees}) or an (ellipsoidal) 

geodetic C{LatLon} point. 

@keyword lon: Optional longitude in degrees (scalar or C{None}). 

@keyword datum: Optional datum to convert (C{Datum}). 

@keyword Osgr: Optional (sub-)class to return the OSGR 

coordinate (L{Osgr}) or C{None}. 

@keyword 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 TypeError: Non-ellipsoidal B{C{latlon}} or B{C{datum}} 

conversion failed. 

 

@raise OSGRError: Invalid B{C{latlon}} or B{C{lon}}. 

 

@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.convertDatum() 

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

elif lon is not None: 

raise OSGRError('%s not %s: %r' % ('lon', None, lon)) 

elif not name: # use latlon.name 

name = nameof(latlon) 

 

E = _OSGB36.ellipsoid 

 

ll = _ll2datum(latlon, _OSGB36, 'latlon') 

a, b = map1(radians, ll.lat, ll.lon) 

 

sa, ca = sincos2(a) 

 

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

v = E.a * _F0 / sqrt(s) # nu 

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

 

x2 = r - 1 # η2 

ta = tan(a) 

 

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

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

 

vsa = v * sa 

I4 = (E.b * _F0 * _M(E.Mabcd, a) + _N0, 

(vsa / 2) * ca, 

(vsa / 24) * ca3 * fsum_(5, -ta2, 9 * x2), 

(vsa / 720) * ca5 * fsum_(61, ta4, -58 * ta2)) 

 

V4 = (_E0, 

(v * ca), 

(v / 6) * ca3 * (r - ta2), 

(v / 120) * ca5 * fdot((-18, 1, 14, -58), ta2, 5 + ta4, x2, ta2 * x2)) 

 

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

n = fdot(I4, 1, d2, d4, d6) 

e = fdot(V4, 1, d, d3, d5) 

 

if Osgr is None: 

r = EasNor2Tuple(e, n) 

else: 

r = Osgr(e, n) 

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

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

return _xnamed(r, name) 

 

# **) 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.