# Coverage for pygeodesy/osgr.py : 95%

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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, _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__ = '20.02.19' _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 _TRIPS = 32 #: (INTERNAL) Convergence 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) @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 OSGRError: No convergence. @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 = self.datum.ellipsoid # _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 sa = Fsum(a) for _ in range(_TRIPS): a = sa.fsum_(m / a_F0) m = n_N0 - b_F0 * _M(E.Mabcd, a) # meridional arc if abs(m) < _10um: break else: t = self.classname, self.toStr(prec=-3), 'toLatLon' raise OSGRError('no convergence %s(%s).%s' % 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 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), 1, 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=self.datum, 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 = '%s:%s' % (Osgr.__name__.upper(), 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.