Coverage for pygeodesy/osgr.py: 97%
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2# -*- coding: utf-8 -*-
4u'''Ordnance Survey Grid References (OSGR) references on the UK U{National Grid
5<https://www.OrdnanceSurvey.co.UK/documents/resources/guide-to-nationalgrid.pdf>}.
7Classes L{Osgr} and L{OSGRError} and functions L{parseOSGR} and L{toOsgr}.
9A pure Python implementation, transcoded from I{Chris Veness}' JavaScript originals U{OS National Grid
10<https://www.Movable-Type.co.UK/scripts/latlong-os-gridref.html>} and U{Module osgridref
11<https://www.Movable-Type.co.UK/scripts/geodesy/docs/module-osgridref.html>} and I{Charles Karney}'s
12C++ class U{OSGB<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1OSGB.html>}.
14OSGR provides geocoordinate references for UK mapping purposes, converted in 2015 to work with the C{WGS84}
15or the original C{OSGB36} datum. In addition, this implementation includes both the OS recommended and the
16Krüger-based method to convert between OSGR and geodetic coordinates (with keyword argument C{kTM} of
17function L{toOsgr}, method L{Osgr.toLatLon} and method C{toOsgr} of any ellipsoidal C{LatLon} class).
19See U{Transverse Mercator: Redfearn series<https://WikiPedia.org/wiki/Transverse_Mercator:_Redfearn_series>},
20Karney's U{"Transverse Mercator with an accuracy of a few nanometers", 2011<https://ArXiv.org/pdf/1002.1417v3.pdf>}
21(building on U{"Konforme Abbildung des Erdellipsoids in der Ebene", 1912<https://bib.GFZ-Potsdam.DE/pub/digi/krueger2.pdf>},
22U{"Die Mathematik der Gauß-Krueger-Abbildung", 2006<https://DE.WikiPedia.org/wiki/Gauß-Krüger-Koordinatensystem>},
23U{A Guide<https://www.OrdnanceSurvey.co.UK/documents/resources/guide-coordinate-systems-great-britain.pdf>}
24and U{Ordnance Survey National Grid<https://WikiPedia.org/wiki/Ordnance_Survey_National_Grid>}.
25'''
26# make sure int/int division yields float quotient, see .basics
27from __future__ import division as _; del _ # PYCHOK semicolon
29from pygeodesy.basics import halfs2, isbool, isfloat, map1, \
30 _splituple, _xsubclassof, typename
31from pygeodesy.constants import _1_0, _10_0, _N_2_0 # PYCHOK used!
32from pygeodesy.datums import Datums, _ellipsoidal_datum, _WGS84
33# from pygeodesy.dms import parseDMS2 # _MODS
34from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB
35from pygeodesy.errors import _parseX, _TypeError, _ValueError, \
36 _xkwds, _xkwds_get, _xkwds_pop2
37from pygeodesy.fmath import Fdot, fpowers
38from pygeodesy.fsums import _Fsumf_
39# from pygeodesy.internals import typename # from .basics
40from pygeodesy.interns import MISSING, NN, _A_, _COLON_, _COMMA_, \
41 _COMMASPACE_, _DMAIN_, _DOT_, _not_, \
42 _ellipsoidal_, _latlon_, _SPACE_
43from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS
44from pygeodesy.named import _name2__, _NamedBase, nameof
45from pygeodesy.namedTuples import EasNor2Tuple, LatLon2Tuple, \
46 LatLonDatum3Tuple
47from pygeodesy.props import Property_RO, property_RO
48from pygeodesy.streprs import _EN_WIDE, enstr2, _enstr2m3, Fmt, \
49 _resolution10, unstr, _xzipairs
50from pygeodesy.units import Easting, Lamd, Lat, Lon, Northing, \
51 Phid, Scalar, _10um, _100km
52from pygeodesy.utily import degrees90, degrees180, sincostan3, truncate
54from math import cos, fabs, radians, sin, sqrt
56__all__ = _ALL_LAZY.osgr
57__version__ = '25.04.12'
59_equivalent_ = 'equivalent'
60_OSGR_ = 'OSGR'
61_ord_A = ord(_A_)
62_TRIPS = 33 # .toLatLon convergence
65class _NG(object):
66 '''Ordnance Survey National Grid parameters.
67 '''
68 @Property_RO
69 def a0(self): # equatoradius, scaled
70 return self.ellipsoid.a * self.k0
72 @Property_RO
73 def b0(self): # polaradius, scaled
74 return self.ellipsoid.b * self.k0
76 @Property_RO
77 def datum(self): # datum, Airy130 ellipsoid
78 return Datums.OSGB36
80 @Property_RO
81 def eas0(self): # False origin easting (C{meter})
82 return Easting(4 * _100km)
84 @Property_RO
85 def easX(self): # easting [0..extent] (C{meter})
86 return Easting(7 * _100km)
88 @Property_RO
89 def ellipsoid(self): # ellipsoid, Airy130
90 return self.datum.ellipsoid
92 def forward2(self, latlon): # convert C{latlon} to (easting, norting), as I{Karney}'s
93 # U{Forward<https://GeographicLib.SourceForge.io/C++/doc/OSGB_8hpp_source.html>}
94 t = self.kTM.forward(latlon.lat, latlon.lon, lon0=self.lon0)
95 e = t.easting + self.eas0
96 n = t.northing + self.nor0ffset
97 return e, n
99 @Property_RO
100 def k0(self): # central scale (C{float}), like I{Karney}'s CentralScale
101 # <https://GeographicLib.SourceForge.io/C++/doc/OSGB_8hpp_source.html>
102 _0_9998268 = (9998268 - 10000000) / 10000000
103 return Scalar(_10_0**_0_9998268) # 0.9996012717...
105 @Property_RO
106 def kTM(self): # the L{KTransverseMercator} instance, like I{Karney}'s OSGBTM
107 # <https://GeographicLib.SourceForge.io/C++/doc/OSGB_8cpp_source.html>
108 return _MODS.ktm.KTransverseMercator(self.datum, lon0=0, k0=self.k0)
110 @Property_RO
111 def lam0(self): # True origin longitude C{radians}
112 return Lamd(self.lon0)
114 @Property_RO
115 def lat0(self): # True origin latitude, 49°N
116 return Lat(49.0)
118 @Property_RO
119 def lon0(self): # True origin longitude, 2°W
120 return Lon(_N_2_0)
122 @Property_RO
123 def Mabcd(self): # meridional coefficients (a, b, c, d)
124 n, n2, n3 = fpowers(self.ellipsoid.n, 3)
125 M = (_Fsumf_(4, 4 * n, 5 * n2, 5 * n3) / 4,
126 _Fsumf_( 24 * n, 24 * n2, 21 * n3) / 8,
127 _Fsumf_( 15 * n2, 15 * n3) / 8,
128 (35 * n3 / 24))
129 return M
131 def Mabcd0(self, a): # meridional arc, scaled
132 c = a + self.phi0
133 s = a - self.phi0
134 R = Fdot(self.Mabcd, s, -sin(s) * cos(c),
135 sin(s * 2) * cos(c * 2),
136 -sin(s * 3) * cos(c * 3))
137 return float(R * self.b0)
139 @Property_RO
140 def nor0(self): # False origin northing (C{meter})
141 return Northing(-_100km)
143 @Property_RO
144 def nor0ffset(self): # like I{Karney}'s computenorthoffset
145 # <https://GeographicLib.SourceForge.io/C++/doc/OSGB_8cpp_source.html>
146 return self.nor0 - self.kTM.forward(self.lat0, 0).northing
148 @Property_RO
149 def norX(self): # northing [0..extent] (C{meter})
150 return Northing(13 * _100km)
152 def nu_rho_eta3(self, sa): # 3-tuple (nu, nu / rho, eta2)
153 E = self.ellipsoid # rho, nu = E.roc2_(sa) # .k0?
154 s = E.e2s2(sa) # == 1 - E.e2 * sa**2
155 v = self.a0 / sqrt(s) # == nu, transverse roc
156 # rho = .a0 * E.e21 / s**1.5 == v * E.e21 / s
157 # r = v * E.e21 / s # == rho, meridional roc
158 # nu / rho == v / (v * E.e21 / s) == s / E.e21 == ...
159 s *= E._1_e21 # ... s * E._1_e21 == s * E.a2_b2
160 return v, s, (s - _1_0) # η2 = nu / rho - 1
162 @Property_RO
163 def phi0(self): # True origin latitude C{radians}
164 return Phid(self.lat0)
166 def reverse(self, osgr): # convert C{osgr} to (ellipsoidal} LatLon, as I{Karney}'s
167 # U{Reverse<https://GeographicLib.SourceForge.io/C++/doc/OSGB_8hpp_source.html>}
168 r = osgr._latlonTM
169 if r is None:
170 x = osgr.easting - self.eas0
171 y = osgr.northing - self.nor0ffset
172 t = self.kTM.reverse(x, y, lon0=self.lon0)
173 r = _LLEB(t.lat, t.lon, datum=self.datum, name=osgr.name)
174 osgr._latlonTM = r
175 return r
177_NG = _NG() # PYCHOK singleton
180class OSGRError(_ValueError):
181 '''Error raised for a L{parseOSGR}, L{Osgr} or other OSGR issue.
182 '''
183 pass
186class Osgr(_NamedBase):
187 '''Ordnance Survey Grid References (OSGR) coordinates on
188 the U{National Grid<https://www.OrdnanceSurvey.co.UK/
189 documents/resources/guide-to-nationalgrid.pdf>}.
190 '''
191 _datum = _NG.datum # default datum (L{Datums.OSGB36})
192 _easting = 0 # Easting (C{meter})
193 _latlon = None # cached B{C{_toLatlon}}
194 _latlonTM = None # cached B{C{_toLatlon kTM}}
195 _northing = 0 # Nothing (C{meter})
196 _resolution = 0 # from L{parseOSGR} (C{meter})
198 def __init__(self, easting, northing, datum=None, resolution=0, **name):
199 '''New L{Osgr} coordinate.
201 @arg easting: Easting from the OS C{National Grid} origin (C{meter}).
202 @arg northing: Northing from the OS C{National Grid} origin (C{meter}).
203 @kwarg datum: Override default datum (C{Datums.OSGB36}).
204 @kwarg resolution: Optional resolution (C{meter}), C{0} for default.
205 @kwarg name: Optional C{B{name}=NN} (C{str}).
207 @raise OSGRError: Invalid or negative B{C{easting}} or B{C{northing}}
208 or B{C{datum}} not an C{Datums.OSGB36} equivalent.
209 '''
210 if datum: # PYCHOK no cover
211 try:
212 self._datum = _ellipsoidal_datum(datum)
213 if self.datum != _NG.datum:
214 raise ValueError(_not_(_NG.datum.name, _equivalent_))
215 except (TypeError, ValueError) as x:
216 raise OSGRError(datum=datum, cause=x)
218 self._easting = Easting( easting, Error=OSGRError, high=_NG.easX)
219 self._northing = Northing(northing, Error=OSGRError, high=_NG.norX)
221 if name:
222 self.name = name
223 if resolution:
224 self._resolution = _resolution10(resolution, Error=OSGRError)
226 def __str__(self):
227 return self.toStr(GD=True, sep=_SPACE_)
229 @Property_RO
230 def datum(self):
231 '''Get the datum (L{Datum}).
232 '''
233 return self._datum
235 @Property_RO
236 def easting(self):
237 '''Get the easting (C{meter}).
238 '''
239 return self._easting
241 @Property_RO
242 def falsing0(self):
243 '''Get the C{OS National Grid} falsing (L{EasNor2Tuple}).
244 '''
245 return EasNor2Tuple(_NG.eas0, _NG.nor0, name=_OSGR_)
247 @property_RO
248 def iteration(self):
249 '''Get the most recent C{Osgr.toLatLon} iteration number
250 (C{int}) or C{None} if not available/applicable.
251 '''
252 return self._iteration
254 @Property_RO
255 def latlon0(self):
256 '''Get the C{OS National Grid} origin (L{LatLon2Tuple}).
257 '''
258 return LatLon2Tuple(_NG.lat, _NG.lon0, name=_OSGR_)
260 @Property_RO
261 def northing(self):
262 '''Get the northing (C{meter}).
263 '''
264 return self._northing
266 def parse(self, strOSGR, **name):
267 '''Parse an OSGR reference to a similar L{Osgr} instance.
269 @arg strOSGR: The OSGR reference (C{str}), see function L{parseOSGR}.
270 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name.
272 @return: The similar instance (L{Osgr})
274 @raise OSGRError: Invalid B{C{strOSGR}}.
275 '''
276 return parseOSGR(strOSGR, Osgr=self.classof, name=self._name__(name))
278 @property_RO
279 def resolution(self):
280 '''Get the OSGR resolution (C{meter}, power of 10) or C{0} if undefined.
281 '''
282 return self._resolution
284 def toLatLon(self, LatLon=None, datum=_WGS84, kTM=False, eps=_10um, **LatLon_kwds):
285 '''Convert this L{Osgr} coordinate to an (ellipsoidal) geodetic
286 point.
288 @kwarg LatLon: Optional ellipsoidal class to return the
289 geodetic point (C{LatLon}) or C{None}.
290 @kwarg datum: Optional datum to convert to (L{Datum},
291 L{Ellipsoid}, L{Ellipsoid2}, L{Ellipsoid2}
292 or L{a_f2Tuple}).
293 @kwarg kTM: If C{True}, use I{Karney}'s Krüger method from
294 module L{ktm}, otherwise use the Ordnance Survey
295 formulation (C{bool}).
296 @kwarg eps: Tolerance for OS convergence (C{meter}).
297 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
298 arguments, ignored if C{B{LatLon} is None}.
300 @return: A B{C{LatLon}} instance or if C{B{LatLon} is None}
301 a L{LatLonDatum3Tuple}C{(lat, lon, datum)}.
303 @note: While OS grid references are based on the OSGB36 datum,
304 the Ordnance Survey have deprecated the use of OSGB36 for
305 lat-/longitude coordinates (in favour of WGS84). Hence,
306 this method returns WGS84 by default with OSGB36 as an
307 option, U{see<https://www.OrdnanceSurvey.co.UK/blog/2014/12/2>}.
309 @note: The formulation implemented here due to Thomas, Redfearn,
310 etc. is as published by the Ordnance Survey, but is
311 inferior to Krüger as used by e.g. Karney 2011.
313 @raise OSGRError: No convergence.
315 @raise TypeError: If B{C{LatLon}} is not ellipsoidal or B{C{datum}}
316 is invalid or conversion to B{C{datum}} failed.
317 '''
318 NG = _NG
319 if kTM:
320 r = NG.reverse(self)
322 elif self._latlon is None:
323 _F = _Fsumf_
324 e0 = self.easting - NG.eas0
325 n0 = m = self.northing - NG.nor0
327 a0 = NG.a0
328 _M = NG.Mabcd0
329 a = NG.phi0
330 _a = fabs
331 _A = _F(a).fsum_
332 for self._iteration in range(1, _TRIPS):
333 a = _A(m / a0)
334 m = n0 - _M(a) # meridional arc
335 if _a(m) < eps:
336 break
337 else: # PYCHOK no cover
338 t = str(self)
339 t = Fmt.PAREN(self.classname, repr(t))
340 t = _DOT_(t, typename(self.toLatLon))
341 t = unstr(t, eps=eps, kTM=kTM)
342 raise OSGRError(Fmt.no_convergence(m), txt=t)
344 sa, ca, ta = sincostan3(a)
345 v, v_r, n2 = NG.nu_rho_eta3(sa)
347 ta2 = ta**2
348 ta4 = ta2**2
350 ta *= v_r / 2
351 d = e0 / v
352 d2 = d**2
354 a = (d2 * ta * (-1 + # Horner-like
355 d2 / 12 * (_F( 5, 3 * ta2, -9 * ta2 * n2, n2) -
356 d2 / 30 * _F(61, 90 * ta2, 45 * ta4)))).fsum_(a)
358 b = (d / ca * ( 1 - # Horner-like
359 d2 / 6 * (_F(v_r, 2 * ta2) -
360 d2 / 20 * (_F( 5, 28 * ta2, 24 * ta4) +
361 d2 / 42 * _F(61, 662 * ta2, 1320 * ta4,
362 720 * ta2 * ta4))))).fsum_(NG.lam0)
364 r = _LLEB(degrees90(a), degrees180(b), datum=self.datum, name=self.name)
365 r._iteration = self._iteration # only ellipsoidal LatLon
366 self._latlon = r
367 else:
368 r = self._latlon
370 return _ll2LatLon3(r, LatLon, datum, LatLon_kwds)
372 @Property_RO
373 def scale0(self):
374 '''Get the C{OS National Grid} central scale (C{scalar}).
375 '''
376 return _NG.k0
378 def toRepr(self, GD=None, fmt=Fmt.SQUARE, sep=_COMMASPACE_, **prec): # PYCHOK expected
379 '''Return a string representation of this L{Osgr} coordinate.
381 @kwarg GD: If C{bool}, in- or exclude the 2-letter grid designation and get
382 the new B{C{prec}} behavior, otherwise if C{None}, default to the
383 DEPRECATED definition C{B{prec}=5} I{for backward compatibility}.
384 @kwarg fmt: Enclosing backets format (C{str}).
385 @kwarg sep: Separator to join (C{str}) or C{None} to return an unjoined 2- or
386 3-C{tuple} of C{str}s.
387 @kwarg prec: Precison C{B{prec}=0}, the number of I{decimal} digits (C{int}) or
388 if negative, the number of I{units to drop}, like MGRS U{PRECISION
389 <https://GeographicLib.SourceForge.io/C++/doc/GeoConvert.1.html#PRECISION>}.
391 @return: This OSGR as (C{str}), C{"[G:GD, E:meter, N:meter]"} or if C{B{GD}=False}
392 C{"[OSGR:easting,northing]"} or C{B{GD}=False} and C{B{prec} > 0} if
393 C{"[OSGR:easting.d,northing.d]"}.
395 @note: OSGR easting and northing values are truncated, not rounded.
397 @raise OSGRError: If C{B{GD} not in (None, True, False)} or if C{B{prec} < -4}
398 and C{B{GD}=False}.
400 @raise ValueError: Invalid B{C{prec}}.
401 '''
402 GD, prec = _GD_prec2(GD, fmt=fmt, sep=sep, **prec)
404 if GD:
405 t = self.toStr(GD=True, prec=prec, sep=None)
406 t = _xzipairs('GEN', t, sep=sep, fmt=fmt)
407 else:
408 t = _COLON_(_OSGR_, self.toStr(GD=False, prec=prec))
409 if fmt:
410 t = fmt % (t,)
411 return t
413 def toStr(self, GD=None, sep=NN, **prec): # PYCHOK expected
414 '''Return this L{Osgr} coordinate as a string.
416 @kwarg GD: If C{bool}, in- or exclude the 2-letter grid designation and get
417 the new B{C{prec}} behavior, otherwise if C{None}, default to the
418 DEPRECATED definition C{B{prec}=5} I{for backward compatibility}.
419 @kwarg sep: Separator to join (C{str}) or C{None} to return an unjoined 2- or
420 3-C{tuple} of C{str}s.
421 @kwarg prec: Precison C{B{prec}=0}, the number of I{decimal} digits (C{int}) or
422 if negative, the number of I{units to drop}, like MGRS U{PRECISION
423 <https://GeographicLib.SourceForge.io/C++/doc/GeoConvert.1.html#PRECISION>}.
425 @return: This OSGR as (C{str}), C{"GD meter meter"} or if C{B{GD}=False}
426 C{"easting,northing"} or if C{B{GD}=False} and C{B{prec} > 0}
427 C{"easting.d,northing.d"}
429 @note: OSGR easting and northing values are truncated, not rounded.
431 @raise OSGRError: If C{B{GD} not in (None, True, False)} or if C{B{prec}
432 < -4} and C{B{GD}=False}.
434 @raise ValueError: Invalid B{C{prec}}.
435 '''
436 def _i2c(i):
437 if i > 7:
438 i += 1
439 return chr(_ord_A + i)
441 GD, prec = _GD_prec2(GD, sep=sep, **prec)
443 if GD:
444 E, e = divmod(self.easting, _100km)
445 N, n = divmod(self.northing, _100km)
446 E, N = int(E), int(N)
447 if 0 > E or E > 6 or \
448 0 > N or N > 12:
449 raise OSGRError(E=E, e=e, N=N, n=n, prec=prec, sep=sep)
450 N = 19 - N
451 EN = _i2c( N - (N % 5) + (E + 10) // 5) + \
452 _i2c((N * 5) % 25 + (E % 5))
453 t = enstr2(e, n, prec, EN)
454 s = sep
456 elif prec <= -_EN_WIDE:
457 raise OSGRError(GD=GD, prec=prec, sep=sep)
458 else:
459 t = enstr2(self.easting, self.northing, prec, dot=True,
460 wide=_EN_WIDE + 1)
461 s = sep if sep is None else (sep or _COMMA_)
463 return t if s is None else s.join(t)
466def _GD_prec2(GD, **prec_et_al):
467 '''(INTERNAL) Handle C{prec} backward compatibility.
468 '''
469 if GD is None: # old C{prec} 5+ or neg
470 prec = _xkwds_get(prec_et_al, prec=_EN_WIDE)
471 GD = prec > 0
472 prec = (prec - _EN_WIDE) if GD else -prec
473 elif isbool(GD):
474 prec = _xkwds_get(prec_et_al, prec=0)
475 else:
476 raise OSGRError(GD=GD, **prec_et_al)
477 return GD, prec
480def _ll2datum(ll, datum, name):
481 '''(INTERNAL) Convert datum if needed.
482 '''
483 if datum:
484 try:
485 if ll.datum != datum:
486 ll = ll.toDatum(datum)
487 except (AttributeError, TypeError, ValueError) as x:
488 raise _TypeError(cause=x, datum=datum.name, **{name: ll})
489 return ll
492def _ll2LatLon3(ll, LatLon, datum, LatLon_kwds):
493 '''(INTERNAL) Convert C{ll} to C{LatLon}
494 '''
495 n = nameof(ll)
496 if LatLon is None:
497 r = _ll2datum(ll, datum, typename(LatLonDatum3Tuple))
498 r = LatLonDatum3Tuple(r.lat, r.lon, r.datum, name=n)
499 else: # must be ellipsoidal
500 _xsubclassof(_LLEB, LatLon=LatLon)
501 r = _ll2datum(ll, datum, typename(LatLon))
502 r = LatLon(r.lat, r.lon, datum=r.datum, **_xkwds(LatLon_kwds, name=n))
503 if r._iteration != ll._iteration:
504 r._iteration = ll._iteration
505 return r
508def parseOSGR(strOSGR, Osgr=Osgr, **name_Osgr_kwds):
509 '''Parse a string representing an OS Grid Reference, consisting of C{"[GD]
510 easting northing"}.
512 Accepts standard OS Grid References like "SU 387 148", with or without
513 whitespace separators, from 2- up to 22-digit references, or all-numeric,
514 comma-separated references in meters, for example "438700,114800".
516 @arg strOSGR: An OSGR coordinate (C{str}).
517 @kwarg Osgr: Optional class to return the OSGR coordinate (L{Osgr}) or C{None}.
518 @kwarg name_Osgr_kwds: Optional C{B{name}=NN} (C{str}) and optionally, additional
519 B{C{Osgr}} keyword arguments, ignored if C{B{Osgr} is None}.
521 @return: An (B{C{Osgr}}) instance or if C{B{Osgr} is None}, an
522 L{EasNor2Tuple}C{(easting, northing)}.
524 @raise OSGRError: Invalid B{C{strOSGR}}.
525 '''
526 def _c2i(G):
527 g = ord(G.upper()) - _ord_A
528 if g > 7:
529 g -= 1
530 if g < 0 or g > 25:
531 raise ValueError
532 return g
534 def _OSGR(strOSGR, Osgr, kwds):
535 s = _splituple(strOSGR.strip())
536 p = len(s)
537 if not p:
538 raise ValueError
539 g = s[0]
540 if p == 2 and isfloat(g, both=True): # "easting,northing"
541 e, n, m = _enstr2m3(*s, wide=_EN_WIDE + 1)
543 else:
544 if p == 1: # "GReastingnorthing"
545 s = halfs2(g[2:])
546 g = g[:2]
547 elif p == 2: # "GReasting northing"
548 s = g[2:], s[1] # for backward ...
549 g = g[:2] # ... compatibility
550 elif p != 3:
551 raise ValueError
552 else: # "GR easting northing"
553 s = s[1:]
555 e, n = map(_c2i, g)
556 n, m = divmod(n, 5)
557 E = ((e - 2) % 5) * 5 + m
558 N = 19 - (e // 5) * 5 - n
559 if 0 > E or E > 6 or \
560 0 > N or N > 12:
561 raise ValueError
563 e, n, m = _enstr2m3(*s, wide=_EN_WIDE)
564 e += E * _100km
565 n += N * _100km
567 name, kwds = _name2__(**kwds)
568 if Osgr is None:
569 _ = _MODS.osgr.Osgr(e, n, resolution=m) # validate
570 r = EasNor2Tuple(e, n, name=name)
571 else:
572 r = Osgr(e, n, name=name, **_xkwds(kwds, resolution=m))
573 return r
575 return _parseX(_OSGR, strOSGR, Osgr, name_Osgr_kwds,
576 strOSGR=strOSGR, Error=OSGRError)
579def toOsgr(latlon, lon=None, kTM=False, datum=_WGS84, Osgr=Osgr, # MCCABE 14
580 **prec_name_Osgr_kwds):
581 '''Convert a lat-/longitude point to an OSGR coordinate.
583 @arg latlon: Latitude (C{degrees}) or an (ellipsoidal) geodetic
584 C{LatLon} point.
585 @kwarg lon: Optional longitude in degrees (scalar or C{None}).
586 @kwarg kTM: If C{True}, use I{Karney}'s Krüger method from
587 module L{ktm}, otherwise use the Ordnance Survey
588 formulation (C{bool}).
589 @kwarg datum: Optional datum to convert B{C{lat, lon}} from
590 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
591 L{a_f2Tuple}).
592 @kwarg Osgr: Optional class to return the OSGR coordinate
593 (L{Osgr}) or C{None}.
594 @kwarg prec_name_Osgr_kwds: Optional C{B{name}=NN} (C{str}),
595 optional L{truncate} precision C{B{prec}=ndigits}
596 and additional B{C{Osgr}} keyword arguments,
597 ignored if C{B{Osgr} is None}.
599 @return: An (B{C{Osgr}}) instance or if C{B{Osgr} is None}
600 an L{EasNor2Tuple}C{(easting, northing)}.
602 @note: If L{isint}C{(B{prec})} both easting and northing are
603 L{truncate}d to the given number of digits.
605 @raise OSGRError: Invalid B{C{latlon}} or B{C{lon}}.
607 @raise TypeError: Non-ellipsoidal B{C{latlon}} or invalid
608 B{C{datum}}, B{C{Osgr}}, B{C{Osgr_kwds}}
609 or conversion to C{Datums.OSGB36} failed.
610 '''
611 if lon is not None:
612 try:
613 lat, lon = _MODS.dms.parseDMS2(latlon, lon)
614 latlon = _LLEB(lat, lon, datum=datum)
615 except Exception as x:
616 raise OSGRError(latlon=latlon, lon=lon, datum=datum, cause=x)
617 elif not isinstance(latlon, _LLEB):
618 raise _TypeError(latlon=latlon, txt=_not_(_ellipsoidal_))
620 NG = _NG
621 # convert latlon to OSGB36 first
622 ll = _ll2datum(latlon, NG.datum, _latlon_)
624 if kTM:
625 e, n = NG.forward2(ll)
627 else:
628 try:
629 a, b = ll.philam
630 except AttributeError:
631 a, b = map1(radians, ll.lat, ll.lon)
633 sa, ca, ta = sincostan3(a)
634 v, v_r, n2 = NG.nu_rho_eta3(sa)
636 m0 = NG.Mabcd0(a)
637 b -= NG.lam0
638 t = b * sa * v / 2
639 d = b * ca
640 d2 = d**2
642 ta2 = -(ta**2)
643 ta4 = ta2**2
645 e = (d * v * ( 1 + # Horner-like
646 d2 / 6 * (_Fsumf_(v_r, ta2) +
647 d2 / 20 * _Fsumf_(5, 18 * ta2, ta4, 14 * n2,
648 58 * n2 * ta2)))).fsum_(NG.eas0)
650 n = (d * t * ( 1 + # Horner-like
651 d2 / 12 * (_Fsumf_( 5, ta2, 9 * n2) +
652 d2 / 30 * _Fsumf_(61, ta4, 58 * ta2)))).fsum_(m0, NG.nor0)
654 t, kwds = _name2__(prec_name_Osgr_kwds, _or_nameof=latlon)
655 if kwds:
656 p, kwds = _xkwds_pop2(kwds, prec=MISSING)
657 if p is not MISSING:
658 e = truncate(e, p)
659 n = truncate(n, p)
661 if Osgr is None:
662 _ = _MODS.osgr.Osgr(e, n) # validate
663 r = EasNor2Tuple(e, n, name=t)
664 else:
665 r = Osgr(e, n, name=t, **kwds) # datum=NG.datum
666 if lon is None and isinstance(latlon, _LLEB):
667 if kTM:
668 r._latlonTM = latlon # XXX weakref(latlon)?
669 else:
670 r._latlon = latlon # XXX weakref(latlon)?
671 return r
674if __name__ == _DMAIN_:
676 from pygeodesy import printf
677 from random import random, seed
678 from time import localtime
680 seed(localtime().tm_yday)
682 def _rnd(X, n):
683 X -= 2
684 d = set()
685 while len(d) < n:
686 r = 1 + int(random() * X)
687 if r not in d:
688 d.add(r)
689 yield r
691 D = _NG.datum
692 i = t = 0
693 t1 = t2 = 0, 0, 0, 0
694 for e in _rnd(_NG.easX, 256):
695 for n in _rnd(_NG.norX, 512):
696 p = False
697 t += 1
699 g = Osgr(e, n)
700 v = g.toLatLon(kTM=False, datum=D)
701 k = g.toLatLon(kTM=True, datum=D)
702 d = max(fabs(v.lat - k.lat), fabs(v.lon - k.lon))
703 if d > t1[2]:
704 t1 = e, n, d, t
705 p = True
707 ll = _LLEB((v.lat + k.lat) / 2,
708 (v.lon + k.lon) / 2, datum=D)
709 v = ll.toOsgr(kTM=False)
710 k = ll.toOsgr(kTM=True)
711 d = max(fabs(v.easting - k.easting),
712 fabs(v.northing - k.northing))
713 if d > t2[2]:
714 t2 = ll.lat, ll.lon, d, t
715 p = True
717 if p:
718 i += 1
719 printf('%5d: %s %s', i,
720 'll(%.2f, %.2f) %.3e %d' % t2,
721 'en(%d, %d) %.3e %d' % t1)
722 printf('%d total %s', t, D.name)
724# **) MIT License
725#
726# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
727#
728# Permission is hereby granted, free of charge, to any person obtaining a
729# copy of this software and associated documentation files (the "Software"),
730# to deal in the Software without restriction, including without limitation
731# the rights to use, copy, modify, merge, publish, distribute, sublicense,
732# and/or sell copies of the Software, and to permit persons to whom the
733# Software is furnished to do so, subject to the following conditions:
734#
735# The above copyright notice and this permission notice shall be included
736# in all copies or substantial portions of the Software.
737#
738# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
739# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
740# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
741# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
742# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
743# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
744# OTHER DEALINGS IN THE SOFTWARE.
746# % python3 -m pygeodesy.osgr
747# 1: ll(53.42, -0.59) 4.672e-07 1 en(493496, 392519) 2.796e-11 1
748# 2: ll(60.86, -0.28) 2.760e-05 2 en(493496, 1220986) 2.509e-10 2
749# 3: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1281644) 2.774e-10 13
750# 4: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1192797) 3.038e-10 20
751# 5: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1192249) 3.073e-10 120
752# 6: ll(61.55, -0.24) 3.120e-05 160 en(493496, 1192249) 3.073e-10 120
753# 7: ll(61.55, -0.24) 3.122e-05 435 en(493496, 1192249) 3.073e-10 120
754# 8: ll(61.57, -0.24) 3.130e-05 473 en(493496, 1192249) 3.073e-10 120
755# 9: ll(58.66, -8.56) 8.084e-04 513 en(19711, 993800) 3.020e-06 513
756# 10: ll(52.83, -7.65) 8.156e-04 518 en(19711, 993800) 3.020e-06 513
757# 11: ll(51.55, -7.49) 8.755e-04 519 en(19711, 993800) 3.020e-06 513
758# 12: ll(60.20, -8.87) 9.439e-04 521 en(19711, 1165686) 4.318e-06 521
759# 13: ll(60.45, -8.92) 9.668e-04 532 en(19711, 1194002) 4.588e-06 532
760# 14: ll(61.17, -9.08) 1.371e-03 535 en(19711, 1274463) 5.465e-06 535
761# 15: ll(61.31, -9.11) 1.463e-03 642 en(19711, 1290590) 5.663e-06 642
762# 16: ll(61.35, -9.12) 1.488e-03 807 en(19711, 1294976) 5.718e-06 807
763# 17: ll(61.38, -9.13) 1.510e-03 929 en(19711, 1298667) 5.765e-06 929
764# 18: ll(61.11, -9.24) 1.584e-03 11270 en(10307, 1268759) 6.404e-06 11270
765# 19: ll(61.20, -9.26) 1.650e-03 11319 en(10307, 1278686) 6.545e-06 11319
766# 20: ll(61.23, -9.27) 1.676e-03 11383 en(10307, 1282514) 6.600e-06 11383
767# 21: ll(61.36, -9.30) 1.776e-03 11437 en(10307, 1297037) 6.816e-06 11437
768# 22: ll(61.38, -9.30) 1.789e-03 11472 en(10307, 1298889) 6.844e-06 11472
769# 23: ll(61.25, -9.39) 1.885e-03 91137 en(4367, 1285831) 7.392e-06 91137
770# 24: ll(61.32, -9.40) 1.944e-03 91207 en(4367, 1293568) 7.519e-06 91207
771# 25: ll(61.34, -9.41) 1.963e-03 91376 en(4367, 1296061) 7.561e-06 91376
772# 26: ll(61.37, -9.41) 1.986e-03 91595 en(4367, 1298908) 7.608e-06 91595
773# 131072 total OSGB36