Coverage for pygeodesy/webmercator.py: 99%
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« prev ^ index » next coverage.py v7.2.2, created at 2024-05-02 14:35 -0400
2# -*- coding: utf-8 -*-
4u'''Web Mercator (WM) projection.
6Classes L{Wm} and L{WebMercatorError} and functions L{parseWM} and L{toWm}.
8Pure Python implementation of a U{Web Mercator<https://WikiPedia.org/wiki/Web_Mercator>}
9(aka I{Pseudo-Mercator}) class and conversion functions for spherical and near-spherical
10earth models.
12@see: U{Google Maps / Bing Maps Spherical Mercator Projection
13<https://AlastairA.WordPress.com/2011/01/23/the-google-maps-bing-maps-spherical-mercator-projection>},
14U{Geomatics Guidance Note 7, part 2<https://www.IOGP.org/wp-content/uploads/2019/09/373-07-02.pdf>}
15and U{Implementation Practice Web Mercator Map Projection<https://Web.Archive.org/web/20141009142830/
16http://earth-info.nga.mil/GandG/wgs84/web_mercator/(U)%20NGA_SIG_0011_1.0.0_WEBMERC.pdf>}.
17'''
18# make sure int/int division yields float quotient, see .basics
19from __future__ import division as _; del _ # PYCHOK semicolon
21from pygeodesy.basics import _splituple, _xinstanceof
22from pygeodesy.constants import PI_2, R_MA, _2_0
23from pygeodesy.datums import Datum, _spherical_datum
24from pygeodesy.dms import clipDegrees, parseDMS2
25from pygeodesy.errors import _parseX, _ValueError, _xattr, _xkwds
26from pygeodesy.interns import NN, _COMMASPACE_, _datum_, _earth_, _easting_, \
27 _northing_, _radius_, _SPACE_, _x_, _y_
28# from pygeodesy.lazily import _ALL_LAZY from .named
29from pygeodesy.named import _NamedBase, _NamedTuple, _ALL_LAZY
30from pygeodesy.namedTuples import LatLon2Tuple, LatLonDatum3Tuple, PhiLam2Tuple
31from pygeodesy.props import deprecated_method, Property_RO
32from pygeodesy.streprs import Fmt, strs, _xzipairs
33from pygeodesy.units import Easting, _isRadius, Lat, Northing, Radius
34from pygeodesy.utily import degrees90, degrees180
36from math import atan, atanh, exp, radians, sin, tanh
38__all__ = _ALL_LAZY.webmercator
39__version__ = '24.02.04'
41# _FalseEasting = 0 # false Easting (C{meter})
42# _FalseNorthing = 0 # false Northing (C{meter})
43_LatLimit = Lat(limit=85.051129) # latitudinal limit (C{degrees})
44# _LonOrigin = 0 # longitude of natural origin (C{degrees})
47class EasNorRadius3Tuple(_NamedTuple):
48 '''3-Tuple C{(easting, northing, radius)}, all in C{meter}.
49 '''
50 _Names_ = (_easting_, _northing_, _radius_)
51 _Units_ = ( Easting, Northing, Radius)
54class WebMercatorError(_ValueError):
55 '''Web Mercator (WM) parser or L{Wm} issue.
56 '''
57 pass
60class Wm(_NamedBase):
61 '''Web Mercator (WM) coordinate.
62 '''
63 _datum = None # set further below
64 _earths = () # dito
65 _radius = R_MA # earth radius (C{meter})
66 _x = 0 # Easting (C{meter})
67 _y = 0 # Northing (C{meter})
69 def __init__(self, x, y, earth=R_MA, name=NN, **radius):
70 '''New L{Wm} Web Mercator (WM) coordinate.
72 @arg x: Easting from central meridian (C{meter}).
73 @arg y: Northing from equator (C{meter}).
74 @kwarg earth: Earth radius (C{meter}), datum or
75 ellipsoid (L{Datum}, L{a_f2Tuple},
76 L{Ellipsoid} or L{Ellipsoid2}).
77 @kwarg name: Optional name (C{str}).
78 @kwarg radius: DEPRECATED, use keyword argument B{C{earth}}.
80 @note: WM is strictly defined for spherical and WGS84
81 ellipsoidal earth models only.
83 @raise WebMercatorError: Invalid B{C{x}}, B{C{y}} or B{C{radius}}.
84 '''
85 self._x = Easting( x=x, Error=WebMercatorError)
86 self._y = Northing(y=y, Error=WebMercatorError)
88 R = radius.get(_radius_, earth)
89 if R not in Wm._earths:
90 self._datum = _datum(R, _radius_ if radius else _earth_)
91 self._radius = self.datum.ellipsoid.a
93 if name:
94 self.name = name
96 @Property_RO
97 def datum(self):
98 '''Get the datum (C{Datum}).
99 '''
100 return self._datum
102 @Property_RO
103 def ellipsoid(self):
104 '''Get the ellipsoid (C{Ellipsoid}).
105 '''
106 return self.datum.ellipsoid
108 @Property_RO
109 def latlon(self):
110 '''Get the lat- and longitude (L{LatLon2Tuple}).
111 '''
112 return self.latlon2()
114 def latlon2(self, datum=None):
115 '''Convert this WM coordinate to a lat- and longitude.
117 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid},
118 L{Ellipsoid2} or L{a_f2Tuple}) or earth
119 radius (C{meter}), overriding this WM's
120 C{radius} and C{datum}.
122 @return: A L{LatLon2Tuple}C{(lat, lon)}.
124 @note: WM is strictly defined for spherical and WGS84
125 ellipsoidal earth models only.
127 @raise TypeError: Invalid or non-ellipsoidal B{C{datum}}.
129 @see: Method C{toLatLon} for other return types.
130 '''
131 d = self.datum if datum in (None, self.datum, self.radius) else _datum(datum)
132 E = d.ellipsoid
133 R = self.radius
134 x = self.x / R
135 y = atan(exp(self.y / R)) * _2_0 - PI_2
136 if E.es or E.a != R: # strictly, WGS84 only
137 # <https://Web.Archive.org/web/20141009142830/http://earth-info.nga.mil/
138 # GandG/wgs84/web_mercator/(U)%20NGA_SIG_0011_1.0.0_WEBMERC.pdf>
139 y = y / R # /= chokes PyChecker
140 y -= E.es_atanh(tanh(y))
141 y *= E.a
142 x *= E.a / R
144 return LatLon2Tuple(degrees90(y), degrees180(x), name=self.name)
146 def parse(self, strWM, name=NN):
147 '''Parse a string to a similar L{Wm} instance.
149 @arg strWM: The WM coordinate (C{str}), see
150 function L{parseWM}.
151 @kwarg name: Optional instance name (C{str}),
152 overriding this name.
154 @return: The similar instance (L{Wm}).
156 @raise WebMercatorError: Invalid B{C{strWM}}.
157 '''
158 return parseWM(strWM, radius=self.radius, Wm=self.classof,
159 name=name or self.name)
161 @deprecated_method
162 def parseWM(self, strWM, name=NN): # PYCHOK no cover
163 '''DEPRECATED, use method L{Wm.parse}.'''
164 return self.parse(strWM, name=name)
166 @Property_RO
167 def philam(self):
168 '''Get the lat- and longitude ((L{PhiLam2Tuple}).
169 '''
170 return PhiLam2Tuple(*map(radians, self.latlon), name=self.name)
172 @Property_RO
173 def radius(self):
174 '''Get the earth radius (C{meter}).
175 '''
176 return self._radius
178 @deprecated_method
179 def to2ll(self, datum=None): # PYCHOK no cover
180 '''DEPRECATED, use method C{latlon2}.
182 @return: A L{LatLon2Tuple}C{(lat, lon)}.
183 '''
184 return self.latlon2(datum=datum)
186 def toLatLon(self, LatLon=None, datum=None, **LatLon_kwds):
187 '''Convert this WM coordinate to a geodetic point.
189 @kwarg LatLon: Ellipsoidal or sphperical C{LatLon} class to
190 return the geodetic point (C{LatLon}) or C{None}.
191 @kwarg datum: Optional, datum (C{Datum}) overriding this WM's.
192 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}}
193 keyword arguments, ignored if
194 C{B{LatLon} is None}.
196 @return: This WM coordinate as B{C{LatLon}} or if
197 C{B{LatLon} is None} a L{LatLonDatum3Tuple}.
199 @raise TypeError: If B{C{LatLon}} and B{C{datum}} are
200 incompatible or if B{C{datum}} is
201 invalid.
202 '''
203 d = datum or self.datum
204 _xinstanceof(Datum, datum=d)
205 r = self.latlon2(datum=d)
206 r = LatLonDatum3Tuple(r.lat, r.lon, d, name=r.name) if LatLon is None else \
207 LatLon(r.lat, r.lon, **_xkwds(LatLon_kwds, datum=d, name=r.name))
208 return r
210 def toRepr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_, radius=False, **unused): # PYCHOK expected
211 '''Return a string representation of this WM coordinate.
213 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
214 @kwarg fmt: Enclosing backets format (C{str}).
215 @kwarg sep: Optional separator between name:value pairs (C{str}).
216 @kwarg radius: If C{True} include the radius (C{bool}) or
217 C{scalar} to override this WM's radius.
219 @return: This WM as "[x:meter, y:meter]" (C{str}) or as "[x:meter,
220 y:meter], radius:meter]" if B{C{radius}} is C{True} or
221 C{scalar}.
223 @raise WebMercatorError: Invalid B{C{radius}}.
224 '''
225 t = self.toStr(prec=prec, sep=None, radius=radius)
226 n = (_x_, _y_, _radius_)[:len(t)]
227 return _xzipairs(n, t, sep=sep, fmt=fmt)
229 def toStr(self, prec=3, fmt=Fmt.F, sep=_SPACE_, radius=False, **unused): # PYCHOK expected
230 '''Return a string representation of this WM coordinate.
232 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
233 @kwarg fmt: Optional C{float} format (C{letter}).
234 @kwarg sep: Optional separator to join (C{str}) or C{None}
235 to return an unjoined C{tuple} of C{str}s.
236 @kwarg radius: If C{True} include the radius (C{bool}) or
237 C{scalar} to override this WM's radius.
239 @return: This WM as "meter meter" (C{str}) or as "meter meter
240 radius" if B{C{radius}} is C{True} or C{scalar}.
242 @raise WebMercatorError: Invalid B{C{radius}}.
243 '''
244 fs = self.x, self.y
245 if _isRadius(radius):
246 fs += (radius,)
247 elif radius: # is True:
248 fs += (self.radius,)
249 elif radius not in (None, False):
250 raise WebMercatorError(radius=radius)
251 t = strs(fs, prec=prec)
252 return t if sep is None else sep.join(t)
254 @Property_RO
255 def x(self):
256 '''Get the easting (C{meter}).
257 '''
258 return self._x
260 @Property_RO
261 def y(self):
262 '''Get the northing (C{meter}).
263 '''
264 return self._y
266Wm._datum = _spherical_datum(Wm._radius, name=Wm.__name__, raiser=_radius_) # PYCHOK defaults
267Wm._earths = (Wm._radius, Wm._datum, Wm._datum.ellipsoid)
270def _datum(earth, name=_datum_):
271 '''(INTERNAL) Make a datum from an C{earth} radius, datum or ellipsoid.
272 '''
273 if earth in Wm._earths:
274 return Wm._datum
275 try:
276 return _spherical_datum(earth, name=name)
277 except Exception as x:
278 raise WebMercatorError(name, earth, cause=x)
281def parseWM(strWM, radius=R_MA, Wm=Wm, name=NN):
282 '''Parse a string C{"e n [r]"} representing a WM coordinate,
283 consisting of easting, northing and an optional radius.
285 @arg strWM: A WM coordinate (C{str}).
286 @kwarg radius: Optional earth radius (C{meter}), needed in
287 case B{C{strWM}} doesn't include C{r}.
288 @kwarg Wm: Optional class to return the WM coordinate (L{Wm})
289 or C{None}.
290 @kwarg name: Optional name (C{str}).
292 @return: The WM coordinate (B{C{Wm}}) or an
293 L{EasNorRadius3Tuple}C{(easting, northing, radius)}
294 if B{C{Wm}} is C{None}.
296 @raise WebMercatorError: Invalid B{C{strWM}}.
297 '''
298 def _WM(strWM, radius, Wm, name):
299 w = _splituple(strWM)
301 if len(w) == 2:
302 w += (radius,)
303 elif len(w) != 3:
304 raise ValueError
305 x, y, R = map(float, w)
307 return EasNorRadius3Tuple(x, y, R, name=name) if Wm is None else \
308 Wm(x, y, earth=R, name=name)
310 return _parseX(_WM, strWM, radius, Wm, name,
311 strWM=strWM, Error=WebMercatorError)
314def toWm(latlon, lon=None, earth=R_MA, Wm=Wm, name=NN, **Wm_kwds):
315 '''Convert a lat-/longitude point to a WM coordinate.
317 @arg latlon: Latitude (C{degrees}) or an (ellipsoidal or
318 spherical) geodetic C{LatLon} point.
319 @kwarg lon: Optional longitude (C{degrees} or C{None}).
320 @kwarg earth: Earth radius (C{meter}), datum or ellipsoid
321 (L{Datum}, L{a_f2Tuple}, L{Ellipsoid} or
322 L{Ellipsoid2}), overridden by B{C{latlon}}'s
323 datum if present.
324 @kwarg Wm: Optional class to return the WM coordinate (L{Wm})
325 or C{None}.
326 @kwarg name: Optional name (C{str}).
327 @kwarg Wm_kwds: Optional, additional B{C{Wm}} keyword arguments,
328 ignored if C{B{Wm} is None}.
330 @return: The WM coordinate (B{C{Wm}}) or if B{C{Wm}} is C{None}
331 an L{EasNorRadius3Tuple}C{(easting, northing, radius)}.
333 @raise ValueError: If B{C{lon}} value is missing, if B{C{latlon}} is not
334 scalar, if B{C{latlon}} is beyond the valid WM range
335 and L{pygeodesy.rangerrors} is set to C{True} or if
336 B{C{earth}} is invalid.
337 '''
338 if _radius_ in Wm_kwds: # remove DEPRECATED, radius
339 d = _datum(Wm_kwds.pop(_radius_), _radius_)
340 else:
341 d = _datum(earth, _earth_)
342 try:
343 y, x = latlon.lat, latlon.lon
344 y = clipDegrees(y, _LatLimit)
345 d = _xattr(latlon, datum=d)
346 n = name or _xattr(latlon, name=NN)
347 except AttributeError:
348 y, x = parseDMS2(latlon, lon, clipLat=_LatLimit)
349 n = name
351 E = d.ellipsoid
352 R = E.a
353 s = sin(radians(y))
354 y = atanh(s) # == log(tand((90 + lat) / 2)) == log(tanPI_2_2(radians(lat)))
355 if E.es:
356 y -= E.es_atanh(s) # strictly, WGS84 only
357 y *= R
358 x = R * radians(x)
359 r = EasNorRadius3Tuple(x, y, R, name=n) if Wm is None else \
360 Wm(x, y, **_xkwds(Wm_kwds, earth=d, name=n))
361 return r
363# **) MIT License
364#
365# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
366#
367# Permission is hereby granted, free of charge, to any person obtaining a
368# copy of this software and associated documentation files (the "Software"),
369# to deal in the Software without restriction, including without limitation
370# the rights to use, copy, modify, merge, publish, distribute, sublicense,
371# and/or sell copies of the Software, and to permit persons to whom the
372# Software is furnished to do so, subject to the following conditions:
373#
374# The above copyright notice and this permission notice shall be included
375# in all copies or substantial portions of the Software.
376#
377# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
378# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
379# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
380# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
381# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
382# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
383# OTHER DEALINGS IN THE SOFTWARE.