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# -*- coding: utf-8 -*- 

 

u'''Web Mercator (WM) classes L{Wm} and L{WebMercatorError} and functions 

L{parseWM} and L{toWm}. 

 

Pure Python implementation of a U{Web Mercator<https://WikiPedia.org/wiki/Web_Mercator>} 

(aka I{Pseudo-Mercator}) class and conversion functions for spherical and 

near-spherical earth models. 

 

References U{Google Maps / Bing Maps Spherical Mercator Projection 

<https://AlastairA.WordPress.com/2011/01/23/the-google-maps-bing-maps-spherical-mercator-projection>}, 

U{Geomatics Guidance Note 7, part 2<https://www.EPSG.org/Portals/0/373-07-02.pdf>} and 

U{Implementation Practice Web Mercator Map Projection 

<https://Earth-Info.NGA.mil/GandG/wgs84/web_mercator/%28U%29%20NGA_SIG_0011_1.0.0_WEBMERC.pdf>}. 

 

@newfield example: Example, Examples 

''' 

 

from pygeodesy.basics import isscalar, issubclassof, property_RO, \ 

_xkwds, _xzipairs 

from pygeodesy.datums import _ellipsoidal_datum 

from pygeodesy.dms import clipDegrees, parseDMS2 

from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB 

from pygeodesy.ellipsoids import R_MA 

from pygeodesy.errors import _IsnotError, _parseX, _TypeError, _ValueError 

from pygeodesy.interns import NN, PI_2, _COMMA_, _COMMA_SPACE_, _easting_, \ 

_ellipsoidal_, _northing_, _radius_, _SPACE_, \ 

_SQUARE_, _x_, _y_ 

from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY 

from pygeodesy.named import _NamedBase, _NamedTuple, nameof, _xnamed 

from pygeodesy.namedTuples import LatLon2Tuple, PhiLam2Tuple 

from pygeodesy.streprs import strs 

from pygeodesy.units import Easting, Lam_, Lat, Lon, Northing, Phi_, \ 

Radius, Radius_ 

from pygeodesy.utily import degrees90, degrees180 

 

from math import atan, atanh, exp, radians, sin, tanh 

 

__all__ = _ALL_LAZY.webmercator 

__version__ = '20.09.27' 

 

# _FalseEasting = 0 # false Easting (C{meter}) 

# _FalseNorthing = 0 # false Northing (C{meter}) 

_LatLimit = Lat(85.051129, name='limit') # latitudinal limit (C{degrees}) 

# _LonOrigin = 0 # longitude of natural origin (C{degrees}) 

 

 

class EasNorRadius3Tuple(_NamedTuple): 

'''3-Tuple C{(easting, northing, radius)}, all in C{meter}. 

''' 

_Names_ = (_easting_, _northing_, _radius_) 

_Units_ = ( Easting, Northing, Radius) 

 

 

class WebMercatorError(_ValueError): 

'''Web Mercator (WM) parser or L{Wm} issue. 

''' 

pass 

 

 

class Wm(_NamedBase): 

'''Web Mercator (WM) coordinate. 

''' 

_latlon = None # cached (L{LatLon2Tuple}) 

_philam = None # cached (L{PhiLam2Tuple}) 

_radius = 0 # earth radius (C{meter}) 

_x = 0 # Easting (C{meter}) 

_y = 0 # Northing (C{meter}) 

 

def __init__(self, x, y, radius=R_MA, name=NN): 

'''New L{Wm} Web Mercator (WM) coordinate. 

 

@arg x: Easting from central meridian (C{meter}). 

@arg y: Northing from equator (C{meter}). 

@kwarg radius: Optional earth radius (C{meter}). 

@kwarg name: Optional name (C{str}). 

 

@raise WebMercatorError: Invalid B{C{x}}, B{C{y}} or B{C{radius}}. 

 

@example: 

 

>>> import pygeodesy 

>>> w = pygeodesy.Wm(448251, 5411932) 

''' 

self._x = Easting( x=x, Error=WebMercatorError) 

self._y = Northing(y=y, Error=WebMercatorError) 

self._radius = Radius_(radius, Error=WebMercatorError) 

 

if name: 

self.name = name 

 

@property_RO 

def latlon(self): 

'''Get the lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}). 

''' 

if self._latlon is None: 

self._latlon = self.latlon2() 

return self._xnamed(self._latlon) 

 

def latlon2(self, datum=None): 

'''Convert this WM coordinate to a lat- and longitude. 

 

@kwarg datum: Optional, ellipsoidal datum (L{Datum}, 

L{Ellipsoid}, L{Ellipsoid2} or 

L{a_f2Tuple}) or C{None}. 

 

@return: A L{LatLon2Tuple}C{(lat, lon)}. 

 

@raise TypeError: Invalid or non-ellipsoidal B{C{datum}}. 

 

@see: Method C{toLatLon}. 

''' 

r = self.radius 

x = self._x / r 

y = 2 * atan(exp(self._y / r)) - PI_2 

if datum is not None: 

E = _ellipsoidal_datum(datum, name=self.name).ellipsoid 

if not E.isEllipsoidal: 

raise _IsnotError(_ellipsoidal_, datum=datum) 

# <https://Earth-Info.NGA.mil/GandG/wgs84/web_mercator/ 

# %28U%29%20NGA_SIG_0011_1.0.0_WEBMERC.pdf> 

y = y / r 

if E.e: 

y -= E.e * atanh(E.e * tanh(y)) # == E.es_atanh(tanh(y)) 

y *= E.a 

x *= E.a / r 

 

r = LatLon2Tuple(Lat(degrees90(y)), Lon(degrees180(x))) 

return self._xnamed(r) 

 

def parse(self, strWM, name=NN): 

'''Parse a string to a similar L{Wm} instance. 

 

@arg strWM: The WM coordinate (C{str}), see 

function L{parseWM}. 

@kwarg name: Optional instance name (C{str}), 

overriding this name. 

 

@return: The similar instance (L{Wm}). 

 

@raise WebMercatorError: Invalid B{C{strWM}}. 

''' 

return parseWM(strWM, radius=self.radius, Wm=self.classof, 

name=name or self.name) 

 

def parseWM(self, strWM, name=NN): 

'''DEPRECATED, use method L{Wm.parse}. 

''' 

return self.parse(strWM, name=name) 

 

@property_RO 

def philam(self): 

'''Get the lat- and longitude ((L{PhiLam2Tuple}C{(phi, lam)}). 

''' 

if self._philam is None: 

r = self.latlon 

self._philam = PhiLam2Tuple(Phi_(r.lat), Lam_(r.lon)) 

return self._xnamed(self._philam) 

 

@property_RO 

def radius(self): 

'''Get the earth radius (C{meter}). 

''' 

return self._radius 

 

def to2ll(self, datum=None): # PYCHOK no cover 

'''DEPRECATED, use method C{latlon2}. 

 

@return: A L{LatLon2Tuple}C{(lat, lon)}. 

''' 

return self.latlon2(datum=datum) 

 

def toLatLon(self, LatLon, datum=None, **LatLon_kwds): 

'''Convert this WM coordinate to a geodetic point. 

 

@arg LatLon: Ellipsoidal class to return the geodetic 

point (C{LatLon}). 

@kwarg datum: Optional datum for ellipsoidal or C{None} 

for spherical B{C{LatLon}} (C{Datum}). 

@kwarg LatLon_kwds: Optional, additional B{C{LatLon}} 

keyword arguments. 

 

@return: Point of this WM coordinate (B{C{LatLon}}). 

 

@raise TypeError: If B{C{LatLon}} and B{C{datum}} are 

incompatible or if B{C{datum}} is 

invalid or not ellipsoidal. 

 

@example: 

 

>>> w = Wm(448251.795, 5411932.678) 

>>> from pygeodesy import sphericalTrigonometry as sT 

>>> ll = w.toLatLon(sT.LatLon) # 43°39′11.58″N, 004°01′36.17″E 

''' 

e = issubclassof(LatLon, _LLEB) 

if e and datum: 

kwds = _xkwds(LatLon_kwds, datum=datum) 

elif not (e or datum): # and LatLon 

kwds = LatLon_kwds 

datum = None 

else: 

raise _TypeError(LatLon=LatLon, datum=datum) 

 

r = self.latlon2(datum=datum) 

r = LatLon(r.lat, r.lon, **kwds) 

return self._xnamed(r) 

 

def toRepr(self, prec=3, fmt=_SQUARE_, sep=_COMMA_SPACE_, radius=False, **unused): # PYCHOK expected 

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

 

@kwarg prec: Optional number of decimals, unstripped (C{int}). 

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

@kwarg sep: Optional separator between name:value pairs (C{str}). 

@kwarg radius: Optionally, include radius (C{bool} or C{scalar}). 

 

@return: This WM as "[x:meter, y:meter]" (C{str}) plus 

", radius:meter]" if B{C{radius}} is C{True} or 

C{scalar}. 

 

@raise WebMercatorError: Invalid B{C{radius}}. 

''' 

t = self.toStr(prec=prec, sep=None, radius=radius) 

return _xzipairs((_x_, _y_, _radius_), t, sep=sep, fmt=fmt) 

 

toStr2 = toRepr # PYCHOK for backward compatibility 

'''DEPRECATED, use method L{Wm.toRepr}.''' 

 

def toStr(self, prec=3, sep=_SPACE_, radius=False, **unused): # PYCHOK expected 

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

 

@kwarg prec: Optional number of decimals, unstripped (C{int}). 

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

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

@kwarg radius: Optionally, include radius (C{bool} or C{scalar}). 

 

@return: This WM as "meter meter" (C{str}) plus " radius" 

if B{C{radius}} is C{True} or C{scalar}. 

 

@raise WebMercatorError: Invalid B{C{radius}}. 

 

@example: 

 

>>> w = Wm(448251, 5411932.0001) 

>>> w.toStr(4) # 448251.0 5411932.0001 

>>> w.toStr(sep=', ') # 448251, 5411932 

''' 

fs = self._x, self._y 

if radius in (False, None): 

pass 

elif radius is True: 

fs += (self._radius,) 

elif isscalar(radius): 

fs += (radius,) 

else: 

raise WebMercatorError(radius=radius) 

t = strs(fs, prec=prec) 

return t if sep is None else sep.join(t) 

 

@property_RO 

def x(self): 

'''Get the easting (C{meter}). 

''' 

return self._x 

 

@property_RO 

def y(self): 

'''Get the northing (C{meter}). 

''' 

return self._y 

 

 

def parseWM(strWM, radius=R_MA, Wm=Wm, name=NN): 

'''Parse a string C{"e n [r]"} representing a WM coordinate, 

consisting of easting, northing and an optional radius. 

 

@arg strWM: A WM coordinate (C{str}). 

@kwarg radius: Optional earth radius (C{meter}). 

@kwarg Wm: Optional class to return the WM coordinate (L{Wm}) 

or C{None}. 

@kwarg name: Optional name (C{str}). 

 

@return: The WM coordinate (B{C{Wm}}) or an 

L{EasNorRadius3Tuple}C{(easting, northing, radius)} 

if B{C{Wm}} is C{None}. 

 

@raise WebMercatorError: Invalid B{C{strWM}}. 

 

@example: 

 

>>> u = parseWM('448251 5411932') 

>>> u.toStr2() # [E:448251, N:5411932] 

''' 

def _WM_(strWM, radius, Wm, name): 

w = strWM.replace(_COMMA_, _SPACE_).strip().split() 

 

if len(w) == 2: 

w += [radius] 

elif len(w) != 3: 

raise ValueError 

x, y, r = map(float, w) 

 

r = EasNorRadius3Tuple(x, y, r) if Wm is None else \ 

Wm(x, y, radius=r) 

return _xnamed(r, name, force=True) 

 

return _parseX(_WM_, strWM, radius, Wm, name, 

strWM=strWM, Error=WebMercatorError) 

 

 

def toWm(latlon, lon=None, radius=R_MA, Wm=Wm, name=NN, **Wm_kwds): 

'''Convert a lat-/longitude point to a WM coordinate. 

 

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

spherical) geodetic C{LatLon} point. 

@kwarg lon: Optional longitude (C{degrees} or C{None}). 

@kwarg radius: Optional earth radius (C{meter}). 

@kwarg Wm: Optional class to return the WM coordinate 

(L{Wm}) or C{None}. 

@kwarg name: Optional name (C{str}). 

@kwarg Wm_kwds: Optional, additional B{C{Wm}} keyword 

arguments, ignored if B{C{Wm=None}}. 

 

@return: The WM coordinate (B{C{Wm}}) or an 

L{EasNorRadius3Tuple}C{(easting, northing, radius)} 

if B{C{Wm}} is C{None}. 

 

@raise ValueError: If B{C{lon}} value is missing, if B{C{latlon}} 

is not scalar, if B{C{latlon}} is beyond the 

valid WM range and L{rangerrors} is set 

to C{True} or if B{C{radius}} is invalid. 

 

@example: 

 

>>> p = LatLon(48.8582, 2.2945) # 448251.8 5411932.7 

>>> w = toWm(p) # 448252 5411933 

>>> p = LatLon(13.4125, 103.8667) # 377302.4 1483034.8 

>>> w = toWm(p) # 377302 1483035 

''' 

e, r = None, Radius(radius) 

try: 

lat, lon = latlon.lat, latlon.lon 

if isinstance(latlon, _LLEB): 

r = latlon.datum.ellipsoid.a 

e = latlon.datum.ellipsoid.e 

if not name: # use latlon.name 

name = nameof(latlon) 

lat = clipDegrees(lat, _LatLimit) 

except AttributeError: 

lat, lon = parseDMS2(latlon, lon, clipLat=_LatLimit) 

 

s = sin(radians(lat)) 

y = atanh(s) # == log(tan((90 + lat) / 2)) == log(tanPI_2_2(radians(lat))) 

if e: 

y -= e * atanh(e * s) 

 

e = r * radians(lon) 

n = r * y 

r = EasNorRadius3Tuple(e, n, r) if Wm is None else \ 

Wm(e, n, **_xkwds(Wm_kwds, radius=r)) 

return _xnamed(r, name) 

 

 

__all__ += _ALL_DOCS(EasNorRadius3Tuple) 

 

# **) 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.