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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.datum import R_MA 

from pygeodesy.dms import clipDMS, parseDMS2 

from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB 

from pygeodesy.fmath import EPS, fStr, isscalar, map1, _IsNotError 

from pygeodesy.lazily import _ALL_LAZY 

from pygeodesy.named import EasNorRadius3Tuple, LatLon2Tuple, \ 

_NamedBase, nameof, _xnamed 

from pygeodesy.utily import PI_2, degrees90, degrees180, issubclassof, \ 

property_RO 

 

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

 

# all public contants, classes and functions 

__all__ = _ALL_LAZY.webmercator 

__version__ = '20.01.22' 

 

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

# _FalseNorthing = 0 #: (INTERNAL) False Northing (C{meter}). 

_LatLimit = 85.051129 #: (INTERNAL) Latitudinal limit (C{degrees}). 

# _LonOrigin = 0 #: (INTERNAL) Longitude of natural origin (C{degrees}). 

 

 

class WebMercatorError(ValueError): 

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

''' 

pass 

 

 

class Wm(_NamedBase): 

'''Web Mercator (WM) coordinate. 

''' 

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

_x = 0 #: (INTERNAL) easting (C{meter}). 

_y = 0 #: (INTERNAL) northing (C{meter}). 

 

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

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

 

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

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

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

@keyword 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) 

''' 

if name: 

self.name = name 

 

try: 

self._x, self._y, r = map1(float, x, y, radius) 

except (TypeError, ValueError): 

raise WebMercatorError('%s invalid: %r' % (Wm.__name__, (x, y, radius))) 

 

if r < EPS: # check radius 

t = '%s.%s' % (self.classname, 'radius') 

raise WebMercatorError('%s invalid: %r' % (t, r)) 

self._radius = r 

 

def parseWM(self, strWM, name=''): 

'''Parse a string to a WM coordinate. 

 

For more details, see function L{parseWM} in 

this module L{webmercator}. 

''' 

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

 

@property_RO 

def radius(self): 

'''Get the earth radius (C{meter}). 

''' 

return self._radius 

 

def to2ll(self, datum=None): 

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

 

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

 

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

 

@raise TypeError: Non-ellipsoidal B{C{datum}}. 

''' 

r = self.radius 

x = self._x / r 

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

if datum: 

E = datum.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)) 

y *= E.a 

x *= E.a / r 

return self._xnamed(LatLon2Tuple(degrees90(y), degrees180(x))) 

 

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

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

 

@param LatLon: Ellipsoidal (sub-)class to return the 

point (C{LatLon}). 

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

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

 

@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 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: 

r = LatLon(*self.to2ll(datum=datum), datum=datum) 

elif LatLon and not (e or datum): 

r = LatLon(*self.to2ll(datum=None)) 

else: 

raise TypeError('%s %r and %s %r' % ('spherical', LatLon, 

'datum', datum)) 

return self._xnamed(r) 

 

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

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

 

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

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

@keyword 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('% invalid: %r' % ('radius', radius)) 

return fStr(fs, prec=prec, sep=sep) 

 

def toStr2(self, prec=3, fmt='[%s]', sep=', ', radius=False): # PYCHOK expected 

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

 

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

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

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

@keyword 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=' ', radius=radius).split() 

k = 'x', 'y', 'radius' 

return fmt % (sep.join('%s:%s' % t for t in zip(k, 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=''): 

'''Parse a string representing a WM coordinate, consisting 

of easting, northing and an optional radius. 

 

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

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

@keyword Wm: Optional (sub-)class to return the WM coordinate 

(L{Wm}) or C{None}. 

@keyword 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] 

''' 

w = strWM.strip().replace(',', ' ').split() 

try: 

if len(w) == 2: 

w += [radius] 

elif len(w) != 3: 

raise ValueError # caught below 

x, y, r = map(float, w) 

 

except (TypeError, ValueError): 

raise WebMercatorError('%s invalid: %r' % ('strWM', strWM)) 

 

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

Wm(x, y, radius=r) 

return _xnamed(r, name) 

 

 

def toWm(latlon, lon=None, radius=R_MA, Wm=Wm, name=''): 

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

 

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

spherical) geodetic C{LatLon} point. 

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

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

@keyword Wm: Optional (sub-)class to return the WM coordinate 

(L{Wm}) or C{None}. 

@keyword 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 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 

''' 

r, e = radius, None 

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 = clipDMS(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, n = r * radians(lon), r * y 

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

Wm(e, n, radius=r) 

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.