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webmercator.py
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webmercator.py
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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 PI_2, isscalar, issubclassof, property_RO, \
_xinstanceof, _xkwds, _xzipairs
from pygeodesy.datum import Datum, R_MA
from pygeodesy.dms import clipDegrees, parseDMS2
from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB
from pygeodesy.errors import _IsnotError, _parseX, _TypeError, _ValueError
from pygeodesy.interns import _COMMA_, _COMMA_SPACE_, _easting_, \
_ellipsoidal_, NN, _northing_, _radius_, \
_SPACE_, _SQUARE_, _x_, _y_
from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY
from pygeodesy.named import LatLon2Tuple, _NamedBase, _NamedTuple, \
nameof, PhiLam2Tuple, _xnamed
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__ = '20.07.08'
# _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 EasNorRadius3Tuple(_NamedTuple):
'''3-Tuple C{(easting, northing, radius)}, all in C{meter}.
'''
_Names_ = (_easting_, _northing_, _radius_)
def __new__(cls, e, n, r):
return _NamedTuple.__new__(cls, Easting( e, Error=WebMercatorError),
Northing(n, Error=WebMercatorError),
Radius( r, Error=WebMercatorError))
class WebMercatorError(_ValueError):
'''Web Mercator (WM) parser or L{Wm} issue.
'''
pass
class Wm(_NamedBase):
'''Web Mercator (WM) coordinate.
'''
_latlon = None #: (INTERNAL) cached (L{LatLon2Tuple}).
_philam = None #: (INTERNAL) Cached (L{PhiLam2Tuple}).
_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=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, name=_x_, Error=WebMercatorError)
self._y = Northing(y, name=_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 (C{Datum}).
@return: A L{LatLon2Tuple}C{(lat, lon)}.
@raise TypeError: 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:
_xinstanceof(Datum, datum=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)) # == 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 parseWM(self, strWM, name=NN):
'''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 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 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 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)
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.