# Coverage for pygeodesy/webmercator.py : 99%

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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>}. ''' from pygeodesy.basics import isscalar, issubclassof 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, _xkwds from pygeodesy.interns import NN, PI_2, _COMMA_, _COMMASPACE_, \ _easting_, _ellipsoidal_, _northing_, \ _radius_, _SPACE_ from pygeodesy.interns import _x_, _y_ # PYCHOK used! from pygeodesy.lazily import _ALL_LAZY from pygeodesy.named import _NamedBase, _NamedTuple, nameof, _xnamed from pygeodesy.namedTuples import LatLon2Tuple, PhiLam2Tuple from pygeodesy.props import deprecated_method, Property_RO from pygeodesy.streprs import Fmt, strs, _xzipairs 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__ = '21.07.31' # _FalseEasting = 0 # false Easting (C{meter}) # _FalseNorthing = 0 # false Northing (C{meter}) _LatLimit = Lat(limit=85.051129) # 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. ''' _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)}). ''' return self.latlon2() 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 return LatLon2Tuple(Lat(degrees90( y)), Lon(degrees180(x)), name=self.name) 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) @deprecated_method def parseWM(self, strWM, name=NN): # PYCHOK no cover '''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)}). ''' r = self.latlon return PhiLam2Tuple(Phi_(r.lat), Lam_(r.lon), name=r.name) @Property_RO def radius(self): '''Get the earth radius (C{meter}). ''' return self._radius @deprecated_method 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) return LatLon(r.lat, r.lon, **_xkwds(kwds, name=r.name)) def toRepr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_, 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) 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.toRepr() # [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) return EasNorRadius3Tuple(x, y, r, name=name) if Wm is None else \ _xnamed(Wm(x, y, radius=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 C{B{Wm} is 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, name=name) if Wm is None else \ _xnamed(Wm(e, n, **_xkwds(Wm_kwds, radius=r)), name) return r # **) MIT License # # Copyright (C) 2016-2021 -- 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.