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# -*- coding: utf-8 -*- 

 

u'''Cassini-Soldner projection classes L{CassiniSoldner}, L{Css} and 

L{CSSError} requiring I{Charles Karney's} U{geographiclib 

<https://PyPI.org/project/geographiclib/>} package to be installed. 

 

@newfield example: Example, Examples 

''' 

 

from pygeodesy.datum import Datums 

from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB 

from pygeodesy.fmath import fStr, _IsNotError 

from pygeodesy.lazily import _ALL_LAZY 

from pygeodesy.named import EasNor2Tuple, EasNor3Tuple, EasNorAziRk4Tuple, \ 

LatLon2Tuple, LatLon4Tuple, LatLonAziRk4Tuple, \ 

_NamedBase, nameof, _xattrs, _xnamed 

from pygeodesy.utily import false2f, issubclassof, property_RO, _TypeError 

 

# all public contants, classes and functions 

__all__ = _ALL_LAZY.css 

__version__ = '19.10.12' 

 

_CassiniSoldner0 = None # default projection 

 

 

def _CassiniSoldner(cs0): 

'''(INTERNAL) Get/set default projection. 

''' 

if cs0 is None: 

global _CassiniSoldner0 

if _CassiniSoldner0 is None: 

_CassiniSoldner0 = CassiniSoldner(0, 0, name='Default') 

cs0 = _CassiniSoldner0 

else: 

_TypeError(CassiniSoldner, cs0=cs0) 

return cs0 

 

 

class CassiniSoldner(_NamedBase): 

'''A Python version of Karney's C++ class U{CassiniSoldner 

<https://GeographicLib.SourceForge.io/1.49/classGeographicLib_1_1CassiniSoldner.html>}. 

''' 

_cb0 = 0 

_datum = Datums.WGS84 #: (INTERNAL) L{Datum}. 

_latlon0 = () 

_meridian = None 

_sb0 = 0 

 

def __init__(self, lat0, lon0, datum=Datums.WGS84, name=''): 

'''New L{CassiniSoldner} projection. 

 

@param lat0: Latitude of center point (C{degrees90}). 

@param lon0: Longitude of center point (C{degrees180}). 

@keyword datum: Optional, the geodesic datum (L{Datum}). 

@keyword name: Optional name (C{str}). 

 

@raise ImportError: Package U{GeographicLib<https://PyPI.org/ 

project/geographiclib>} missing. 

 

@example: 

 

>>> p = CassiniSoldner(48 + 50/60.0, 2 + 20/60.0) # Paris 

>>> p.forward(50.9, 1.8) # Calais 

(-37518.854545, 230003.561828) 

 

>>> p.reverse4(-38e3, 230e3) 

(50.899937, 1.793161, 89.580797, 0.999982) 

''' 

if name: 

self.name = name 

 

if datum and datum != self._datum: 

self._datum = datum 

 

self.reset(lat0, lon0) 

 

def _xcopy(self, *attrs): 

'''(INTERNAL) Make copy with add'l, subclass attributes. 

''' 

return _xattrs(self.classof(self.lat0, self.lon0, 

datum=self.datum), 

self, *attrs) 

 

def copy(self): 

'''Copy this Cassini-Soldner projection. 

 

@return: The copy (L{CassiniSoldner} or subclass thereof). 

''' 

return self._xcopy() 

 

@property_RO 

def datum(self): 

'''Get the datum (L{Datum}). 

''' 

return self._datum 

 

@property_RO 

def flattening(self): 

'''Get the geodesic's flattening (C{float}). 

''' 

return self.geodesic.f 

 

def forward(self, lat, lon): 

'''Convert an (ellipsoidal) geodetic location Cassini-Soldner 

easting and northing. 

 

@param lat: Latitude of the location (C{degrees90}). 

@param lon: Longitude of the location (C{degrees180}). 

 

@return: An L{EasNor2Tuple}C{(easting, northing)}. 

''' 

r = EasNor2Tuple(*self.forward4(lat, lon)[:2]) 

return self._xnamed(r) 

 

def forward4(self, lat, lon): 

'''Convert an (ellipsoidal) geodetic location Cassini-Soldner 

easting and northing. 

 

@param lat: Latitude of the location (C{degrees90}). 

@param lon: Longitude of the location (C{degrees180}). 

 

@return: An L{EasNorAziRk4Tuple}C{(easting, 

northing, azimuth, reciprocal)}. 

''' 

g, M = self.datum.ellipsoid._geodesic2 

 

d = M.AngDiff(self.lon0, lon)[0] # _2sum 

r = g.Inverse(lat, -abs(d), lat, abs(d)) 

z1, a = r['azi1'], (r['a12'] * 0.5) 

z2, s = r['azi2'], (r['s12'] * 0.5) 

if s == 0: 

z = M.AngDiff(z1, z2)[0] * 0.5 # _2sum 

c = -90 if abs(d) > 90 else 90 

z1, z2 = c - z, c + z 

if d < 0: 

a, s, z2 = -a, -s, z1 

 

# z: azimuth of easting direction 

e, z = s, M.AngNormalize(z2) 

p = g.Line(lat, d, z, g.DISTANCE | g.GEODESICSCALE) 

# rk: reciprocal of azimuthal northing scale 

rk = p.ArcPosition(-a, g.GEODESICSCALE)['M21'] 

# rk = p._GenPosition(True, -a, g.DISTANCE)[7] 

 

# s, c = M.sincosd(p.EquatorialAzimuth()) 

s, c = M.sincosd(M.atan2d(p._salp0, p._calp0)) 

sb1 = -c if lat < 0 else c 

cb1 = -abs(s) if abs(d) > 90 else abs(s) # copysign(s, 90 - abs(d)) 

d = M.atan2d(sb1 * self._cb0 - cb1 * self._sb0, 

cb1 * self._cb0 + sb1 * self._sb0) 

n = self._meridian.ArcPosition(d, g.DISTANCE)['s12'] 

# n = self._meridian._GenPosition(True, d, g.DISTANCE)[4] 

r = EasNorAziRk4Tuple(e, n, z, rk) 

return self._xnamed(r) 

 

@property_RO 

def geodesic(self): 

'''Get this projection's U{Geodesic 

<https://GeographicLib.SourceForge.io/html/python/code.html>}, 

provided package U{geographiclib 

<https://PyPI.org/project/geographiclib>} is installed. 

''' 

return self._datum.ellipsoid.geodesic 

 

@property_RO 

def lat0(self): 

'''Get the center latitude (C{degrees90}). 

''' 

return self._latlon0.lat 

 

@property_RO 

def latlon0(self): 

'''Get the center lat- and longitude (L{LatLon2Tuple}). 

''' 

return self._latlon0 

 

@property_RO 

def lon0(self): 

'''Get the center longitude (C{degrees180}). 

''' 

return self._latlon0.lon 

 

@property_RO 

def majoradius(self): 

'''Get the geodesic's major (equatorial) radius (C{float}). 

''' 

return self.geodetic.a 

 

def reset(self, lat0, lon0): 

'''Set the center point of this projection. 

 

@param lat0: Latitude of center point (C{degrees90}). 

@param lon0: Longitude of center point (C{degrees180}). 

''' 

g, M = self.datum.ellipsoid._geodesic2 

 

self._meridian = m = g.Line(lat0, lon0, 0.0, g.STANDARD | g.DISTANCE_IN) 

self._latlon0 = LatLon2Tuple(m.lat1, m.lon1) 

s, c = M.sincosd(m.lat1) # == self.lat0 == self..LatitudeOrigin() 

self._sb0, self._cb0 = M.norm(s * (1.0 - g.f), c) 

 

def reverse(self, easting, northing, LatLon=None): 

'''Convert a Cassini-Soldner location to (ellipsoidal) geodetic 

lat- and longitude. 

 

@param easting: Easting of the location (C{meter}). 

@param northing: Northing of the location (C{meter}). 

@keyword LatLon: Optional, ellipsoidal (sub-)class to return 

the location as (C{LatLon}) or C{None}. 

 

@return: Geodetic location B{C{LatLon}} or a 

L{LatLon2Tuple}C{(lat, lon)} if 

B{C{LatLon}} is C{None}. 

 

@raise TypeError: If B{C{LatLon}} is not ellipsoidal. 

''' 

a, b = self.reverse4(easting, northing)[:2] 

if LatLon is None: 

r = LatLon2Tuple(a, b) 

elif issubclassof(LatLon, _LLEB): 

r = LatLon(a, b, datum=self.datum) 

else: 

raise _IsNotError(_LLEB.__name__, LatLon=LatLon) 

return self._xnamed(r) 

 

toLatLon = reverse 

 

def reverse4(self, easting, northing): 

'''Convert a Cassini-Soldner location to (ellipsoidal) geodetic lat- 

and longitude. 

 

@param easting: Easting of the location (C{meter}). 

@param northing: Northing of the location (C{meter}). 

 

@return: A L{LatLonAziRk4Tuple}C{(lat, lon, azimuth, reciprocal)}. 

''' 

g = self.geodesic 

 

r = self._meridian.Position(northing) 

a, b, z = r['lat2'], r['lon2'], r['azi2'] 

r = g.Direct(a, b, z + 90, easting, g.STANDARD | g.GEODESICSCALE) 

# include azimuth of easting direction and reciprocal of 

# azimuthal northing scale (see C++ member Direct() 5/6 

# <https://GeographicLib.SourceForge.io/1.49/classGeographicLib_1_1Geodesic.html>) 

r = LatLonAziRk4Tuple(r['lat2'], r['lon2'], r['azi2'], r['M12']) 

return self._xnamed(r) 

 

def toStr(self, prec=6, sep=' '): # PYCHOK expected 

'''Return a string representation of this projection. 

 

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

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

 

@return: This projection as C{"lat0 lon0"} (C{str}). 

''' 

return fStr(self.latlon0, prec=prec, sep=sep) 

 

def toStr2(self, prec=6): # PYCHOK expected 

'''Return a string representation of this projection. 

 

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

 

@return: This projection as C{"<classname>(lat0, lon0, ...)"} 

(C{str}). 

''' 

t = self.toStr(prec=prec, sep=', ') 

n = self.name or '' 

if n: 

n = ', name=%r' % (n,) 

return '%s(%s%s)' % (self.classname, t, n) 

 

 

class CSSError(ValueError): 

'''Cassini-Soldner (CSS) conversion or other L{Css} issue. 

''' 

pass 

 

 

class Css(_NamedBase): 

'''Cassini-Soldner East-/Northing location. 

''' 

_azi = None #: (INTERNAL) azimuth of easting direction (C{degrees}) 

_cs0 = None #: (INTERNAL) projection (L{CassiniSoldner}) 

_easting = 0 #: (INTERNAL) Easting (C{float}) 

_height = 0 #: (INTERNAL) Height (C{meter}) 

_latlon = None #: (INTERNAL) Geodetic (lat, lon) 

_northing = 0 #: (INTERNAL) Northing (C{float}) 

_rk = None #: (INTERNAL) reciprocal of azimuthal northing scale (C{float}) 

 

def __init__(self, e, n, h=0, cs0=_CassiniSoldner0, name=''): 

'''New L{Css} Cassini-Soldner position. 

 

@param e: Easting (C{meter}). 

@param n: Northing (C{meter}). 

@keyword h: Optional height (C{meter}). 

@keyword cs0: Optional, the Cassini-Soldner projection 

(L{CassiniSoldner}). 

@keyword name: Optional name (C{str}). 

 

@return: The Cassini-Soldner location (L{Css}). 

 

@raise CSSError: If B{C{e}} or B{C{n}} is invalid. 

 

@raise ImportError: Package U{GeographicLib<https://PyPI.org/ 

project/geographiclib>} missing. 

 

@raise TypeError: If B{C{cs0}} is not L{CassiniSoldner}. 

 

@example: 

 

>>> cs = Css(448251, 5411932.0001) 

''' 

self._cs0 = _CassiniSoldner(cs0) 

self._easting = false2f(e, 'easting', false=False, Error=CSSError) 

self._northing = false2f(n, 'northing', false=False, Error=CSSError) 

if h: 

self._height = float(h) 

if name: 

self.name = name 

 

def _reverse4(self): 

'''(INTERNAL) Convert to geodetic location. 

''' 

r = self.cs0.reverse4(self.easting, self.northing) 

self._latlon = LatLon2Tuple(r.lat, r.lon) 

self._azi, self._rk = r.azimuth, r.reciprocal 

return r # LatLonAziRk4Tuple 

 

def _xcopy(self, *attrs): 

'''(INTERNAL) Make copy with add'l, subclass attributes. 

''' 

return _xattrs(self.classof(self.easting, self.northing, 

h=self.height, cs0=self.cs0), 

self, *attrs) 

 

@property_RO 

def azi(self): 

'''Get the azimuth of easting direction (C{degrees}). 

''' 

if self._azi is None: 

self._reverse4() 

return self._azi 

 

azimuth = azi 

 

@property_RO 

def cs0(self): 

'''Get the projection (L{CassiniSoldner}). 

''' 

return self._cs0 

 

def copy(self): 

'''Copy this Css location. 

 

@return: The copy (L{Css} or subclass thereof). 

''' 

return self._xcopy() 

 

@property_RO 

def easting(self): 

'''Get the easting (C{meter}). 

''' 

return self._easting 

 

@property_RO 

def height(self): 

'''Get the height (C{meter}). 

''' 

return self._height 

 

@property_RO 

def latlon(self): 

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

''' 

if self._latlon is None: 

self._reverse4() 

return self._latlon 

 

@property_RO 

def northing(self): 

'''Get the northing (C{meter}). 

''' 

return self._northing 

 

@property_RO 

def rk(self): 

'''Get the reciprocal of azimuthal northing scale (C{degrees}). 

''' 

if self._rk is None: 

self._reverse4() 

return self._rk 

 

reciprocal = rk 

 

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

'''Convert this L{Css} to an (ellipsoidal) geodetic point. 

 

@keyword LatLon: Optional, ellipsoidal (sub-)class to return 

the geodetic point (C{LatLon}) or C{None}. 

@keyword height: Optional height for the point, overriding 

the default height (C{meter}). 

 

@return: The point (B{C{LatLon}}) or a 

L{LatLon4Tuple}C{(lat, lon, height, 

datum)} if B{C{LatLon}} is C{None}. 

 

@raise TypeError: If B{C{LatLon}} or B{C{datum}} is not ellipsoidal. 

''' 

if LatLon and not issubclassof(LatLon, _LLEB): 

raise _IsNotError(_LLEB.__name__, LatLon=LatLon) 

 

a, b = self.latlon 

d = self.cs0.datum 

h = self.height if height is None else height 

 

r = LatLon4Tuple(a, b, h, d) if LatLon is None else \ 

LatLon(a, b, height=h, datum=d) 

return self._xnamed(r) 

 

def toStr(self, prec=6, sep=' ', m='m'): # PYCHOK expected 

'''Return a string representation of this L{Css} position. 

 

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

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

@keyword m: Optional height units, default C{meter} (C{str}). 

 

@return: This position as C{"easting nothing"} C{str} in 

C{meter} plus C{" height"} and C{'m'} if heigth 

is non-zero (C{str}). 

''' 

t = [fStr(self.easting, prec=prec), 

fStr(self.northing, prec=prec)] 

if self.height: 

t += ['%+.2f%s' % (self.height, m)] 

return sep.join(t) 

 

def toStr2(self, prec=6, fmt='[%s]', sep=', ', m='m', C=False): # PYCHOK expected 

'''Return a string representation of this L{Css} position. 

 

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

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

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

@keyword m: Optional unit of the height, default meter (C{str}). 

@keyword C: Optionally, include name of projection (C{bool}). 

 

@return: This position as C{"[E:meter, N:meter, H:m, name:'', 

C:Conic.Datum]"} (C{str}). 

''' 

t = self.toStr(prec=prec, sep=' ', m=m).split() 

k = ('E', 'N', 'H')[:len(t)] 

if self.name: 

k += 'name', 

t += [repr(self.name)] 

if C: 

k += 'C', 

t += [repr(self.cs0)] 

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

 

 

def toCss(latlon, cs0=_CassiniSoldner0, height=None, Css=Css, name=''): 

'''Convert an (ellipsoidal) geodetic point to a Cassini-Soldner location. 

 

@param latlon: Ellipsoidal point (C{LatLon}). 

@keyword cs0: Optional, the Cassini-Soldner projection to use 

(L{CassiniSoldner}). 

@keyword height: Optional height for the point, overriding 

the default height (C{meter}). 

@keyword Css: Optional (sub-)class to return the location 

(L{Css}) or C{None}. 

@keyword name: Optional B{C{Css}} name (C{str}). 

 

@return: The Cassini-Soldner location (B{C{Css}}) or an 

L{EasNor3Tuple}C{(easting, northing, height)} 

if B{C{Css}} is C{None}. 

 

@raise CSSError: Mismatch of this and the B{C{latlon}} ellipsoidal. 

 

@raise ImportError: Package U{GeographicLib<https://PyPI.org/ 

project/geographiclib>} missing. 

 

@raise TypeError: If B{C{latlon}} is not ellipsoidal. 

''' 

if not isinstance(latlon, _LLEB): 

raise _IsNotError(_LLEB.__name__, latlon=latlon) 

 

cs = _CassiniSoldner(cs0) 

 

C, E = cs.datum.ellipsoid, latlon.datum.ellipsoid 

if C != E: 

raise CSSError('%s mistmatch: %r vs %r' % ('ellipsoidal', C, E)) 

 

c = cs.forward4(latlon.lat, latlon.lon) 

h = latlon.height if height is None else height 

 

if Css is None: 

r = EasNor3Tuple(c.easting, c.northing, h) 

else: 

r = Css(c.easting, c.northing, h=h, cs0=cs) 

r._latlon = LatLon2Tuple(latlon.lat, latlon.lon) 

r._azi, r._rk = c.azimuth, c.reciprocal 

return _xnamed(r, name or nameof(latlon)) 

 

# **) 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 

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