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# -*- coding: utf-8 -*- 

 

u'''I{Karney}'s Universal Polar Stereographic (UPS) projection. 

 

Classes L{Ups} and L{UPSError} and functions L{parseUPS5}, L{toUps8} and L{upsZoneBand5}. 

 

A pure Python implementation, partially transcoded from C++ class U{PolarStereographic 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1PolarStereographic.html>} 

by I{Charles Karney}. 

 

The U{UPS<https://WikiPedia.org/wiki/Universal_polar_stereographic_coordinate_system>} 

system is used in conjuction with U{UTM 

<https://WikiPedia.org/wiki/Universal_Transverse_Mercator_coordinate_system>} 

for locations on the polar regions of the earth. UPS covers areas south of 79.5°S 

and north of 83.5°N (slightly overlapping the UTM range from 80°S to 84°N by 30' at 

each end). 

''' 

 

# from pygeodesy.basics import neg as _neg # from .dms 

from pygeodesy.datums import _ellipsoidal_datum, _WGS84 

from pygeodesy.dms import degDMS, _neg, parseDMS2 

from pygeodesy.errors import RangeError, _ValueError 

from pygeodesy.fmath import hypot, hypot1, sqrt0 

from pygeodesy.interns import EPS, EPS0, NN, _COMMASPACE_, _EPSmin as _Tol90, \ 

_N_, _inside_, _pole_, _range_, _S_, _SPACE_, \ 

_to_, _UTM_, _0_0, _0_5, _1_0, _2_0, _90_0 

from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS 

from pygeodesy.named import nameof, _xnamed 

from pygeodesy.namedTuples import EasNor2Tuple, UtmUps5Tuple, \ 

UtmUps8Tuple, UtmUpsLatLon5Tuple 

from pygeodesy.props import deprecated_method, property_doc_, \ 

Property_RO, _update_all 

# from pygeodesy.streprs import Fmt # from .utmupsBase 

from pygeodesy.units import Meter, Lat, Scalar, Scalar_ 

from pygeodesy.utily import degrees90, degrees180, sincos2d 

from pygeodesy.utmupsBase import Fmt, _LLEB, _hemi, _parseUTMUPS5, _to4lldn, \ 

_to3zBhp, _to3zll, _UPS_BANDS as _Bands, \ 

_UPS_LAT_MAX, _UPS_LAT_MIN, _UPS_ZONE, \ 

_UPS_ZONE_STR, UtmUpsBase 

 

from math import atan, atan2, radians, tan 

 

__all__ = _ALL_LAZY.ups 

__version__ = '22.04.22' 

 

_Falsing = Meter(2000e3) # false easting and northing (C{meter}) 

_K0_UPS = Scalar(0.994) # central UPS scale factor 

_K1_UPS = Scalar(_1_0) # rescale point scale factor 

 

 

def _scale(E, rho, tau): 

# compute the point scale factor, ala Karney 

t = hypot1(tau) 

return Scalar((rho / E.a) * t * sqrt0(E.e12 + E.e2 / t**2)) 

 

 

def _toBand(a_lat, b_lon): # see utm._toBand 

'''(INTERNAL) Get the I{polar} Band letter from 

the signs of (phi, lam) or (lat, lon). 

''' 

return _Bands[(0 if a_lat < 0 else 2) + (0 if b_lon < 0 else 1)] 

 

 

class UPSError(_ValueError): 

'''Universal Polar Stereographic (UPS) parse or other L{Ups} issue. 

''' 

pass 

 

 

class Ups(UtmUpsBase): 

'''Universal Polar Stereographic (UPS) coordinate. 

''' 

# _band = NN # polar band ('A', 'B', 'Y' or 'Z') 

_Bands = _Bands # polar Band letters (tuple) 

_Error = UPSError # Error class 

_pole = NN # UPS projection top/center ('N' or 'S') 

# _scale = None # point scale factor (C{scalar}) 

_scale0 = _K0_UPS # central scale factor (C{scalar}) 

 

def __init__(self, zone, pole, easting, northing, band=NN, # PYCHOK expected 

datum=_WGS84, falsed=True, 

convergence=None, scale=None, name=NN): 

'''New L{Ups} UPS coordinate. 

 

@arg zone: UPS zone (C{int}, zero) or zone with/-out I{polar} Band 

letter (C{str}, '00', '00A', '00B', '00Y' or '00Z'). 

@arg pole: Top/center of (stereographic) projection (C{str}, 

C{'N[orth]'} or C{'S[outh]'}). 

@arg easting: Easting, see B{C{falsed}} (C{meter}). 

@arg northing: Northing, see B{C{falsed}} (C{meter}). 

@kwarg band: Optional, I{polar} Band (C{str}, 'A'|'B'|'Y'|'Z'). 

@kwarg datum: Optional, this coordinate's datum (L{Datum}, 

L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). 

@kwarg falsed: If C{True}, both B{C{easting}} and B{C{northing}} 

are falsed (C{bool}). 

@kwarg convergence: Optional, meridian convergence gamma 

to save (C{degrees}). 

@kwarg scale: Optional, computed scale factor k to save 

(C{scalar}). 

@kwarg name: Optional name (C{str}). 

 

@raise TypeError: Invalid B{C{datum}}. 

 

@raise UPSError: Invalid B{C{zone}}, B{C{pole}}, B{C{easting}}, 

B{C{northing}}, B{C{band}}, B{C{convergence}} 

or B{C{scale}}. 

''' 

if name: 

self.name = name 

 

try: 

z, B, p = _to3zBhp(zone, band, hemipole=pole) 

if z != _UPS_ZONE or (B and (B not in _Bands)): 

raise ValueError 

except (TypeError, ValueError) as x: 

raise UPSError(zone=zone, pole=pole, band=band, txt=str(x)) 

self._pole = p 

UtmUpsBase.__init__(self, easting, northing, band=B, datum=datum, falsed=falsed, 

convergence=convergence, scale=scale) 

 

def __eq__(self, other): 

return isinstance(other, Ups) and other.zone == self.zone \ 

and other.pole == self.pole \ 

and other.easting == self.easting \ 

and other.northing == self.northing \ 

and other.band == self.band \ 

and other.datum == self.datum 

 

@property_doc_(''' the I{polar} band.''') 

def band(self): 

'''Get the I{polar} band (C{'A'|'B'|'Y'|'Z'}). 

''' 

if not self._band: 

self._toLLEB() 

return self._band 

 

@band.setter # PYCHOK setter! 

def band(self, band): 

'''Set or reset the I{polar} band. 

 

@arg band: The I{polar} band letter (C{'A'|'B'|'Y'|'Z'}) 

or C{None} or C{""} to reset. 

 

@raise TypeError: Invalid B{C{band}}. 

 

@raise ValueError: Invalid B{C{band}}. 

''' 

self._band1(band) 

 

@Property_RO 

def falsed2(self): 

'''Get the easting and northing falsing (L{EasNor2Tuple}C{(easting, northing)}). 

''' 

f = _Falsing if self.falsed else 0 

return EasNor2Tuple(f, f) 

 

@Property_RO 

def _mgrs(self): 

'''(INTERNAL) Cache for L{toMgrs}. 

''' 

return self.toUtm(None).toMgrs() 

 

def parse(self, strUPS, name=NN): 

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

 

@arg strUPS: The UPS coordinate (C{str}), 

see function L{parseUPS5}. 

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

overriding this name. 

 

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

 

@raise UTMError: Invalid B{C{strUPS}}. 

 

@see: Functions L{parseUTM5} and L{pygeodesy.parseUTMUPS5}. 

''' 

return parseUPS5(strUPS, datum=self.datum, Ups=self.classof, 

name=name or self.name) 

 

@deprecated_method 

def parseUPS(self, strUPS): # PYCHOK no cover 

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

return self.parse(strUPS) 

 

@Property_RO 

def pole(self): 

'''Get the top/center of (stereographic) projection (C{'N'|'S'} or C{""}). 

''' 

return self._pole 

 

def rescale0(self, lat, scale0=_K0_UPS): 

'''Set the central scale factor for this UPS projection. 

 

@arg lat: Northern latitude (C{degrees}). 

@arg scale0: UPS k0 scale at B{C{lat}} latitude (C{scalar}). 

 

@raise RangeError: If B{C{lat}} outside the valid range and 

L{pygeodesy.rangerrors} set to C{True}. 

 

@raise UPSError: Invalid B{C{scale}}. 

''' 

s0 = Scalar_(scale0=scale0, Error=UPSError, low=EPS) # <= 1.003 or 1.0016? 

u = toUps8(abs(Lat(lat)), _0_0, datum=self.datum, Ups=_Ups_K1) 

k = s0 / u.scale 

if self.scale0 != k: 

_update_all(self) 

self._band = NN # force re-compute 

self._latlon = self._utm = None 

self._scale0 = Scalar(scale0=k) 

 

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

'''Convert this UPS coordinate to an (ellipsoidal) geodetic point. 

 

@kwarg LatLon: Optional, ellipsoidal class to return the 

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

@kwarg unfalse: Unfalse B{C{easting}} and B{C{northing}} 

if falsed (C{bool}). 

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

arguments, ignored if C{B{LatLon} is None}. 

 

@return: This UPS coordinate (B{C{LatLon}}) or if B{C{LatLon}} 

is C{None}, a L{LatLonDatum5Tuple}C{(lat, lon, datum, 

convergence, scale)}. 

 

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

 

@raise UPSError: Invalid meridional radius or H-value. 

''' 

if self._latlon and self._latlon._toLLEB_args == (unfalse,): 

return self._latlon5(LatLon) 

else: 

self._toLLEB(unfalse=unfalse) 

return self._latlon5(LatLon, **LatLon_kwds) 

 

def _toLLEB(self, unfalse=True): # PYCHOK signature 

'''(INTERNAL) Compute (ellipsoidal) lat- and longitude. 

''' 

E = self.datum.ellipsoid # XXX vs LatLon.datum.ellipsoid 

 

x, y = self.eastingnorthing2(falsed=not unfalse) 

 

r = hypot(x, y) 

t = (r / (_2_0 * self.scale0 * E.a / E.es_c)) if r > 0 else EPS0 

t = E.es_tauf((1 / t - t) * _0_5) 

a = atan(t) 

if self._pole == _N_: 

b, c = atan2(x, -y), 1 

else: 

a, b, c = _neg(a), atan2(x, y), -1 

ll = _LLEB(degrees90(a), degrees180(b), datum=self._datum, name=self.name) 

 

ll._convergence = b * c # gamma 

ll._scale = _scale(E, r, t) if r > 0 else self.scale0 

self._latlon5args(ll, _toBand, unfalse) 

 

def toMgrs(self): 

'''Convert this UPS coordinate to an MGRS grid reference. 

 

@return: The MGRS grid reference (L{Mgrs}). 

 

@see: Methods L{Ups.toUtm} and L{Utm.toMgrs}. 

 

@note: If not specified, the I{polar} C{band} is computed 

from the (geodetic) latitude and the C{datum}. 

''' 

return self._mgrs 

 

def toRepr(self, prec=0, fmt=Fmt.SQUARE, sep=_COMMASPACE_, B=False, cs=False, **unused): # PYCHOK expected 

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

 

Note that UPS coordinates are rounded, not truncated (unlike 

MGRS grid references). 

 

@kwarg prec: Number of (decimal) digits, unstripped (C{int}). 

@kwarg fmt: Enclosing backets format (C{str}). 

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

@kwarg B: Optionally, include polar band letter (C{bool}). 

@kwarg cs: Optionally, include gamma meridian convergence and 

point scale factor (C{bool} or non-zero C{int} to 

specify the precison like B{C{prec}}). 

 

@return: This UPS as a string with C{00[Band] pole, easting, 

northing, [convergence, scale]} as C{"[Z:00[Band], 

P:N|S, E:meter, N:meter]"} plus C{", C:DMS, S:float"} 

if B{C{cs}} is C{True}, where C{[Band]} is present and 

C{'A'|'B'|'Y'|'Z'} only if B{C{B}} is C{True} and 

convergence C{DMS} is in I{either} degrees, minutes 

I{or} seconds (C{str}). 

 

@note: Pseudo zone zero (C{"00"}) for UPS follows I{Karney}'s U{zone UPS 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1UTMUPS.html>}. 

''' 

return self._toRepr(fmt, B, cs, prec, sep) 

 

def toStr(self, prec=0, sep=_SPACE_, B=False, cs=False): # PYCHOK expected 

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

 

Note that UPS coordinates are rounded, not truncated (unlike 

MGRS grid references). 

 

@kwarg prec: Number of (decimal) digits, 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 B: Optionally, include and polar band letter (C{bool}). 

@kwarg cs: Optionally, include gamma meridian convergence and 

point scale factor (C{bool} or non-zero C{int} to 

specify the precison like B{C{prec}}). 

 

@return: This UPS as a string with C{00[Band] pole, easting, 

northing, [convergence, scale]} as C{"00[B] N|S 

meter meter"} plus C{" DMS float"} if B{C{cs}} is C{True}, 

where C{[Band]} is present and C{'A'|'B'|'Y'|'Z'} only 

if B{C{B}} is C{True} and convergence C{DMS} is in 

I{either} degrees, minutes I{or} seconds (C{str}). 

 

@note: Zone zero (C{"00"}) for UPS follows I{Karney}'s U{zone UPS 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1UTMUPS.html>}. 

''' 

return self._toStr(self.pole, B, cs, prec, sep) # PYCHOK pole 

 

def toUps(self, pole=NN, **unused): 

'''Duplicate this UPS coordinate. 

 

@kwarg pole: Optional top/center of the UPS projection, 

(C{str}, 'N[orth]'|'S[outh]'). 

 

@return: A copy of this UPS coordinate (L{Ups}). 

 

@raise UPSError: Invalid B{C{pole}} or attempt to transfer 

the projection top/center. 

''' 

if self.pole == pole or not pole: 

return self.copy() 

t = _SPACE_(_pole_, repr(self.pole), _to_, repr(pole)) 

raise UPSError('no transfer', txt=t) 

 

def toUtm(self, zone, falsed=True, **unused): 

'''Convert this UPS coordinate to a UTM coordinate. 

 

@arg zone: The UTM zone (C{int}). 

@kwarg falsed: False both easting and northing (C{bool}). 

 

@return: The UTM coordinate (L{Utm}). 

''' 

u = self._utm 

if u is None or u.zone != zone or falsed != u.falsed: 

ll = self.toLatLon(LatLon=None, unfalse=True) 

self._utm = _MODS.utm.toUtm8(ll, Utm=_MODS.utm.Utm, falsed=falsed, 

name=self.name, zone=zone) 

return self._utm 

 

@Property_RO 

def zone(self): 

'''Get the polar pseudo zone (C{0}), like I{Karney}'s U{zone UPS<https:// 

GeographicLib.SourceForge.io/html/classGeographicLib_1_1UTMUPS.html>}. 

''' 

return _UPS_ZONE 

 

 

class _Ups_K1(Ups): 

'''(INTERNAL) For method L{Ups.rescale0}. 

''' 

_scale0 = _K1_UPS 

 

 

def parseUPS5(strUPS, datum=_WGS84, Ups=Ups, falsed=True, name=NN): 

'''Parse a string representing a UPS coordinate, consisting of 

C{"[zone][band] pole easting northing"} where B{C{zone}} is 

pseudo zone C{"00"|"0"|""} and C{band} is C{'A'|'B'|'Y'|'Z'|''}. 

 

@arg strUPS: A UPS coordinate (C{str}). 

@kwarg datum: Optional datum to use (L{Datum}). 

@kwarg Ups: Optional class to return the UPS coordinate (L{Ups}) 

or C{None}. 

@kwarg falsed: Both B{C{easting}} and B{C{northing}} are falsed (C{bool}). 

@kwarg name: Optional B{C{Ups}} name (C{str}). 

 

@return: The UPS coordinate (B{C{Ups}}) or a 

L{UtmUps5Tuple}C{(zone, hemipole, easting, northing, 

band)} if B{C{Ups}} is C{None}. The C{hemipole} is 

the C{'N'|'S'} pole, the UPS projection top/center. 

 

@raise UPSError: Invalid B{C{strUPS}}. 

''' 

z, p, e, n, B = _parseUTMUPS5(strUPS, _UPS_ZONE_STR, Error=UPSError) 

if z != _UPS_ZONE or (B and B not in _Bands): 

raise UPSError(strUPS=strUPS, zone=z, band=B) 

 

if Ups is None: 

r = UtmUps5Tuple(z, p, e, n, B, Error=UPSError, name=name) 

else: 

r = Ups(z, p, e, n, band=B, falsed=falsed, datum=datum) 

r = _xnamed(r, name) 

return r 

 

 

def toUps8(latlon, lon=None, datum=None, Ups=Ups, pole=NN, 

falsed=True, strict=True, name=NN): 

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

 

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

geodetic C{LatLon} point. 

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

B{C{latlon}} is a C{LatLon}. 

@kwarg datum: Optional datum for this UPS coordinate, 

overriding B{C{latlon}}'s datum (C{Datum}, 

L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). 

@kwarg Ups: Optional class to return the UPS coordinate 

(L{Ups}) or C{None}. 

@kwarg pole: Optional top/center of (stereographic) projection 

(C{str}, C{'N[orth]'} or C{'S[outh]'}). 

@kwarg falsed: False both easting and northing (C{bool}). 

@kwarg strict: Restrict B{C{lat}} to UPS ranges (C{bool}). 

@kwarg name: Optional B{C{Ups}} name (C{str}). 

 

@return: The UPS coordinate (B{C{Ups}}) or a 

L{UtmUps8Tuple}C{(zone, hemipole, easting, northing, 

band, datum, convergence, scale)} if B{C{Ups}} is 

C{None}. The C{hemipole} is the C{'N'|'S'} pole, 

the UPS projection top/center. 

 

@raise RangeError: If B{C{strict}} and B{C{lat}} outside the valid 

UPS bands or if B{C{lat}} or B{C{lon}} outside 

the valid range and L{pygeodesy.rangerrors} set 

to C{True}. 

 

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

B{C{datum}} invalid. 

 

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

is invalid. 

 

@see: I{Karney}'s C++ class U{UPS 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1UPS.html>}. 

''' 

lat, lon, d, name = _to4lldn(latlon, lon, datum, name) 

z, B, p, lat, lon = upsZoneBand5(lat, lon, strict=strict) # PYCHOK UtmUpsLatLon5Tuple 

 

d = _ellipsoidal_datum(d, name=name) 

E = d.ellipsoid 

 

p = str(pole or p)[:1].upper() 

N = p == _N_ # is north 

 

a = lat if N else -lat 

A = abs(a - _90_0) < _Tol90 # at pole 

 

t = tan(radians(a)) 

T = E.es_taupf(t) 

r = hypot1(T) + abs(T) 

if T >= _0_0: 

r = _0_0 if A else _1_0 / r 

 

k0 = getattr(Ups, '_scale0', _K0_UPS) # Ups is class or None 

r *= 2 * k0 * E.a / E.es_c 

 

k = k0 if A else _scale(E, r, t) 

c = lon # [-180, 180) from .upsZoneBand5 

x, y = sincos2d(c) 

x *= r 

y *= r 

if N: 

y = _neg(y) 

else: 

c = _neg(c) 

 

if falsed: 

x += _Falsing 

y += _Falsing 

 

n = name or nameof(latlon) 

if Ups is None: 

r = UtmUps8Tuple(z, p, x, y, B, d, c, k, Error=UPSError, name=n) 

else: 

if z != _UPS_ZONE and not strict: 

z = _UPS_ZONE # ignore UTM zone 

r = _xnamed(Ups(z, p, x, y, band=B, datum=d, falsed=falsed, 

convergence=c, scale=k), n) 

if isinstance(latlon, _LLEB) and d is latlon.datum: # see utm._toXtm8 

r._latlon5args(latlon, _toBand, falsed) # XXX weakref(latlon)? 

latlon._convergence = c 

latlon._scale = k 

else: 

r._hemisphere = _hemi(lat) 

if not r._band: 

r._band = _toBand(lat, lon) 

return r 

 

 

def upsZoneBand5(lat, lon, strict=True, name=NN): 

'''Return the UTM/UPS zone number, I{polar} Band letter, pole and 

clipped lat- and longitude for a given location. 

 

@arg lat: Latitude in degrees (C{scalar} or C{str}). 

@arg lon: Longitude in degrees (C{scalar} or C{str}). 

@kwarg strict: Restrict B{C{lat}} to UPS ranges (C{bool}). 

@kwarg name: Optional name (C{str}). 

 

@return: A L{UtmUpsLatLon5Tuple}C{(zone, band, hemipole, 

lat, lon)} where C{hemipole} is the C{'N'|'S'} pole, 

the UPS projection top/center. 

 

@raise RangeError: If B{C{strict}} and B{C{lat}} in the UTM 

and not the UPS range or if B{C{lat}} or 

B{C{lon}} outside the valid range and 

L{pygeodesy.rangerrors} set to C{True}. 

 

@raise ValueError: Invalid B{C{lat}} or B{C{lon}}. 

''' 

z, lat, lon = _to3zll(*parseDMS2(lat, lon)) 

if lat < _UPS_LAT_MIN: # includes 30' overlap 

z, B, p = _UPS_ZONE, _toBand(lat, lon), _S_ 

 

elif lat > _UPS_LAT_MAX: # includes 30' overlap 

z, B, p = _UPS_ZONE, _toBand(lat, lon), _N_ 

 

elif strict: 

r = _range_(_UPS_LAT_MIN, _UPS_LAT_MAX) 

t = _SPACE_(_inside_, _UTM_, _range_, r) 

raise RangeError(lat=degDMS(lat), txt=t) 

 

else: 

B, p = NN, _hemi(lat) 

return UtmUpsLatLon5Tuple(z, B, p, lat, lon, Error=UPSError, name=name) 

 

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