# Coverage for pygeodesy/ups.py : 97%

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Classes L{Ups} and L{UPSError} and functions L{parseUPS5}, L{toUps8} and L{upsZoneBand5}. A pure Python implementation, partially transcoded from I{Karney}'s C++ class U{PolarStereographic <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1PolarStereographic.html>}. 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. Env variable C{PYGEODESY_UPS_POLES} determines the UPS zones I{at} latitude 90°S and 90°N. By default, the encoding follows I{Karney}'s and U{Appendix B-3 of DMA TM8358.1<https://Web.Archive.org/web/ 20161226192038/http://earth-info.nga.mil/GandG/publications/tm8358.1/pdf/TM8358_1.pdf>}, using only zones C{'B'} respectively C{'Z'} and digraph C{'AN'}. If C{PYGEODESY_UPS_POLES} is set to anything other than C{"std"}, zones C{'A'} and C{'Y'} are used for negative, west longitudes I{at} latitude 90°S respectively 90°N (for backward compatibility). ''' # from pygeodesy.basics import neg as _neg # from .dms from pygeodesy.constants import EPS, EPS0, _EPSmin as _Tol90, \ isnear90, _0_0, _0_5, _1_0, _2_0 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 NN, _COMMASPACE_, _inside_, _N_, _pole_, \ _range_, _S_, _SPACE_, _std_, _to_, _UTM_ from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS, _getenv 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 Float, Float_, Meter, Lat 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__ = '22.09.20' _BZ_UPS = _getenv('PYGEODESY_UPS_POLES', _std_) == _std_ _Falsing = Meter(2000e3) # false easting and northing (C{meter}) _K0_UPS = Float(_K0_UPS= 0.994) # scale factor at central meridian _K1_UPS = Float(_K1_UPS=_1_0) # rescale point scale factor def _scale(E, rho, tau): # compute the point scale factor, ala Karney t = hypot1(tau) return Float(scale=(rho / E.a) * t * sqrt0(E.e21 + E.e2 / t**2)) def _toBand(lat, lon): # see utm._toBand '''(INTERNAL) Get the I{polar} Band letter for a (lat, lon). ''' return _Bands[(0 if lat < 0 else 2) + (0 if -180 < 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 (C{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=0, pole=_N_, easting=_Falsing, # PYCHOK expected northing=_Falsing, band=NN, datum=_WGS84, falsed=True, convergence=None, scale=None, name=NN): '''New L{Ups} UPS coordinate. @kwarg zone: UPS zone (C{int}, zero) or zone with/-out I{polar} Band letter (C{str}, '00', '00A', '00B', '00Y' or '00Z'). @kwarg pole: Top/center of (stereographic) projection (C{str}, C{'N[orth]'} or C{'S[outh]'}). @kwarg easting: Easting, see B{C{falsed}} (C{meter}). @kwarg 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 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) 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 = Float_(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 = Float(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 * E.es_c / (self.scale0 * E.a * _2_0)) if r > 0 else EPS0 t = E.es_tauf((_1_0 / 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 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/C++/doc/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/C++/doc/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 != bool(u.falsed): ll = self.toLatLon(LatLon=None, unfalse=True) utm = _MODS.utm self._utm = u = utm.toUtm8(ll, Utm=utm.Utm, falsed=falsed, name=self.name, zone=zone) return u @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) r = UtmUps5Tuple(z, p, e, n, B, Error=UPSError) if Ups is None \ else Ups(z, p, e, n, band=B, falsed=falsed, datum=datum) return _xnamed(r, name) 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/C++/doc/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() S = p == _S_ # at south[pole] a = -lat if S else lat P = isnear90(a, eps90=_Tol90) # at pole t = tan(radians(a)) T = E.es_taupf(t) r = (hypot1(T) - T) if T < 0 else (_0_0 if P else _1_0 / (hypot1(T) + T)) k0 = getattr(Ups, '_scale0', _K0_UPS) # Ups is class or None r *= k0 * E.a * _2_0 / E.es_c k = k0 if P else _scale(E, r, t) c = lon # [-180, 180) from .upsZoneBand5 x, y = sincos2d(c) x *= r y *= r if S: c = _neg(c) else: y = _neg(y) 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 = Ups(z, p, x, y, band=B, datum=d, falsed=falsed, convergence=c, scale=k, name=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 and C{lon} [-180..180). @note: The C{lon} is set to C{0} if B{C{lat}} is C{-90} or C{90}, see env variable C{PYGEODESY_UPS_POLES} in module L{pygeodesy.ups}. @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 _BZ_UPS and lon < 0 and isnear90(abs(lat), eps90=_Tol90): # DMA TM8358.1 only ... lon = 0 # ... zones B and Z at 90°S and 90°N, see also GeoConvert 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, prec=1) 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) # **) MIT License # # Copyright (C) 2016-2022 -- 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.