# Coverage for pygeodesy/ups.py : 95%

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A pure Python implementation, partially transcribed 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). @newfield example: Example, Examples ''' from pygeodesy.basics import EPS, property_RO from pygeodesy.datum import Datums, _TOL from pygeodesy.dms import clipDMS, degDMS, parseDMS2, _parseUTMUPS, RangeError from pygeodesy.fmath import hypot, hypot1 from pygeodesy.lazily import _ALL_LAZY from pygeodesy.named import EasNor2Tuple, UtmUps5Tuple, UtmUps8Tuple, \ UtmUpsLatLon5Tuple, _xnamed from pygeodesy.utily import degrees90, degrees180, sincos2d from pygeodesy.utmupsBase import _LLEB, _hemi, _to4lldn, _to3zBhp, _to3zll, \ _UPS_LAT_MAX, _UPS_LAT_MIN, _UPS_ZONE, \ _UPS_ZONE_STR, UtmUpsBase from math import atan, atan2, radians, sqrt, tan # all public contants, classes and functions __all__ = _ALL_LAZY.ups __version__ = '20.03.20' _Bands = 'A', 'B', 'Y', 'Z' #: (INTERNAL) Polar bands. _Falsing = 2000e3 #: (INTERNAL) False easting and northing (C{meter}). _K0 = 0.994 #: (INTERNAL) Central UPS scale factor. _K1 = 1.0 #: (INTERNAL) Rescale point scale factor. class UPSError(ValueError): '''Universal Polar Stereographic (UPS) parse or other L{Ups} issue. ''' pass def _Band(a, b): # determine the polar band letter return _Bands[(0 if a < 0 else 2) + (0 if b < 0 else 1)] def _scale(E, rho, tau): # compute the point scale factor, ala Karney t = hypot1(tau) return (rho / E.a) * t * sqrt(E.e12 + E.e2 / t**2) class Ups(UtmUpsBase): '''Universal Polar Stereographic (UPS) coordinate. ''' _band = '' #: (INTERNAL) Polar band ('A', 'B', 'Y' or 'Z'). _latlon_args = True #: (INTERNAL) unfalse from _latlon (C{bool}). _pole = '' #: (INTERNAL) UPS projection top/center ('N' or 'S'). _scale = None #: (INTERNAL) Point scale factor (C{scalar}). _scale0 = _K0 #: (INTERNAL) Central scale factor (C{scalar}). _utm = None #: (INTERNAL) toUtm cache (L{Utm}). def __init__(self, zone, pole, easting, northing, band='', # PYCHOK expected datum=Datums.WGS84, falsed=True, convergence=None, scale=None, name=''): '''New L{Ups} UPS coordinate. @arg zone: UPS zone (C{int}, zero) or zone with/-out 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, polar Band (C{str}, 'A'|'B'|'Y'|'Z'). @kwarg datum: Optional, this coordinate's datum (L{Datum}). @kwarg falsed: 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 UPSError: Invalid B{C{zone}}, B{C{pole}} or B{C{band}}. ''' if name: self.name = name try: z, B, p = _to3zBhp(zone, band=band, hemipole=pole) if z != _UPS_ZONE or (B and B not in _Bands): raise ValueError except ValueError: raise UPSError('%s, %s or %s invalid: %r' % ('zone', 'pole', 'band', (zone, pole, band))) self._band = B self._convergence = convergence self._easting = float(easting) self._falsed = falsed self._northing = float(northing) self._pole = p self._datum = datum self._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_RO def band(self): '''Get the polar band letter ('A', 'B', 'Y' or 'Z'). ''' if not self._band: self.toLatLon(unfalse=True) return self._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 hemisphere(self): '''Get the hemisphere (C{str}, 'N'|'S'). ''' if not self._hemisphere: self.toLatLon(unfalse=True) return self._hemisphere def parseUPS(self, strUPS): '''Parse a string to a UPS coordinate. @return: The coordinate (L{Ups}). @see: Function L{parseUPS5} in this module L{ups}. ''' return parseUPS5(strUPS, datum=self.datum, Ups=self.classof) @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): '''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{rangerrors} set to C{True}. @raise ValueError: Invalid B{C{scale}}. ''' try: s0 = float(scale0) if not 0 < s0: # <= 1.003 or 1.0016? raise ValueError except (TypeError, ValueError): raise ValueError('%s invalid: %r' % ('scale', scale0)) lat = clipDMS(lat, 90) # clip and force N u = toUps8(abs(lat), 0, datum=self.datum, Ups=_UpsK1) k = s0 / u.scale if self.scale0 != k: self._band = '' # force re-compute self._latlon = self._epsg = self._mgrs = self._utm = None self._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 B{C{LatLon=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_args == unfalse: return self._latlon5(LatLon) E = self.datum.ellipsoid # XXX vs LatLon.datum.ellipsoid x, y = self.to2en(falsed=not unfalse) r = hypot(x, y) t = (r / (2 * self.scale0 * E.a / E.es_c)) if r > 0 else EPS**2 t = E.es_tauf((1 / t - t) * 0.5) if self._pole == 'N': a, b, c = atan(t), atan2(x, -y), 1 else: a, b, c = -atan(t), atan2(x, y), -1 a, b = degrees90(a), degrees180(b) if not self._band: self._band = _Band(a, b) if not self._hemisphere: self._hemisphere = _hemi(a) ll = _LLEB(a, 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._latlon_to(ll, unfalse) return self._latlon5(LatLon, **LatLon_kwds) def _latlon_to(self, ll, unfalse): '''(INTERNAL) See C{.toLatLon}, C{toUps8}. ''' self._latlon, self._latlon_args = ll, 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}. ''' if self._mgrs is None: self._mgrs = self.toUtm(None).toMgrs() # via .toUtm return self._mgrs def toStr(self, prec=0, sep=' ', 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: Optional number of decimals, unstripped (C{int}). @kwarg sep: Optional separator to join (C{str}). @kwarg B: Optionally, include and polar band letter (C{bool}). @kwarg cs: Optionally, include gamma meridian convergence and point scale factor (C{bool}). @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 Karney's U{zone UPS <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1UTMUPS.html>}. ''' return self._toStr4_6(self.pole, B, cs, prec, sep) # PYCHOK pole def toStr2(self, prec=0, fmt='[%s]', sep=', ', 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: 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 B: Optionally, include polar band letter (C{bool}). @kwarg cs: Optionally, include gamma meridian convergence and point scale factor (C{bool}). @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 Karney's U{zone UPS <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1UTMUPS.html>}. ''' return self._toStr2(prec=prec, fmt=fmt, sep=sep, B=B, cs=cs) def toUps(self, pole='', **unused): '''Duplicate this UPS coordinate. @kwarg pole: Optional top/center of the UPS projection, (C{str}, 'N[orth]'|'S[outh]'). @return: A copt 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: # PYCHOK pole return self.copy() raise UPSError('%s transfer invalid: %r to %r' % ('pole', self.pole, pole)) # PYCHOK pole 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: from pygeodesy.utm import toUtm8, Utm # PYCHOK recursive import ll = self.toLatLon(LatLon=None, unfalse=True) self._utm = toUtm8(ll, 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 Karney's U{zone UPS<https:// GeographicLib.SourceForge.io/html/classGeographicLib_1_1UTMUPS.html>}. ''' return _UPS_ZONE class _UpsK1(Ups): '''(INTERNAL) For method L{Ups.rescale}. ''' _scale0 = _K1 def parseUPS5(strUPS, datum=Datums.WGS84, Ups=Ups, falsed=True, name=''): '''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}}. ''' try: u = strUPS.lstrip() if not u.startswith(_UPS_ZONE_STR): raise ValueError z, p, e, n, B = _parseUTMUPS(u) if z != _UPS_ZONE or (B and B not in _Bands): raise ValueError except (AttributeError, TypeError, ValueError): raise UPSError('%s invalid: %r' % ('strUPS', strUPS)) if Ups is None: r = UtmUps5Tuple(z, p, e, n, B) else: r = 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='', falsed=True, strict=True, name=''): '''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}). @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{rangerrors} set to C{True}. @raise TypeError: If B{C{latlon}} is not ellipsoidal. @raise ValueError: If B{C{lon}} value is missing or if B{C{latlon}} is invalid. @see: 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 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) < _TOL # at pole t = tan(radians(a)) T = E.es_taupf(t) r = hypot1(T) + abs(T) if T >= 0: r = 0 if A else 1 / r k0 = getattr(Ups, '_scale0', _K0) # 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 = -y else: c = -c if falsed: x += _Falsing y += _Falsing if Ups is None: r = UtmUps8Tuple(z, p, x, y, B, d, c, k) 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) r._hemisphere = _hemi(lat) if isinstance(latlon, _LLEB) and d is latlon.datum: r._latlon_to(latlon, falsed) # XXX weakref(latlon)? return _xnamed(r, name) def upsZoneBand5(lat, lon, strict=True): '''Return the UTM/UPS zone number, (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}). @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{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, _Band(lat, lon), 'S' elif lat > _UPS_LAT_MAX: # includes 30' overlap z, B, p = _UPS_ZONE, _Band(lat, lon), 'N' elif strict: x = '%s [%s, %s]' % ('range', _UPS_LAT_MIN, _UPS_LAT_MAX) raise RangeError('%s inside UTM %s: %s' % ('lat', x, degDMS(lat))) else: B, p = '', _hemi(lat) return UtmUpsLatLon5Tuple(z, B, p, lat, lon) # **) 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.