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# -*- coding: utf-8 -*- 

 

u'''I{Veness}' Universal Transverse Mercator (UTM) projection. 

 

Classes L{Utm} and L{UTMError} and functions L{parseUTM5}, L{toUtm8} 

and L{utmZoneBand5}. 

 

Pure Python implementation of UTM / WGS-84 conversion functions using 

an ellipsoidal earth model, transcoded from JavaScript originals by 

I{(C) Chris Veness 2011-2016} published under the same MIT Licence**, see 

U{UTM<https://www.Movable-Type.co.UK/scripts/latlong-utm-mgrs.html>} and 

U{Module utm<https://www.Movable-Type.co.UK/scripts/geodesy/docs/module-utm.html>}. 

 

The U{UTM<https://WikiPedia.org/wiki/Universal_Transverse_Mercator_coordinate_system>} 

system is a 2-dimensional Cartesian coordinate system providing another way 

to identify locations on the surface of the earth. UTM is a set of 60 

transverse Mercator projections, normally based on the WGS-84 ellipsoid. 

Within each zone, coordinates are represented as B{C{easting}}s and B{C{northing}}s, 

measured in metres. 

 

This module includes some of I{Charles Karney}'s U{'Transverse Mercator with an 

accuracy of a few nanometers'<https://Arxiv.org/pdf/1002.1417v3.pdf>}, 2011 

(building on Krüger's U{'Konforme Abbildung des Erdellipsoids in der Ebene' 

<https://bib.GFZ-Potsdam.DE/pub/digi/krueger2.pdf>}, 1912) and C++ class 

U{TransverseMercator 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1TransverseMercator.html>}. 

 

Some other references are U{Universal Transverse Mercator coordinate system 

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

U{Transverse Mercator Projection<https://GeographicLib.SourceForge.io/tm.html>} 

and Henrik Seidel U{'Die Mathematik der Gauß-Krueger-Abbildung' 

<https://Henrik-Seidel.GMXhome.DE/gausskrueger.pdf>}, 2006. 

''' 

 

from pygeodesy.basics import len2, map2, neg # splice 

from pygeodesy.datums import _ellipsoidal_datum, _WGS84 

from pygeodesy.dms import degDMS, parseDMS2 

from pygeodesy.errors import RangeError, _ValueError, \ 

_xkwds_get, _xkwds_not 

from pygeodesy.fmath import fdot3, Fsum, hypot, hypot1 

from pygeodesy.interns import EPS, EPS0, MISSING, NN, _by_, \ 

_COMMASPACE_, _float, _NS_, \ 

_outside_, _range_, _S_, _SPACE_, \ 

_UTM_, _V_, _X_, _zone_, _0_0, _1_0 

from pygeodesy.lazily import _ALL_LAZY 

from pygeodesy.named import _xnamed 

from pygeodesy.namedTuples import EasNor2Tuple, UtmUps5Tuple, \ 

UtmUps8Tuple, UtmUpsLatLon5Tuple 

from pygeodesy.props import deprecated_method, Property_RO 

from pygeodesy.streprs import Fmt 

from pygeodesy.units import Band, Int, Lat, Lon, Zone 

from pygeodesy.utily import degrees90, degrees180, sincos2 

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

_to4lldn, _to3zBhp, _to3zll, \ 

_UTM_LAT_MAX, _UTM_LAT_MIN, \ 

_UTM_ZONE_MIN, _UTM_ZONE_MAX, \ 

_UTM_ZONE_OFF_MAX, UtmUpsBase 

 

from math import asinh, atan, atanh, atan2, cos, cosh, \ 

degrees, radians, sin, sinh, tan, tanh 

from operator import mul 

 

__all__ = _ALL_LAZY.utm 

__version__ = '21.06.21' 

 

# Latitude bands C..X of 8° each, covering 80°S to 84°N with X repeated 

# for 80-84°N 

_Bands = 'CDEFGHJKLMNPQRSTUVWXX' # latitude bands 

_FalseEasting = _float( 500e3) # falsed offset (C{meter}) 

_FalseNorthing = _float(10000e3) # falsed offset (C{meter}) 

_K0_UTM = _float(0.9996) # UTM scale, central meridian 

 

 

class UTMError(_ValueError): 

'''Universal Transverse Mercator (UTM parse or other L{Utm} issue. 

''' 

pass 

 

 

class _Kseries(object): 

'''(INTERNAL) Alpha or Beta Krüger series. 

 

Krüger series summations for B{C{eta}}, B{C{ksi}}, B{C{p}} and B{C{q}}, 

caching the C{cos}, C{cosh}, C{sin} and C{sinh} values for 

the given B{C{eta}} and B{C{ksi}} angles (in C{radians}). 

''' 

def __init__(self, AB, x, y): 

'''(INTERNAL) New Alpha or Beta Krüger series 

 

@arg AB: Krüger Alpha or Beta series coefficients 

(C{4-, 6- or 8-tuple}). 

@arg x: Eta angle (C{radians}). 

@arg y: Ksi angle (C{radians}). 

''' 

n, j2 = len2(range(2, len(AB) * 2 + 1, 2)) 

 

self._ab = AB 

self._pq = map2(mul, j2, self._ab) 

# assert len(self._ab) == len(self._pq) == n 

 

x2 = map2(mul, j2, (x,) * n) 

self._chx = map2(cosh, x2) 

self._shx = map2(sinh, x2) 

# assert len(x2) == len(self._chx) == len(self._shx) == n 

 

y2 = map2(mul, j2, (y,) * n) 

self._cy = map2(cos, y2) 

self._sy = map2(sin, y2) 

# self._sy, self._cy = splice(sincos2(*y2)) # PYCHOK false 

# assert len(y2) == len(self._cy) == len(self._sy) == n 

 

def xs(self, x0): 

'''(INTERNAL) Eta summation (C{float}). 

''' 

return fdot3(self._ab, self._cy, self._shx, start=x0) 

 

def ys(self, y0): 

'''(INTERNAL) Ksi summation (C{float}). 

''' 

return fdot3(self._ab, self._sy, self._chx, start=y0) 

 

def ps(self, p0): 

'''(INTERNAL) P summation (C{float}). 

''' 

return fdot3(self._pq, self._cy, self._chx, start=p0) 

 

def qs(self, q0): 

'''(INTERNAL) Q summation (C{float}). 

''' 

return fdot3(self._pq, self._sy, self._shx, start=q0) 

 

 

def _cmlon(zone): 

'''(INTERNAL) Central meridian longitude (C{degrees180}). 

''' 

return (zone * 6) - 183 

 

 

def _false2(e, n, h): 

'''(INTERNAL) False easting and northing. 

''' 

# Karney, "Test data for the transverse Mercator projection (2009)" 

# <https://GeographicLib.SourceForge.io/html/transversemercator.html> 

# and <https://Zenodo.org/record/32470#.W4LEJS2ZON8> 

e += _FalseEasting # make e relative to central meridian 

if h == _S_: 

n += _FalseNorthing # make n relative to equator 

return e, n 

 

 

def _to3zBlat(zone, band, Error=UTMError): # imported by .mgrs 

'''(INTERNAL) Check and return zone, Band and band latitude. 

 

@arg zone: Zone number or string. 

@arg band: Band letter. 

@arg Error: Exception to raise (L{UTMError}). 

 

@return: 3-Tuple (zone, Band, latitude). 

''' 

z, B, _ = _to3zBhp(zone, band, Error=Error) 

if _UTM_ZONE_MIN > z or z > _UTM_ZONE_MAX: 

raise Error(zone=zone) 

 

b = None 

if B: 

b = _Bands.find(B) 

if b < 0: 

raise Error(band=band or B) 

b = Int((b << 3) - 80, name='bandLat') 

B = Band(B) 

elif Error is not UTMError: 

raise Error(band=band, txt=MISSING) 

 

return Zone(z), B, b 

 

 

def _to3zBll(lat, lon, cmoff=True): 

'''(INTERNAL) Return zone, Band and lat- and (central) longitude in degrees. 

 

@arg lat: Latitude (C{degrees}). 

@arg lon: Longitude (C{degrees}). 

@kwarg cmoff: Offset B{C{lon}} from zone's central meridian. 

 

@return: 4-Tuple (zone, Band, lat, lon). 

''' 

z, lat, lon = _to3zll(lat, lon) # in .utmupsBase 

 

if _UTM_LAT_MIN > lat or lat >= _UTM_LAT_MAX: # [-80, 84) like Veness 

r = _range_(_UTM_LAT_MIN, _UTM_LAT_MAX, ropen=True) 

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

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

B = _Bands[int(lat + 80) >> 3] 

 

x = lon - _cmlon(z) # z before Norway/Svaldbard 

if abs(x) > _UTM_ZONE_OFF_MAX: 

t = _SPACE_(_outside_, _UTM_, _zone_, str(z), _by_, degDMS(x, prec=6)) 

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

 

if B == _X_: # and 0 <= int(lon) < 42: z = int(lon + 183) // 6 + 1 

x = {32: 9, 34: 21, 36: 33}.get(z, None) 

if x: # Svalbard 

z += 1 if lon >= x else -1 

elif B == _V_ and z == 31 and lon >= 3: 

z += 1 # SouthWestern Norway 

 

if cmoff: # lon off central meridian 

lon -= _cmlon(z) # z after Norway/Svaldbard 

return Zone(z), Band(B), Lat(lat), Lon(lon) 

 

 

def _to7zBlldfn(latlon, lon, datum, falsed, name, zone, Error, **cmoff): 

'''(INTERNAL) Determine 7-tuple (zone, band, lat, lon, datum, 

falsed, name) for L{toEtm8} and L{toUtm8}. 

''' 

f = falsed and _xkwds_get(cmoff, cmoff=True) # DEPRECATED 

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

z, B, lat, lon = _to3zBll(lat, lon, cmoff=f) 

if zone: # re-zone for ETM/UTM 

r, _, _ = _to3zBhp(zone, B) 

if r != z: 

if not _UTM_ZONE_MIN <= r <= _UTM_ZONE_MAX: 

raise Error(zone=zone) 

if f: # re-offset from central meridian 

lon += _cmlon(z) - _cmlon(r) 

z = r 

return z, B, lat, lon, d, f, name 

 

 

class Utm(UtmUpsBase): 

'''Universal Transverse Mercator (UTM) coordinate. 

''' 

# _band = NN # latitude band letter ('C..X') 

_Error = UTMError # or etm.ETMError 

_latlon_args = () # (eps, unfalse) from _latlon (C{float}, C{bool}) 

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

_scale0 = _K0_UTM # central scale factor (C{scalar}) 

_zone = 0 # longitudinal zone (C{int} 1..60) 

 

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

datum=_WGS84, falsed=True, 

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

'''New L{Utm} UTM coordinate. 

 

@arg zone: Longitudinal UTM zone (C{int}, 1..60) or zone 

with/-out (latitudinal) Band letter (C{str}, 

'01C'..'60X'). 

@arg hemisphere: Northern or southern hemisphere (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, (latitudinal) band (C{str}, 'C'..'X'). 

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

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

@kwarg falsed: Both B{C{easting}} and B{C{northing}} are 

falsed (C{bool}). 

@kwarg convergence: Optional meridian convergence, bearing 

off grid North, clockwise from true North 

(C{degrees}) or C{None}. 

@kwarg scale: Optional grid scale factor (C{scalar}) or C{None}. 

@kwarg name: Optional name (C{str}). 

 

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

 

@raise UTMError: Invalid B{C{zone}}, B{C{hemishere}}, B{C{easting}}, 

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

B{C{scale}}. 

 

@example: 

 

>>> import pygeodesy 

>>> u = pygeodesy.Utm(31, 'N', 448251, 5411932) 

''' 

if name: 

self.name = name 

 

self._zone, B, _ = _to3zBlat(zone, band) 

 

h = str(hemisphere)[:1].upper() 

if h not in _NS_: 

raise self._Error(hemisphere=hemisphere) 

 

e, n = easting, northing # Easting(easting), ... 

# if not falsed: 

# e, n = _false2(e, n, h) 

# # check easting/northing (with 40km overlap 

# # between zones) - is this worthwhile? 

# @raise RangeError: If B{C{easting}} or B{C{northing}} outside 

# the valid UTM range. 

# if 120e3 > e or e > 880e3: 

# raise RangeError(easting=easting) 

# if 0 > n or n > _FalseNorthing: 

# raise RangeError(northing=northing) 

 

self._hemisphere = h 

UtmUpsBase.__init__(self, e, n, band=B, datum=datum, falsed=falsed, 

convergence=convergence, scale=scale) 

 

def __eq__(self, other): 

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

and other.hemisphere == self.hemisphere \ 

and other.easting == self.easting \ 

and other.northing == self.northing \ 

and other.band == self.band \ 

and other.datum == self.datum 

 

def __repr__(self): 

return self.toRepr(B=True) 

 

def __str__(self): 

return self.toStr() 

 

def _xcopy2(self, Xtm, name=NN): 

'''(INTERNAL) Make copy as an B{C{Xtm}} instance. 

 

@arg Xtm: Class to return the copy (C{Xtm=Etm}, 

C{Xtm=Utm} or C{self.classof}). 

''' 

return Xtm(self.zone, self.hemisphere, 

self.easting, self.northing, 

band=self.band, datum=self.datum, 

falsed=self.falsed, scale=self.scale, 

convergence=self.convergence, 

name=name or self.name) 

 

@Property_RO 

def band(self): 

'''Get the (latitudinal) band (C{str}, 'C'..'X' or ''). 

''' 

return self._band 

 

@Property_RO 

def _etm(self): 

'''(INTERNAL) Cache for L{toEtm}. 

''' 

from pygeodesy.etm import Etm 

return self._xcopy2(Etm) 

 

@Property_RO 

def falsed2(self): 

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

''' 

e = n = 0 

if self.falsed: 

e = _FalseEasting # relative to central meridian 

if self.hemisphere == _S_: # relative to equator 

n = _FalseNorthing 

return EasNor2Tuple(e, n) 

 

@Property_RO 

def _lowerleft(self): # by .ellipsoidalBase.LatLon.toUtm 

'''Get this UTM C{un}-centered (L{Utm}) to its C{lowerleft}. 

''' 

return _lowerleft(self, 0) 

 

@Property_RO 

def _mgrs(self): 

'''(INTERNAL) Cache for L{toMgrs}. 

''' 

return _toMgrs(self) 

 

@Property_RO 

def _mgrs_lowerleft(self): 

'''(INTERNAL) Cache for L{toMgrs}, I{un}-centered. 

''' 

u = self._lowerleft 

return self._mgrs if u is self else _toMgrs(u) 

 

def parse(self, strUTM, name=NN): 

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

 

@arg strUTM: The UTM coordinate (C{str}), 

see function L{parseUTM5}. 

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

overriding this name. 

 

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

 

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

 

@see: Function L{parseUPS5} and L{parseUTMUPS5}. 

''' 

return parseUTM5(strUTM, datum=self.datum, Utm=self.classof, 

name=name or self.name) 

 

@deprecated_method 

def parseUTM(self, strUTM): # PYCHOK no cover 

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

return self.parse(strUTM) 

 

@Property_RO 

def pole(self): 

'''Get the top center of (stereographic) projection, C{""} always. 

''' 

return NN # N/A for UTM 

 

def toEtm(self): 

'''Copy this UTM to an ETM coordinate. 

 

@return: The ETM coordinate (L{Etm}). 

''' 

return self._etm 

 

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

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

 

@kwarg LatLon: Optional, ellipsoidal class to return the 

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

@kwarg eps: Optional convergence limit, L{EPS} or above 

(C{float}). 

@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}=None}. 

 

@return: This UTM as (B{C{LatLon}}) or if B{C{LatLon}} is 

C{None}, as L{LatLonDatum5Tuple}C{(lat, lon, datum, 

convergence, scale)}. 

 

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

 

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

 

@example: 

 

>>> u = Utm(31, 'N', 448251.795, 5411932.678) 

>>> from pygeodesy import ellipsoidalVincenty as eV 

>>> ll = u.toLatLon(eV.LatLon) # 48°51′29.52″N, 002°17′40.20″E 

''' 

if eps < EPS: 

eps = EPS # less doesn't converge 

 

if self._latlon and self._latlon_args == (eps, unfalse): 

return self._latlon5(LatLon) 

 

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

 

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

 

# from Karney 2011 Eq 15-22, 36 

A0 = self.scale0 * E.A 

if A0 < EPS0: 

raise self._Error(meridional=A0) 

x /= A0 # η eta 

y /= A0 # ξ ksi 

 

K = _Kseries(E.BetaKs, x, y) # Krüger series 

y = neg(K.ys(-y)) # ξ' 

x = neg(K.xs(-x)) # η' 

 

shx = sinh(x) 

sy, cy = sincos2(y) 

 

H = hypot(shx, cy) 

if H < EPS0: 

raise self._Error(H=H) 

 

T = t0 = sy / H # τʹ 

S = Fsum(T) 

q = _1_0 / E.e12 

P = 7 # -/+ toggle trips 

d = _1_0 + eps 

while abs(d) > eps and P > 0: 

p = -d # previous d, toggled 

h = hypot1(T) 

s = sinh(E.e * atanh(E.e * T / h)) 

t = T * hypot1(s) - s * h 

d = (t0 - t) / hypot1(t) * ((q + T**2) / h) 

T, d = S.fsum2_(d) # τi, (τi - τi-1) 

if d == p: # catch -/+ toggling of d 

P -= 1 

# else: 

# P = 0 

 

a = atan(T) # lat 

b = atan2(shx, cy) 

if unfalse and self.falsed: 

b += radians(_cmlon(self.zone)) 

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

 

# convergence: Karney 2011 Eq 26, 27 

p = neg(K.ps(-1)) 

q = K.qs(0) 

ll._convergence = degrees(atan(tan(y) * tanh(x)) + atan2(q, p)) 

 

# scale: Karney 2011 Eq 28 

ll._scale = E.e2s(sin(a)) * hypot1(T) * H * (A0 / E.a / hypot(p, q)) 

 

self._latlon_to(ll, eps, unfalse) 

return self._latlon5(LatLon, **LatLon_kwds) 

 

def _latlon_to(self, ll, eps, unfalse): 

'''(INTERNAL) See C{.toLatLon}, C{toUtm8}, C{_toXtm8}. 

''' 

self._latlon, self._latlon_args = ll, (eps, unfalse) 

 

def toMgrs(self, center=False): 

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

 

@kwarg center: If C{True}, I{un}-center this UTM 

to its C{lowerleft} (C{bool}) or 

by C{B{center} meter} (C{scalar}). 

 

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

 

@see: Function L{toMgrs} in L{mgrs} for more details. 

''' 

return self._mgrs if center in (False, 0, _0_0) else ( 

self._mgrs_lowerleft if center in (True,) else 

_toMgrs(_lowerleft(self, center))) # PYCHOK indent 

 

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

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

 

Note that UTM 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 latitudinal band (C{bool}). 

@kwarg cs: Optionally, include meridian convergence and grid 

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

the precison like B{C{prec}}). 

 

@return: This UTM as a string C{"[Z:09[band], H:N|S, E:meter, 

N:meter]"} plus C{", C:degrees, S:float"} if B{C{cs}} is 

C{True} (C{str}). 

''' 

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 UTM coordinate. 

 

To distinguish from MGRS grid zone designators, a space is 

left between the zone and the hemisphere. 

 

Note that UTM 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}) or C{None} 

to return an unjoined C{tuple} of C{str}s. 

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

@kwarg cs: Optionally, include meridian convergence and grid 

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

the precison like B{C{prec}}). 

 

@return: This UTM as a string with C{zone[band], hemisphere, 

easting, northing, [convergence, scale]} in 

C{"00 N|S meter meter"} plus C{" degrees float"} if 

B{C{cs}} is C{True} (C{str}). 

 

@example: 

 

>>> u = Utm(3, 'N', 448251, 5411932.0001) 

>>> u.toStr(4) # 03 N 448251.0 5411932.0001 

>>> u.toStr(sep=', ') # 03 N, 448251, 5411932 

''' 

 

return self._toStr(self.hemisphere, B, cs, prec, sep) 

 

def toUps(self, pole=NN, eps=EPS, falsed=True, **unused): 

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

 

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

(C{str}, 'N[orth]'|'S[outh]'). 

@kwarg eps: Optional convergence limit, L{EPS} or above 

(C{float}), see method L{Utm.toLatLon}. 

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

 

@return: The UPS coordinate (L{Ups}). 

''' 

u = self._ups 

if u is None or u.pole != (pole or u.pole) or falsed != bool(u.falsed): 

from pygeodesy.ups import toUps8, Ups 

ll = self.toLatLon(LatLon=_LLEB, eps=eps, unfalse=True) 

self._ups = u = toUps8(ll, Ups=Ups, falsed=falsed, pole=pole, 

strict=False, name=self.name) 

return u 

 

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

'''Convert this UTM coordinate to a different zone. 

 

@arg zone: New UTM zone (C{int}). 

@kwarg eps: Optional convergence limit, L{EPS} or above 

(C{float}), see method L{Utm.toLatLon}. 

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

 

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

''' 

if zone == self.zone and falsed == self.falsed: 

return self.copy() 

elif zone: 

u = self._utm 

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

ll = self.toLatLon(LatLon=_LLEB, eps=eps, unfalse=True) 

self._utm = u = toUtm8(ll, Utm=self.classof, falsed=falsed, 

name=self.name, zone=zone) 

return u 

raise self._Error(zone=zone) 

 

@Property_RO 

def zone(self): 

'''Get the (longitudinal) zone (C{int}, 1..60). 

''' 

return self._zone 

 

 

def _lowerleft(utm, center): # by .ellipsoidalBase.LatLon.toUtm 

'''(INTERNAL) I{Un}-center a B{C{utm}} to its C{lowerleft} by 

C{B{center} meter} or by a I{guess} if B{C{center}} is C{0}. 

''' 

if center: 

e = n = -center 

else: 

c = 5 # center 

for _ in range(3): 

c *= 10 # 50, 500, 5000 

t = c * 2 

e = int(utm.easting % t) 

n = int(utm.northing % t) 

if (e == c and n in (c, c - 1)) or \ 

(n == c and e in (c, c - 1)): 

break 

else: 

return utm # unchanged 

 

r = _xkwds_not(None, datum=utm.datum, scale=utm.scale, 

convergence=utm.convergence) 

return utm.classof(utm.zone, utm.hemisphere, 

utm.easting - e, utm.northing - n, 

band=utm.band, falsed=utm.falsed, **r) 

 

 

def _parseUTM5(strUTM, datum, Xtm, falsed, Error=UTMError, name=NN): # imported by .etm 

'''(INTERNAL) Parse a string representing a UTM coordinate, 

consisting of C{"zone[band] hemisphere easting northing"}, 

see L{parseETM5} and L{parseUTM5}. 

''' 

z, h, e, n, B = _parseUTMUPS5(strUTM, None, Error=Error) 

if _UTM_ZONE_MIN > z or z > _UTM_ZONE_MAX or (B and B not in _Bands): 

raise Error(strUTM=strUTM, zone=z, band=B) 

 

if Xtm is None: 

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

else: 

r = Xtm(z, h, e, n, band=B, datum=datum, falsed=falsed) 

if name: 

r = _xnamed(r, name, force=True) 

return r 

 

 

def parseUTM5(strUTM, datum=_WGS84, Utm=Utm, falsed=True, name=NN): 

'''Parse a string representing a UTM coordinate, consisting 

of C{"zone[band] hemisphere easting northing"}. 

 

@arg strUTM: A UTM coordinate (C{str}). 

@kwarg datum: Optional datum to use (L{Datum}, L{Ellipsoid}, 

L{Ellipsoid2} or L{a_f2Tuple}). 

@kwarg Utm: Optional class to return the UTM coordinate 

(L{Utm}) or C{None}. 

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

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

 

@return: The UTM coordinate (B{C{Utm}}) or if B{C{Utm}} 

is C{None}, a L{UtmUps5Tuple}C{(zone, hemipole, 

easting, northing, band)}. The C{hemipole} is 

the C{'N'|'S'} hemisphere. 

 

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

 

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

 

@example: 

 

>>> u = parseUTM5('31 N 448251 5411932') 

>>> u.toRepr() # [Z:31, H:N, E:448251, N:5411932] 

>>> u = parseUTM5('31 N 448251.8 5411932.7') 

>>> u.toStr() # 31 N 448252 5411933 

''' 

r = _parseUTM5(strUTM, datum, Utm, falsed, name=name) 

return r 

 

 

def _toMgrs(utm): 

'''(INTERNAL) Convert a L{Utm} to an L{Mgrs} instance. 

''' 

from pygeodesy.mgrs import toMgrs 

return toMgrs(utm, datum=utm.datum, name=utm.name) 

 

 

def toUtm8(latlon, lon=None, datum=None, Utm=Utm, falsed=True, name=NN, 

zone=None, **cmoff): 

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

 

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

geodetic C{LatLon} point. 

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

@kwarg datum: Optional datum for this UTM coordinate, 

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

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

@kwarg Utm: Optional class to return the UTM coordinate 

(L{Utm}) or C{None}. 

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

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

@kwarg zone: Optional UTM zone to enforce (C{int} or C{str}). 

@kwarg cmoff: DEPRECATED, use B{C{falsed}}. Offset longitude 

from the zone's central meridian (C{bool}). 

 

@return: The UTM coordinate (B{C{Utm}}) or if B{C{Utm}} is 

C{None} or not B{C{falsed}}, a L{UtmUps8Tuple}C{(zone, 

hemipole, easting, northing, band, datum, convergence, 

scale)}. The C{hemipole} is the C{'N'|'S'} hemisphere. 

 

@raise RangeError: If B{C{lat}} outside the valid UTM bands or 

if B{C{lat}} or B{C{lon}} outside the valid 

range and L{rangerrors} set to C{True}. 

 

@raise TypeError: Invalid B{C{datum}} or B{C{latlon}} not ellipsoidal. 

 

@raise UTMError: Invalid B{C{zone}}. 

 

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

B{C{latlon}} is invalid. 

 

@note: Implements Karney’s method, using 8-th order Krüger series, 

giving results accurate to 5 nm (or better) for distances 

up to 3900 km from the central meridian. 

 

@example: 

 

>>> p = LatLon(48.8582, 2.2945) # 31 N 448251.8 5411932.7 

>>> u = toUtm(p) # 31 N 448252 5411933 

>>> p = LatLon(13.4125, 103.8667) # 48 N 377302.4 1483034.8 

>>> u = toUtm(p) # 48 N 377302 1483035 

''' 

z, B, lat, lon, d, f, name = _to7zBlldfn(latlon, lon, datum, 

falsed, name, zone, 

UTMError, **cmoff) 

d = _ellipsoidal_datum(d, name=name) 

E = d.ellipsoid 

 

a, b = radians(lat), radians(lon) 

# easting, northing: Karney 2011 Eq 7-14, 29, 35 

sb, cb = sincos2(b) 

 

T = tan(a) 

T12 = hypot1(T) 

S = sinh(E.e * atanh(E.e * T / T12)) 

 

T_ = T * hypot1(S) - S * T12 

H = hypot(T_, cb) 

 

y = atan2(T_, cb) # ξ' ksi 

x = asinh(sb / H) # η' eta 

 

A0 = E.A * getattr(Utm, '_scale0', _K0_UTM) # Utm is class or None 

 

K = _Kseries(E.AlphaKs, x, y) # Krüger series 

y = K.ys(y) * A0 # ξ 

x = K.xs(x) * A0 # η 

 

# convergence: Karney 2011 Eq 23, 24 

p_ = K.ps(1) 

q_ = K.qs(0) 

c = degrees(atan(T_ / hypot1(T_) * tan(b)) + atan2(q_, p_)) 

 

# scale: Karney 2011 Eq 25 

k = E.e2s(sin(a)) * T12 / H * (A0 / E.a * hypot(p_, q_)) 

 

return _toXtm8(Utm, z, lat, x, y, 

B, d, c, k, f, name, latlon, EPS) 

 

 

def _toXtm8(Xtm, z, lat, x, y, B, d, c, k, f, # PYCHOK 13+ args 

name, latlon, eps, Error=UTMError): 

'''(INTERNAL) Helper for L{toEtm8} and L{toUtm8}. 

''' 

h = _hemi(lat) 

if f: 

x, y = _false2(x, y, h) 

if Xtm is None: # DEPRECATED 

r = UtmUps8Tuple(z, h, x, y, B, d, c, k, Error=Error, name=name) 

else: 

r = _xnamed(Xtm(z, h, x, y, band=B, datum=d, falsed=f, 

convergence=c, scale=k), name) 

if isinstance(latlon, _LLEB) and d is latlon.datum: 

r._latlon_to(latlon, eps, f) # XXX weakref(latlon)? 

latlon._convergence = c 

latlon._scale = k 

return r 

 

 

def utmZoneBand5(lat, lon, cmoff=False, name=NN): 

'''Return the UTM zone number, Band letter, hemisphere 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 cmoff: Offset longitude from the zone's central 

meridian (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'} 

UTM hemisphere. 

 

@raise RangeError: If B{C{lat}} outside the valid UTM bands 

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}}. 

''' 

lat, lon = parseDMS2(lat, lon) 

z, B, lat, lon = _to3zBll(lat, lon, cmoff=cmoff) 

return UtmUpsLatLon5Tuple(z, B, _hemi(lat), lat, lon, name=name) 

 

# **) MIT License 

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