def check_valid_zone(zone_number, zone_letter):
if not 1 <= zone_number <= 60:
raise OutOfRangeError(
'zone number out of range (must be between 1 and 60)')
if zone_letter:
zone_letter = zone_letter.upper()
if not 'C' <= zone_letter <= 'X' or zone_letter in ['I', 'O']:
raise OutOfRangeError(
'zone letter out of range (must be between C and X)')
def to_latlon(easting,
northing,
zone_number,
zone_letter=None,
northern=None,
strict=True):
"""This function convert an UTM coordinate into Latitude and Longitude
Parameters
----------
easting: int
Easting value of UTM coordinate
northing: int
Northing value of UTM coordinate
zone number: int
Zone Number is represented with global map numbers of an UTM Zone
Numbers Map. More information see utmzones [1]_
zone_letter: str
Zone Letter can be represented as string values. Where UTM Zone
Designators can be accessed in [1]_
northern: bool
You can set True or False to set this parameter. Default is None
.. _[1]: http://www.jaworski.ca/utmzones.htm
"""
if not zone_letter and northern is None:
raise ValueError('either zone_letter or northern needs to be set')
elif zone_letter and northern is not None:
raise ValueError('set either zone_letter or northern, but not both')
if strict:
if not in_bounds(easting, 100000, 1000000, upper_strict=True):
raise OutOfRangeError(
'easting out of range (must be between 100.000 m and 999.999 m)'
)
if not in_bounds(northing, 0, 10000000):
raise OutOfRangeError(
'northing out of range (must be between 0 m and 10.000.000 m)')
check_valid_zone(zone_number, zone_letter)
if zone_letter:
zone_letter = zone_letter.upper()
northern = (zone_letter >= 'N')
x = easting - 500000
y = northing
if not northern:
y -= 10000000
m = y / K0
mu = m / (R * M1)
p_rad = (mu + P2 * mathlib.sin(2 * mu) + P3 * mathlib.sin(4 * mu) +
P4 * mathlib.sin(6 * mu) + P5 * mathlib.sin(8 * mu))
p_sin = mathlib.sin(p_rad)
p_sin2 = p_sin * p_sin
p_cos = mathlib.cos(p_rad)
p_tan = p_sin / p_cos
p_tan2 = p_tan * p_tan
p_tan4 = p_tan2 * p_tan2
ep_sin = 1 - E * p_sin2
ep_sin_sqrt = mathlib.sqrt(1 - E * p_sin2)
n = R / ep_sin_sqrt
r = (1 - E) / ep_sin
c = _E * p_cos**2
c2 = c * c
d = x / (n * K0)
d2 = d * d
d3 = d2 * d
d4 = d3 * d
d5 = d4 * d
d6 = d5 * d
latitude = (
p_rad - (p_tan / r) * (d2 / 2 - d4 / 24 *
(5 + 3 * p_tan2 + 10 * c - 4 * c2 - 9 * E_P2)) +
d6 / 720 *
(61 + 90 * p_tan2 + 298 * c + 45 * p_tan4 - 252 * E_P2 - 3 * c2))
longitude = (
d - d3 / 6 * (1 + 2 * p_tan2 + c) + d5 / 120 *
(5 - 2 * c + 28 * p_tan2 - 3 * c2 + 8 * E_P2 + 24 * p_tan4)) / p_cos
return (mathlib.degrees(latitude), mathlib.degrees(longitude) +
zone_number_to_central_longitude(zone_number))
def from_latlon(latitude,
longitude,
force_zone_number=None,
force_zone_letter=None):
"""This function convert Latitude and Longitude to UTM coordinate
Parameters
----------
latitude: float
Latitude between 80 deg S and 84 deg N, e.g. (-80.0 to 84.0)
longitude: float
Longitude between 180 deg W and 180 deg E, e.g. (-180.0 to 180.0).
force_zone number: int
Zone Number is represented with global map numbers of an UTM Zone
Numbers Map. You may force conversion including one UTM Zone Number.
More information see utmzones [1]_
.. _[1]: http://www.jaworski.ca/utmzones.htm
"""
if not in_bounds(latitude, -80.0, 84.0):
raise OutOfRangeError(
'latitude out of range (must be between 80 deg S and 84 deg N)')
if not in_bounds(longitude, -180.0, 180.0):
raise OutOfRangeError(
'longitude out of range (must be between 180 deg W and 180 deg E)')
if force_zone_number is not None:
check_valid_zone(force_zone_number, force_zone_letter)
lat_rad = mathlib.radians(latitude)
lat_sin = mathlib.sin(lat_rad)
lat_cos = mathlib.cos(lat_rad)
lat_tan = lat_sin / lat_cos
lat_tan2 = lat_tan * lat_tan
lat_tan4 = lat_tan2 * lat_tan2
if force_zone_number is None:
zone_number = latlon_to_zone_number(latitude, longitude)
else:
zone_number = force_zone_number
if force_zone_letter is None:
zone_letter = latitude_to_zone_letter(latitude)
else:
zone_letter = force_zone_letter
lon_rad = mathlib.radians(longitude)
central_lon = zone_number_to_central_longitude(zone_number)
central_lon_rad = mathlib.radians(central_lon)
n = R / mathlib.sqrt(1 - E * lat_sin**2)
c = E_P2 * lat_cos**2
a = lat_cos * (lon_rad - central_lon_rad)
a2 = a * a
a3 = a2 * a
a4 = a3 * a
a5 = a4 * a
a6 = a5 * a
m = R * (M1 * lat_rad - M2 * mathlib.sin(2 * lat_rad) +
M3 * mathlib.sin(4 * lat_rad) - M4 * mathlib.sin(6 * lat_rad))
easting = K0 * n * (
a + a3 / 6 * (1 - lat_tan2 + c) + a5 / 120 *
(5 - 18 * lat_tan2 + lat_tan4 + 72 * c - 58 * E_P2)) + 500000
northing = K0 * (m + n * lat_tan *
(a2 / 2 + a4 / 24 *
(5 - lat_tan2 + 9 * c + 4 * c**2) + a6 / 720 *
(61 - 58 * lat_tan2 + lat_tan4 + 600 * c - 330 * E_P2)))
if mixed_signs(latitude):
raise ValueError("latitudes must all have the same sign")
elif negative(latitude):
northing += 10000000
return easting, northing, zone_number, zone_letter