Created
October 12, 2017 13:45
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UTM to Latitude / Longitude
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import math | |
def utm_to_latlng(easting, northing, zone=25, northernHemisphere=False): | |
if not northernHemisphere: | |
northing = 10000000 - northing | |
a = 6378137 | |
e = 0.081819191 | |
e1sq = 0.006739497 | |
k0 = 0.9996 | |
arc = northing / k0 | |
mu = arc / (a * (1 - math.pow(e, 2) / 4.0 - 3 * math.pow(e, 4) / 64.0 - 5 * math.pow(e, 6) / 256.0)) | |
ei = (1 - math.pow((1 - e * e), (1 / 2.0))) / (1 + math.pow((1 - e * e), (1 / 2.0))) | |
ca = 3 * ei / 2 - 27 * math.pow(ei, 3) / 32.0 | |
cb = 21 * math.pow(ei, 2) / 16 - 55 * math.pow(ei, 4) / 32 | |
cc = 151 * math.pow(ei, 3) / 96 | |
cd = 1097 * math.pow(ei, 4) / 512 | |
phi1 = mu + ca * math.sin(2 * mu) + cb * math.sin(4 * mu) + cc * math.sin(6 * mu) + cd * math.sin(8 * mu) | |
n0 = a / math.pow((1 - math.pow((e * math.sin(phi1)), 2)), (1 / 2.0)) | |
r0 = a * (1 - e * e) / math.pow((1 - math.pow((e * math.sin(phi1)), 2)), (3 / 2.0)) | |
fact1 = n0 * math.tan(phi1) / r0 | |
_a1 = 500000 - easting | |
dd0 = _a1 / (n0 * k0) | |
fact2 = dd0 * dd0 / 2 | |
t0 = math.pow(math.tan(phi1), 2) | |
Q0 = e1sq * math.pow(math.cos(phi1), 2) | |
fact3 = (5 + 3 * t0 + 10 * Q0 - 4 * Q0 * Q0 - 9 * e1sq) * math.pow(dd0, 4) / 24 | |
fact4 = (61 + 90 * t0 + 298 * Q0 + 45 * t0 * t0 - 252 * e1sq - 3 * Q0 * Q0) * math.pow(dd0, 6) / 720 | |
lof1 = _a1 / (n0 * k0) | |
lof2 = (1 + 2 * t0 + Q0) * math.pow(dd0, 3) / 6.0 | |
lof3 = (5 - 2 * Q0 + 28 * t0 - 3 * math.pow(Q0, 2) + 8 * e1sq + 24 * math.pow(t0, 2)) * math.pow(dd0, 5) / 120 | |
_a2 = (lof1 - lof2 + lof3) / math.cos(phi1) | |
_a3 = _a2 * 180 / math.pi | |
latitude = 180 * (phi1 - fact1 * (fact2 + fact3 + fact4)) / math.pi | |
if not northernHemisphere: | |
latitude = -latitude | |
longitude = ((zone > 0) and (6 * zone - 183.0) or 3.0) - _a3 | |
return (latitude, longitude) |
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