Эхний хэсэгт геодезийн солбицолоос тэгш өнцөгтөд хөрвөсөн тэгвэл үүний эсрэг процесс заавал байж таараа тэр нь энэ.
Converting UTM to Latitude and Longitude
y = northing, x = easting (relative to central meridian; subtract 500,000 from conventional UTM coordinate).
Calculate the Meridional Arc
This is easy: M = y/k0.
Calculate Footprint Latitude
* mu = M/[a(1 - e2/4 - 3e4/64 - 5e6/256...)
* e1 = [1 - (1 - e2)1/2]/[1 + (1 - e2)1/2]
footprint latitude fp = mu + J1sin(2mu) + J2sin(4mu) + J3sin(6mu) + J4sin(8mu), where:
* J1 = (3e1/2 - 27e13/32 ..)
* J2 = (21e12/16 - 55e14/32 ..)
* J3 = (151e13/96 ..)
* J4 = (1097e14/512 ..)
Calculate Latitude and Longitude
* e'2 = (ea/b)2 = e2/(1-e2)
* C1 = e'2cos2(fp)
* T1 = tan2(fp)
* R1 = a(1-e2)/(1-e2sin2(fp))3/2. This is the same as rho in the forward conversion formulas above, but calculated for fp instead of lat.
* N1 = a/(1-e2sin2(fp))1/2. This is the same as nu in the forward conversion formulas above, but calculated for fp instead of lat.
* D = x/(N1k0)
lat = fp - Q1(Q2 - Q3 + Q4), where:
* Q1 = N1 tan(fp)/R1
* Q2 = (D2/2)
* Q3 = (5 + 3T1 + 10C1 - 4C12 -9e'2)D4/24
* Q4 = (61 + 90T1 + 298C1 +45T12 - 3C12 -252e'2)D6/720
long = long0 + (Q5 - Q6 + Q7)/cos(fp), where:
* Q5 = D
* Q6 = (1 + 2T1 + C1)D3/6
* Q7 = (5 - 2C1 + 28T1 - 3C12 + 8e'2 + 24T12)D5/120
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