高斯坐标反算公式——python实现
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高斯坐标反算公式——python实现
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#!/ usr/bin/python
# -*- coding:utf-8 -*-import mathdef LatLon2XY(latitude, longitude):a = 6378137.0# b = 6356752.3142# c = 6399593.6258# alpha = 1 / 298.257223563e2 = 0.0066943799013# epep = 0.00673949674227#將經緯度轉換為弧度latitude2Rad = (math.pi / 180.0) * latitudebeltNo = int((longitude + 1.5) / 3.0) #計算3度帶投影度帶號L = beltNo * 3 #計算中央經線l0 = longitude - L #經差tsin = math.sin(latitude2Rad)tcos = math.cos(latitude2Rad)t = math.tan(latitude2Rad)m = (math.pi / 180.0) * l0 * tcoset2 = e2 * pow(tcos, 2)et3 = e2 * pow(tsin, 2)X = 111132.9558 * latitude - 16038.6496 * math.sin(2 * latitude2Rad) + 16.8607 * math.sin(4 * latitude2Rad) - 0.0220 * math.sin(6 * latitude2Rad)N = a / math.sqrt(1 - et3)x = X + N * t * (0.5 * pow(m, 2) + (5.0 - pow(t, 2) + 9.0 * et2 + 4 * pow(et2, 2)) * pow(m, 4) / 24.0 + (61.0 - 58.0 * pow(t, 2) + pow(t, 4)) * pow(m, 6) / 720.0)y = 500000 + N * (m + (1.0 - pow(t, 2) + et2) * pow(m, 3) / 6.0 + (5.0 - 18.0 * pow(t, 2) + pow(t, 4) + 14.0 * et2 - 58.0 * et2 * pow(t, 2)) * pow(m, 5) / 120.0)return x, y#x為帶代號的坐標,L0為中央經線
def XY2LatLon(X, Y, L0):iPI = 0.0174532925199433a = 6378137.0f= 0.00335281006247ZoneWide = 3 #按3度帶進行投影ProjNo = int(X / 1000000)L0 = L0 * iPIX0 = ProjNo * 1000000 + 500000Y0 = 0xval = X - X0yval = Y - Y0e2 = 2 * f - f * f #第一偏心率平方e1 = (1.0 - math.sqrt(1 - e2)) / (1.0 + math.sqrt(1 - e2))ee = e2 / (1 - e2) #第二偏心率平方M = yvalu = M / (a * (1 - e2 / 4 - 3 * e2 * e2 / 64 - 5 * e2 * e2 * e2 / 256))fai = u \+ (3 * e1 / 2 - 27 * e1 * e1 * e1 / 32) * math.sin(2 * u) \+ (21 * e1 * e1 / 16 - 55 * e1 * e1 * e1 * e1 / 32) * math.sin(4 * u) \+ (151 * e1 * e1 * e1 / 96) * math.sin(6 * u)\+ (1097 * e1 * e1 * e1 * e1 / 512) * math.sin(8 * u)C = ee * math.cos(fai) * math.cos(fai)T = math.tan(fai) * math.tan(fai)NN = a / math.sqrt(1.0 - e2 * math.sin(fai) * math.sin(fai))R = a * (1 - e2) / math.sqrt((1 - e2 * math.sin(fai) * math.sin(fai)) * (1 - e2 * math.sin(fai) * math.sin(fai)) * (1 - e2 * math.sin(fai) * math.sin(fai)))D = xval / NN#計算經緯度(弧度單位的經緯度)longitude1 = L0 + (D - (1 + 2 * T + C) * D * D * D / 6 + (5 - 2 * C + 28 * T - 3 * C * C + 8 * ee + 24 * T * T) * D * D * D * D * D / 120) / math.cos(fai)latitude1 = fai - (NN * math.tan(fai) / R) * (D * D / 2 - (5 + 3 * T + 10 * C - 4 * C * C - 9 * ee) * D * D * D * D / 24 + (61 + 90 * T + 298 * C + 45 * T * T - 256 * ee - 3 * C * C) * D * D * D * D * D * D / 720)#換換為deglongitude = longitude1 / iPIlatitude = latitude1 / iPIreturn latitude, longitude
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