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108 lines
3.4 KiB
108 lines
3.4 KiB
import numpy as np
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"""
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Coordinate transformation module. All methods accept arrays as input
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with each row as a position.
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"""
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a = 6378137
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b = 6356752.3142
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esq = 6.69437999014 * 0.001
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e1sq = 6.73949674228 * 0.001
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def geodetic2ecef(geodetic, radians=False):
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geodetic = np.array(geodetic)
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input_shape = geodetic.shape
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geodetic = np.atleast_2d(geodetic)
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ratio = 1.0 if radians else (np.pi / 180.0)
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lat = ratio*geodetic[:,0]
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lon = ratio*geodetic[:,1]
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alt = geodetic[:,2]
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xi = np.sqrt(1 - esq * np.sin(lat)**2)
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x = (a / xi + alt) * np.cos(lat) * np.cos(lon)
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y = (a / xi + alt) * np.cos(lat) * np.sin(lon)
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z = (a / xi * (1 - esq) + alt) * np.sin(lat)
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ecef = np.array([x, y, z]).T
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return ecef.reshape(input_shape)
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def ecef2geodetic(ecef, radians=False):
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"""
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Convert ECEF coordinates to geodetic using ferrari's method
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"""
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# Save shape and export column
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ecef = np.atleast_1d(ecef)
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input_shape = ecef.shape
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ecef = np.atleast_2d(ecef)
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x, y, z = ecef[:, 0], ecef[:, 1], ecef[:, 2]
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ratio = 1.0 if radians else (180.0 / np.pi)
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# Conver from ECEF to geodetic using Ferrari's methods
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# https://en.wikipedia.org/wiki/Geographic_coordinate_conversion#Ferrari.27s_solution
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r = np.sqrt(x * x + y * y)
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Esq = a * a - b * b
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F = 54 * b * b * z * z
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G = r * r + (1 - esq) * z * z - esq * Esq
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C = (esq * esq * F * r * r) / (pow(G, 3))
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S = np.cbrt(1 + C + np.sqrt(C * C + 2 * C))
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P = F / (3 * pow((S + 1 / S + 1), 2) * G * G)
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Q = np.sqrt(1 + 2 * esq * esq * P)
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r_0 = -(P * esq * r) / (1 + Q) + np.sqrt(0.5 * a * a*(1 + 1.0 / Q) - \
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P * (1 - esq) * z * z / (Q * (1 + Q)) - 0.5 * P * r * r)
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U = np.sqrt(pow((r - esq * r_0), 2) + z * z)
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V = np.sqrt(pow((r - esq * r_0), 2) + (1 - esq) * z * z)
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Z_0 = b * b * z / (a * V)
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h = U * (1 - b * b / (a * V))
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lat = ratio*np.arctan((z + e1sq * Z_0) / r)
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lon = ratio*np.arctan2(y, x)
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# stack the new columns and return to the original shape
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geodetic = np.column_stack((lat, lon, h))
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return geodetic.reshape(input_shape)
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class LocalCoord(object):
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"""
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Allows conversions to local frames. In this case NED.
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That is: North East Down from the start position in
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meters.
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"""
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def __init__(self, init_geodetic, init_ecef):
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self.init_ecef = init_ecef
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lat, lon, _ = (np.pi/180)*np.array(init_geodetic)
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self.ned2ecef_matrix = np.array([[-np.sin(lat)*np.cos(lon), -np.sin(lon), -np.cos(lat)*np.cos(lon)],
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[-np.sin(lat)*np.sin(lon), np.cos(lon), -np.cos(lat)*np.sin(lon)],
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[np.cos(lat), 0, -np.sin(lat)]])
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self.ecef2ned_matrix = self.ned2ecef_matrix.T
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@classmethod
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def from_geodetic(cls, init_geodetic):
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init_ecef = geodetic2ecef(init_geodetic)
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return LocalCoord(init_geodetic, init_ecef)
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@classmethod
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def from_ecef(cls, init_ecef):
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init_geodetic = ecef2geodetic(init_ecef)
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return LocalCoord(init_geodetic, init_ecef)
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def ecef2ned(self, ecef):
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ecef = np.array(ecef)
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return np.dot(self.ecef2ned_matrix, (ecef - self.init_ecef).T).T
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def ned2ecef(self, ned):
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ned = np.array(ned)
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# Transpose so that init_ecef will broadcast correctly for 1d or 2d ned.
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return (np.dot(self.ned2ecef_matrix, ned.T).T + self.init_ecef)
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def geodetic2ned(self, geodetic):
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ecef = geodetic2ecef(geodetic)
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return self.ecef2ned(ecef)
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def ned2geodetic(self, ned):
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ecef = self.ned2ecef(ned)
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return ecef2geodetic(ecef)
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