Module pymap3d.ecef
Transforms involving ECEF: earth-centered, earth-fixed frame
Source code
""" Transforms involving ECEF: earth-centered, earth-fixed frame """
try:
from numpy import radians, sin, cos, tan, arctan as atan, hypot, degrees, arctan2 as atan2, sqrt, pi, vectorize
from .eci import eci2ecef
except ImportError:
from math import radians, sin, cos, tan, atan, hypot, degrees, atan2, sqrt, pi
vectorize = eci2ecef = None
import typing
from datetime import datetime
from .ellipsoid import Ellipsoid
from .utils import sanitize
# py < 3.6 compatible
tau = 2 * pi
__all__ = ["geodetic2ecef", "ecef2geodetic", "ecef2enuv", "ecef2enu", "enu2uvw", "uvw2enu", "eci2geodetic", "enu2ecef"]
def geodetic2ecef(lat: float, lon: float, alt: float, ell: Ellipsoid = None, deg: bool = True) -> typing.Tuple[float, float, float]:
"""
point transformation from Geodetic of specified ellipsoid (default WGS-84) to ECEF
Parameters
----------
lat : float
target geodetic latitude
lon : float
target geodetic longitude
h : float
target altitude above geodetic ellipsoid (meters)
ell : Ellipsoid, optional
reference ellipsoid
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
ECEF (Earth centered, Earth fixed) x,y,z
x : float
target x ECEF coordinate (meters)
y : float
target y ECEF coordinate (meters)
z : float
target z ECEF coordinate (meters)
"""
lat, ell = sanitize(lat, ell, deg)
if deg:
lon = radians(lon)
# radius of curvature of the prime vertical section
N = ell.semimajor_axis ** 2 / sqrt(ell.semimajor_axis ** 2 * cos(lat) ** 2 + ell.semiminor_axis ** 2 * sin(lat) ** 2)
# Compute cartesian (geocentric) coordinates given (curvilinear) geodetic
# coordinates.
x = (N + alt) * cos(lat) * cos(lon)
y = (N + alt) * cos(lat) * sin(lon)
z = (N * (ell.semiminor_axis / ell.semimajor_axis) ** 2 + alt) * sin(lat)
return x, y, z
def ecef2geodetic(x: float, y: float, z: float, ell: Ellipsoid = None, deg: bool = True) -> typing.Tuple[float, float, float]:
if vectorize is not None:
fun = vectorize(ecef2geodetic_point)
return fun(x, y, z, ell, deg)
else:
return ecef2geodetic_point(x, y, z, ell, deg)
def ecef2geodetic_point(x: float, y: float, z: float, ell: Ellipsoid = None, deg: bool = True) -> typing.Tuple[float, float, float]:
"""
convert ECEF (meters) to geodetic coordinates
Parameters
----------
x : float
target x ECEF coordinate (meters)
y : float
target y ECEF coordinate (meters)
z : float
target z ECEF coordinate (meters)
ell : Ellipsoid, optional
reference ellipsoid
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
lat : float
target geodetic latitude
lon : float
target geodetic longitude
h : float
target altitude above geodetic ellipsoid (meters)
based on:
You, Rey-Jer. (2000). Transformation of Cartesian to Geodetic Coordinates without Iterations.
Journal of Surveying Engineering. doi: 10.1061/(ASCE)0733-9453
"""
if ell is None:
ell = Ellipsoid()
r = sqrt(x ** 2 + y ** 2 + z ** 2)
E = sqrt(ell.semimajor_axis ** 2 - ell.semiminor_axis ** 2)
# eqn. 4a
u = sqrt(0.5 * (r ** 2 - E ** 2) + 0.5 * sqrt((r ** 2 - E ** 2) ** 2 + 4 * E ** 2 * z ** 2))
Q = hypot(x, y)
huE = hypot(u, E)
# eqn. 4b
try:
Beta = atan(huE / u * z / hypot(x, y))
except ZeroDivisionError:
if z >= 0:
Beta = pi / 2
else:
Beta = -pi / 2
# eqn. 13
eps = ((ell.semiminor_axis * u - ell.semimajor_axis * huE + E ** 2) * sin(Beta)) / (
ell.semimajor_axis * huE * 1 / cos(Beta) - E ** 2 * cos(Beta)
)
Beta += eps
# %% final output
lat = atan(ell.semimajor_axis / ell.semiminor_axis * tan(Beta))
lon = atan2(y, x)
# eqn. 7
alt = hypot(z - ell.semiminor_axis * sin(Beta), Q - ell.semimajor_axis * cos(Beta))
# inside ellipsoid?
inside = x ** 2 / ell.semimajor_axis ** 2 + y ** 2 / ell.semimajor_axis ** 2 + z ** 2 / ell.semiminor_axis ** 2 < 1
if inside:
alt = -alt
if deg:
lat = degrees(lat)
lon = degrees(lon)
return lat, lon, alt
def ecef2enuv(u: float, v: float, w: float, lat0: float, lon0: float, deg: bool = True) -> typing.Tuple[float, float, float]:
"""
VECTOR from observer to target ECEF => ENU
Parameters
----------
u : float
target x ECEF coordinate (meters)
v : float
target y ECEF coordinate (meters)
w : float
target z ECEF coordinate (meters)
lat0 : float
Observer geodetic latitude
lon0 : float
Observer geodetic longitude
h0 : float
observer altitude above geodetic ellipsoid (meters)
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
uEast : float
target east ENU coordinate (meters)
vNorth : float
target north ENU coordinate (meters)
wUp : float
target up ENU coordinate (meters)
"""
if deg:
lat0 = radians(lat0)
lon0 = radians(lon0)
t = cos(lon0) * u + sin(lon0) * v
uEast = -sin(lon0) * u + cos(lon0) * v
wUp = cos(lat0) * t + sin(lat0) * w
vNorth = -sin(lat0) * t + cos(lat0) * w
return uEast, vNorth, wUp
def ecef2enu(
x: float, y: float, z: float, lat0: float, lon0: float, h0: float, ell: Ellipsoid = None, deg: bool = True
) -> typing.Tuple[float, float, float]:
"""
from observer to target, ECEF => ENU
Parameters
----------
x : float
target x ECEF coordinate (meters)
y : float
target y ECEF coordinate (meters)
z : float
target z ECEF coordinate (meters)
lat0 : float
Observer geodetic latitude
lon0 : float
Observer geodetic longitude
h0 : float
observer altitude above geodetic ellipsoid (meters)
ell : Ellipsoid, optional
reference ellipsoid
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
East : float
target east ENU coordinate (meters)
North : float
target north ENU coordinate (meters)
Up : float
target up ENU coordinate (meters)
"""
x0, y0, z0 = geodetic2ecef(lat0, lon0, h0, ell, deg=deg)
return uvw2enu(x - x0, y - y0, z - z0, lat0, lon0, deg=deg)
def enu2uvw(east: float, north: float, up: float, lat0: float, lon0: float, deg: bool = True) -> typing.Tuple[float, float, float]:
"""
Parameters
----------
e1 : float
target east ENU coordinate (meters)
n1 : float
target north ENU coordinate (meters)
u1 : float
target up ENU coordinate (meters)
Results
-------
u : float
v : float
w : float
"""
if deg:
lat0 = radians(lat0)
lon0 = radians(lon0)
t = cos(lat0) * up - sin(lat0) * north
w = sin(lat0) * up + cos(lat0) * north
u = cos(lon0) * t - sin(lon0) * east
v = sin(lon0) * t + cos(lon0) * east
return u, v, w
def uvw2enu(u: float, v: float, w: float, lat0: float, lon0: float, deg: bool = True) -> typing.Tuple[float, float, float]:
"""
Parameters
----------
u : float
v : float
w : float
Results
-------
East : float
target east ENU coordinate (meters)
North : float
target north ENU coordinate (meters)
Up : float
target up ENU coordinate (meters)
"""
if deg:
lat0 = radians(lat0)
lon0 = radians(lon0)
t = cos(lon0) * u + sin(lon0) * v
East = -sin(lon0) * u + cos(lon0) * v
Up = cos(lat0) * t + sin(lat0) * w
North = -sin(lat0) * t + cos(lat0) * w
return East, North, Up
def eci2geodetic(x: float, y: float, z: float, t: datetime, useastropy: bool = True) -> typing.Tuple[float, float, float]:
"""
convert Earth Centered Internal ECI to geodetic coordinates
Parameters
----------
x : float
ECI x-location [meters]
y : float
ECI y-location [meters]
z : float
ECI z-location [meters]
t : datetime.datetime, float
length N vector of datetime OR greenwich sidereal time angle [radians].
Results
-------
lat : float
geodetic latitude
lon : float
geodetic longitude
alt : float
altitude above ellipsoid (meters)
Notes
-----
Conversion is idealized: doesn't consider nutations, perterbations,
etc. like the IAU-76/FK5 or IAU-2000/2006 model-based conversions
from ECI to ECEF
eci2geodetic() a.k.a. eci2lla()
"""
if eci2ecef is None:
raise ImportError("pip install numpy")
xecef, yecef, zecef = eci2ecef(x, y, z, t, useastropy=useastropy)
return ecef2geodetic(xecef, yecef, zecef)
def enu2ecef(
e1: float, n1: float, u1: float, lat0: float, lon0: float, h0: float, ell: Ellipsoid = None, deg: bool = True
) -> typing.Tuple[float, float, float]:
"""
ENU to ECEF
Parameters
----------
e1 : float
target east ENU coordinate (meters)
n1 : float
target north ENU coordinate (meters)
u1 : float
target up ENU coordinate (meters)
lat0 : float
Observer geodetic latitude
lon0 : float
Observer geodetic longitude
h0 : float
observer altitude above geodetic ellipsoid (meters)
ell : Ellipsoid, optional
reference ellipsoid
deg : bool, optional
degrees input/output (False: radians in/out)
Results
-------
x : float
target x ECEF coordinate (meters)
y : float
target y ECEF coordinate (meters)
z : float
target z ECEF coordinate (meters)
"""
x0, y0, z0 = geodetic2ecef(lat0, lon0, h0, ell, deg=deg)
dx, dy, dz = enu2uvw(e1, n1, u1, lat0, lon0, deg=deg)
return x0 + dx, y0 + dy, z0 + dzFunctions
def ecef2enu(x, y, z, lat0, lon0, h0, ell=None, deg=True)-
from observer to target, ECEF => ENU
Parameters
x:float- target x ECEF coordinate (meters)
y:float- target y ECEF coordinate (meters)
z:float- target z ECEF coordinate (meters)
lat0:float- Observer geodetic latitude
lon0:float- Observer geodetic longitude
h0:float- observer altitude above geodetic ellipsoid (meters)
ell:Ellipsoid, optional- reference ellipsoid
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
East:float- target east ENU coordinate (meters)
North:float- target north ENU coordinate (meters)
Up:float- target up ENU coordinate (meters)
Source code
def ecef2enu( x: float, y: float, z: float, lat0: float, lon0: float, h0: float, ell: Ellipsoid = None, deg: bool = True ) -> typing.Tuple[float, float, float]: """ from observer to target, ECEF => ENU Parameters ---------- x : float target x ECEF coordinate (meters) y : float target y ECEF coordinate (meters) z : float target z ECEF coordinate (meters) lat0 : float Observer geodetic latitude lon0 : float Observer geodetic longitude h0 : float observer altitude above geodetic ellipsoid (meters) ell : Ellipsoid, optional reference ellipsoid deg : bool, optional degrees input/output (False: radians in/out) Returns ------- East : float target east ENU coordinate (meters) North : float target north ENU coordinate (meters) Up : float target up ENU coordinate (meters) """ x0, y0, z0 = geodetic2ecef(lat0, lon0, h0, ell, deg=deg) return uvw2enu(x - x0, y - y0, z - z0, lat0, lon0, deg=deg) def ecef2enuv(u, v, w, lat0, lon0, deg=True)-
VECTOR from observer to target ECEF => ENU
Parameters
u:float- target x ECEF coordinate (meters)
v:float- target y ECEF coordinate (meters)
w:float- target z ECEF coordinate (meters)
lat0:float- Observer geodetic latitude
lon0:float- Observer geodetic longitude
h0:float- observer altitude above geodetic ellipsoid (meters)
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
uEast:float- target east ENU coordinate (meters)
vNorth:float- target north ENU coordinate (meters)
wUp:float- target up ENU coordinate (meters)
Source code
def ecef2enuv(u: float, v: float, w: float, lat0: float, lon0: float, deg: bool = True) -> typing.Tuple[float, float, float]: """ VECTOR from observer to target ECEF => ENU Parameters ---------- u : float target x ECEF coordinate (meters) v : float target y ECEF coordinate (meters) w : float target z ECEF coordinate (meters) lat0 : float Observer geodetic latitude lon0 : float Observer geodetic longitude h0 : float observer altitude above geodetic ellipsoid (meters) deg : bool, optional degrees input/output (False: radians in/out) Returns ------- uEast : float target east ENU coordinate (meters) vNorth : float target north ENU coordinate (meters) wUp : float target up ENU coordinate (meters) """ if deg: lat0 = radians(lat0) lon0 = radians(lon0) t = cos(lon0) * u + sin(lon0) * v uEast = -sin(lon0) * u + cos(lon0) * v wUp = cos(lat0) * t + sin(lat0) * w vNorth = -sin(lat0) * t + cos(lat0) * w return uEast, vNorth, wUp def ecef2geodetic(x, y, z, ell=None, deg=True)-
Source code
def ecef2geodetic(x: float, y: float, z: float, ell: Ellipsoid = None, deg: bool = True) -> typing.Tuple[float, float, float]: if vectorize is not None: fun = vectorize(ecef2geodetic_point) return fun(x, y, z, ell, deg) else: return ecef2geodetic_point(x, y, z, ell, deg) def eci2geodetic(x, y, z, t, useastropy=True)-
convert Earth Centered Internal ECI to geodetic coordinates
Parameters
x:float- ECI x-location [meters]
y:float- ECI y-location [meters]
z:float- ECI z-location [meters]
t:datetime.datetime,float- length N vector of datetime OR greenwich sidereal time angle [radians].
Results
lat:float- geodetic latitude
lon:float- geodetic longitude
alt:float- altitude above ellipsoid (meters)
Notes
Conversion is idealized: doesn't consider nutations, perterbations, etc. like the IAU-76/FK5 or IAU-2000/2006 model-based conversions from ECI to ECEF
eci2geodetic() a.k.a. eci2lla()
Source code
def eci2geodetic(x: float, y: float, z: float, t: datetime, useastropy: bool = True) -> typing.Tuple[float, float, float]: """ convert Earth Centered Internal ECI to geodetic coordinates Parameters ---------- x : float ECI x-location [meters] y : float ECI y-location [meters] z : float ECI z-location [meters] t : datetime.datetime, float length N vector of datetime OR greenwich sidereal time angle [radians]. Results ------- lat : float geodetic latitude lon : float geodetic longitude alt : float altitude above ellipsoid (meters) Notes ----- Conversion is idealized: doesn't consider nutations, perterbations, etc. like the IAU-76/FK5 or IAU-2000/2006 model-based conversions from ECI to ECEF eci2geodetic() a.k.a. eci2lla() """ if eci2ecef is None: raise ImportError("pip install numpy") xecef, yecef, zecef = eci2ecef(x, y, z, t, useastropy=useastropy) return ecef2geodetic(xecef, yecef, zecef) def enu2ecef(e1, n1, u1, lat0, lon0, h0, ell=None, deg=True)-
ENU to ECEF
Parameters
e1:float- target east ENU coordinate (meters)
n1:float- target north ENU coordinate (meters)
u1:float- target up ENU coordinate (meters)
lat0:float- Observer geodetic latitude
lon0:float- Observer geodetic longitude
h0:float- observer altitude above geodetic ellipsoid (meters)
ell:Ellipsoid, optional- reference ellipsoid
deg:bool, optional- degrees input/output (False: radians in/out)
Results
x:float- target x ECEF coordinate (meters)
y:float- target y ECEF coordinate (meters)
z:float- target z ECEF coordinate (meters)
Source code
def enu2ecef( e1: float, n1: float, u1: float, lat0: float, lon0: float, h0: float, ell: Ellipsoid = None, deg: bool = True ) -> typing.Tuple[float, float, float]: """ ENU to ECEF Parameters ---------- e1 : float target east ENU coordinate (meters) n1 : float target north ENU coordinate (meters) u1 : float target up ENU coordinate (meters) lat0 : float Observer geodetic latitude lon0 : float Observer geodetic longitude h0 : float observer altitude above geodetic ellipsoid (meters) ell : Ellipsoid, optional reference ellipsoid deg : bool, optional degrees input/output (False: radians in/out) Results ------- x : float target x ECEF coordinate (meters) y : float target y ECEF coordinate (meters) z : float target z ECEF coordinate (meters) """ x0, y0, z0 = geodetic2ecef(lat0, lon0, h0, ell, deg=deg) dx, dy, dz = enu2uvw(e1, n1, u1, lat0, lon0, deg=deg) return x0 + dx, y0 + dy, z0 + dz def enu2uvw(east, north, up, lat0, lon0, deg=True)-
Parameters
e1:float- target east ENU coordinate (meters)
n1:float- target north ENU coordinate (meters)
u1:float- target up ENU coordinate (meters)
Results
u:floatv:floatw:float
Source code
def enu2uvw(east: float, north: float, up: float, lat0: float, lon0: float, deg: bool = True) -> typing.Tuple[float, float, float]: """ Parameters ---------- e1 : float target east ENU coordinate (meters) n1 : float target north ENU coordinate (meters) u1 : float target up ENU coordinate (meters) Results ------- u : float v : float w : float """ if deg: lat0 = radians(lat0) lon0 = radians(lon0) t = cos(lat0) * up - sin(lat0) * north w = sin(lat0) * up + cos(lat0) * north u = cos(lon0) * t - sin(lon0) * east v = sin(lon0) * t + cos(lon0) * east return u, v, w def geodetic2ecef(lat, lon, alt, ell=None, deg=True)-
point transformation from Geodetic of specified ellipsoid (default WGS-84) to ECEF
Parameters
lat:float- target geodetic latitude
lon:float- target geodetic longitude
h:float- target altitude above geodetic ellipsoid (meters)
ell:Ellipsoid, optional- reference ellipsoid
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
ECEF(Earthcentered,Earthfixed)x,y,zx:float- target x ECEF coordinate (meters)
y:float- target y ECEF coordinate (meters)
z:float- target z ECEF coordinate (meters)
Source code
def geodetic2ecef(lat: float, lon: float, alt: float, ell: Ellipsoid = None, deg: bool = True) -> typing.Tuple[float, float, float]: """ point transformation from Geodetic of specified ellipsoid (default WGS-84) to ECEF Parameters ---------- lat : float target geodetic latitude lon : float target geodetic longitude h : float target altitude above geodetic ellipsoid (meters) ell : Ellipsoid, optional reference ellipsoid deg : bool, optional degrees input/output (False: radians in/out) Returns ------- ECEF (Earth centered, Earth fixed) x,y,z x : float target x ECEF coordinate (meters) y : float target y ECEF coordinate (meters) z : float target z ECEF coordinate (meters) """ lat, ell = sanitize(lat, ell, deg) if deg: lon = radians(lon) # radius of curvature of the prime vertical section N = ell.semimajor_axis ** 2 / sqrt(ell.semimajor_axis ** 2 * cos(lat) ** 2 + ell.semiminor_axis ** 2 * sin(lat) ** 2) # Compute cartesian (geocentric) coordinates given (curvilinear) geodetic # coordinates. x = (N + alt) * cos(lat) * cos(lon) y = (N + alt) * cos(lat) * sin(lon) z = (N * (ell.semiminor_axis / ell.semimajor_axis) ** 2 + alt) * sin(lat) return x, y, z def uvw2enu(u, v, w, lat0, lon0, deg=True)-
Parameters
u:floatv:floatw:float
Results
East:float- target east ENU coordinate (meters)
North:float- target north ENU coordinate (meters)
Up:float- target up ENU coordinate (meters)
Source code
def uvw2enu(u: float, v: float, w: float, lat0: float, lon0: float, deg: bool = True) -> typing.Tuple[float, float, float]: """ Parameters ---------- u : float v : float w : float Results ------- East : float target east ENU coordinate (meters) North : float target north ENU coordinate (meters) Up : float target up ENU coordinate (meters) """ if deg: lat0 = radians(lat0) lon0 = radians(lon0) t = cos(lon0) * u + sin(lon0) * v East = -sin(lon0) * u + cos(lon0) * v Up = cos(lat0) * t + sin(lat0) * w North = -sin(lat0) * t + cos(lat0) * w return East, North, Up