Module pymap3d.latitude
geodetic transforms to auxilary coordinate systems involving latitude
Source code
"""geodetic transforms to auxilary coordinate systems involving latitude"""
from .ellipsoid import Ellipsoid
from .utils import sanitize
try:
from numpy import radians, degrees, tan, sin, exp, pi, sqrt, inf, vectorize
from numpy import arctan as atan, arcsinh as asinh, arctanh as atanh # noqa: A001
use_numpy = True
except ImportError:
from math import atan, radians, degrees, tan, sin, asinh, atanh, exp, pi, sqrt, inf
use_numpy = False
__all__ = [
"geodetic2isometric",
"isometric2geodetic",
"geodetic2rectifying",
"rectifying2geodetic",
"geodetic2conformal",
"conformal2geodetic",
"geodetic2parametric",
"parametric2geodetic",
"geodetic2geocentric",
"geocentric2geodetic",
"geodetic2authalic",
"authalic2geodetic",
]
def geodetic2geocentric(geodetic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
"""
convert geodetic latitude to geocentric latitude.
like Matlab geocentricLatitude()
Parameters
----------
geodetic_lat : float
geodetic latitude
ell : Ellipsoid, optional
reference ellipsoid (default WGS84)
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
geocentric_lat : float
geocentric latiude
Notes
-----
Equations from J. P. Snyder, "Map Projections - A Working Manual",
US Geological Survey Professional Paper 1395, US Government Printing
Office, Washington, DC, 1987, pp. 13-18.
"""
geodetic_lat, ell = sanitize(geodetic_lat, ell, deg)
geocentric_lat = atan((1 - (ell.eccentricity) ** 2) * tan(geodetic_lat))
return degrees(geocentric_lat) if deg else geocentric_lat
def geocentric2geodetic(geocentric_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
"""
converts from geocentric latitude to geodetic latitude
like Matlab geodeticLatitudeFromGeocentric()
Parameters
----------
geocentric_lat : float
geocentric latitude
ell : Ellipsoid, optional
reference ellipsoid (default WGS84)
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
geodetic_lat : float
geodetic latiude
Notes
-----
Equations from J. P. Snyder, "Map Projections - A Working Manual",
US Geological Survey Professional Paper 1395, US Government Printing
Office, Washington, DC, 1987, pp. 13-18.
"""
geocentric_lat, ell = sanitize(geocentric_lat, ell, deg)
geodetic_lat = atan(tan(geocentric_lat) / (1 - (ell.eccentricity) ** 2))
return degrees(geodetic_lat) if deg else geodetic_lat
def geodetic2isometric_point(geodetic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
geodetic_lat, ell = sanitize(geodetic_lat, ell, deg)
e = ell.eccentricity
if abs(geodetic_lat - pi / 2) <= 1e-9:
isometric_lat = inf
elif abs(-geodetic_lat - pi / 2) <= 1e-9:
isometric_lat = -inf
else:
isometric_lat = asinh(tan(geodetic_lat)) - e * atanh(e * sin(geodetic_lat))
# same results
# a1 = e * sin(geodetic_lat)
# y = (1 - a1) / (1 + a1)
# a2 = pi / 4 + geodetic_lat / 2
# isometric_lat = log(tan(a2) * (y ** (e / 2)))
# isometric_lat = log(tan(a2)) + e/2 * log((1-e*sin(geodetic_lat)) / (1+e*sin(geodetic_lat)))
return degrees(isometric_lat) if deg else isometric_lat
def geodetic2isometric(geodetic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
"""
computes isometric latitude on an ellipsoid
like Matlab map.geodesy.IsometricLatitudeConverter.forward()
Parameters
----------
lat : float
geodetic latitude
ell : Ellipsoid, optional
reference ellipsoid (default WGS84)
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
isolat : float
isometric latiude
Notes
-----
Isometric latitude is an auxiliary latitude proportional to the spacing
of parallels of latitude on an ellipsoidal mercator projection.
Based on Deakin, R.E., 2010, 'The Loxodrome on an Ellipsoid', Lecture Notes,
School of Mathematical and Geospatial Sciences, RMIT University,
January 2010
"""
if use_numpy:
fun = vectorize(geodetic2isometric_point)
return fun(geodetic_lat, ell, deg)
else:
return geodetic2isometric_point(geodetic_lat, ell, deg)
def isometric2geodetic(isometric_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
"""
converts from isometric latitude to geodetic latitude
like Matlab map.geodesy.IsometricLatitudeConverter.inverse()
Parameters
----------
isometric_lat : float
isometric latitude
ell : Ellipsoid, optional
reference ellipsoid (default WGS84)
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
geodetic_lat : float
geodetic latiude
Notes
-----
Equations from J. P. Snyder, "Map Projections - A Working Manual",
US Geological Survey Professional Paper 1395, US Government Printing
Office, Washington, DC, 1987, pp. 13-18.
"""
# NOT sanitize for isometric2geo
if deg:
isometric_lat = radians(isometric_lat)
conformal_lat = 2 * atan(exp(isometric_lat)) - (pi / 2)
geodetic_lat = conformal2geodetic(conformal_lat, ell, deg=False)
return degrees(geodetic_lat) if deg else geodetic_lat
def conformal2geodetic(conformal_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
"""
converts from conformal latitude to geodetic latitude
like Matlab map.geodesy.ConformalLatitudeConverter.inverse()
Parameters
----------
conformal_lat : float
conformal latitude
ell : Ellipsoid, optional
reference ellipsoid (default WGS84)
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
geodetic_lat : float
geodetic latiude
Notes
-----
Equations from J. P. Snyder, "Map Projections - A Working Manual",
US Geological Survey Professional Paper 1395, US Government Printing
Office, Washington, DC, 1987, pp. 13-18.
"""
conformal_lat, ell = sanitize(conformal_lat, ell, deg)
e = ell.eccentricity
f1 = e ** 2 / 2 + 5 * e ** 4 / 24 + e ** 6 / 12 + 13 * e ** 8 / 360
f2 = 7 * e ** 4 / 48 + 29 * e ** 6 / 240 + 811 * e ** 8 / 11520
f3 = 7 * e ** 6 / 120 + 81 * e ** 8 / 1120
f4 = 4279 * e ** 8 / 161280
geodetic_lat = (
conformal_lat
+ f1 * sin(2 * conformal_lat)
+ f2 * sin(4 * conformal_lat)
+ f3 * sin(6 * conformal_lat)
+ f4 * sin(8 * conformal_lat)
)
return degrees(geodetic_lat) if deg else geodetic_lat
def geodetic2conformal(geodetic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
"""
converts from geodetic latitude to conformal latitude
like Matlab map.geodesy.ConformalLatitudeConverter.forward()
Parameters
----------
geodetic_lat : float
geodetic latitude
ell : Ellipsoid, optional
reference ellipsoid (default WGS84)
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
conformal_lat : float
conformal latiude
Notes
-----
Equations from J. P. Snyder, "Map Projections - A Working Manual",
US Geological Survey Professional Paper 1395, US Government Printing
Office, Washington, DC, 1987, pp. 13-18.
"""
if use_numpy:
fun = vectorize(geodetic2conformal_point)
return fun(geodetic_lat, ell, deg)
else:
return geodetic2conformal_point(geodetic_lat, ell, deg)
def geodetic2conformal_point(geodetic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
geodetic_lat, ell = sanitize(geodetic_lat, ell, deg)
e = ell.eccentricity
f1 = 1 - e * sin(geodetic_lat)
f2 = 1 + e * sin(geodetic_lat)
f3 = 1 - sin(geodetic_lat)
f4 = 1 + sin(geodetic_lat)
# compute conformal latitudes with correction for points at +90
try:
conformal_lat = 2 * atan(sqrt((f4 / f3) * ((f1 / f2) ** e))) - (pi / 2)
except ZeroDivisionError:
conformal_lat = pi / 2
return degrees(conformal_lat) if deg else conformal_lat
# %% rectifying
def geodetic2rectifying(geodetic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
"""
converts from geodetic latitude to rectifying latitude
like Matlab map.geodesy.RectifyingLatitudeConverter.forward()
Parameters
----------
geodetic_lat : float
geodetic latitude
ell : Ellipsoid, optional
reference ellipsoid (default WGS84)
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
rectifying_lat : float
rectifying latiude
Notes
-----
Equations from J. P. Snyder, "Map Projections - A Working Manual",
US Geological Survey Professional Paper 1395, US Government Printing
Office, Washington, DC, 1987, pp. 13-18.
"""
geodetic_lat, ell = sanitize(geodetic_lat, ell, deg)
n = ell.thirdflattening
f1 = 3 * n / 2 - 9 * n ** 3 / 16
f2 = 15 * n ** 2 / 16 - 15 * n ** 4 / 32
f3 = 35 * n ** 3 / 48
f4 = 315 * n ** 4 / 512
rectifying_lat = (
geodetic_lat
- f1 * sin(2 * geodetic_lat)
+ f2 * sin(4 * geodetic_lat)
- f3 * sin(6 * geodetic_lat)
+ f4 * sin(8 * geodetic_lat)
)
return degrees(rectifying_lat) if deg else rectifying_lat
def rectifying2geodetic(rectifying_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
"""
converts from rectifying latitude to geodetic latitude
like Matlab map.geodesy.RectifyingLatitudeConverter.inverse()
Parameters
----------
rectifying_lat : float
latitude
ell : Ellipsoid, optional
reference ellipsoid (default WGS84)
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
geodetic_lat : float
geodetic latiude
Notes
-----
Equations from J. P. Snyder, "Map Projections - A Working Manual",
US Geological Survey Professional Paper 1395, US Government Printing
Office, Washington, DC, 1987, pp. 13-18.
"""
rectifying_lat, ell = sanitize(rectifying_lat, ell, deg)
n = ell.thirdflattening
f1 = 3 * n / 2 - 27 * n ** 3 / 32
f2 = 21 * n ** 2 / 16 - 55 * n ** 4 / 32
f3 = 151 * n ** 3 / 96
f4 = 1097 * n ** 4 / 512
geodetic_lat = (
rectifying_lat
+ f1 * sin(2 * rectifying_lat)
+ f2 * sin(4 * rectifying_lat)
+ f3 * sin(6 * rectifying_lat)
+ f4 * sin(8 * rectifying_lat)
)
return degrees(geodetic_lat) if deg else geodetic_lat
# %% authalic
def geodetic2authalic(geodetic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
"""
converts from geodetic latitude to authalic latitude
like Matlab map.geodesy.AuthalicLatitudeConverter.forward()
Parameters
----------
geodetic_lat : float
geodetic latitude
ell : Ellipsoid, optional
reference ellipsoid (default WGS84)
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
authalic_lat : float
authalic latiude
Notes
-----
Equations from J. P. Snyder, "Map Projections - A Working Manual",
US Geological Survey Professional Paper 1395, US Government Printing
Office, Washington, DC, 1987, pp. 13-18.
"""
geodetic_lat, ell = sanitize(geodetic_lat, ell, deg)
e = ell.eccentricity
f1 = e ** 2 / 3 + 31 * e ** 4 / 180 + 59 * e ** 6 / 560
f2 = 17 * e ** 4 / 360 + 61 * e ** 6 / 1260
f3 = 383 * e ** 6 / 45360
authalic_lat = geodetic_lat - f1 * sin(2 * geodetic_lat) + f2 * sin(4 * geodetic_lat) - f3 * sin(6 * geodetic_lat)
return degrees(authalic_lat) if deg else authalic_lat
def authalic2geodetic(authalic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
"""
converts from authalic latitude to geodetic latitude
like Matlab map.geodesy.AuthalicLatitudeConverter.inverse()
Parameters
----------
authalic_lat : float
latitude
ell : Ellipsoid, optional
reference ellipsoid (default WGS84)
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
geodetic_lat : float
geodetic latiude
Notes
-----
Equations from J. P. Snyder, "Map Projections - A Working Manual",
US Geological Survey Professional Paper 1395, US Government Printing
Office, Washington, DC, 1987, pp. 13-18.
"""
authalic_lat, ell = sanitize(authalic_lat, ell, deg)
e = ell.eccentricity
f1 = e ** 2 / 3 + 31 * e ** 4 / 180 + 517 * e ** 6 / 5040
f2 = 23 * e ** 4 / 360 + 251 * e ** 6 / 3780
f3 = 761 * e ** 6 / 45360
geodetic_lat = authalic_lat + f1 * sin(2 * authalic_lat) + f2 * sin(4 * authalic_lat) + f3 * sin(6 * authalic_lat)
return degrees(geodetic_lat) if deg else geodetic_lat
# %% parametric
def geodetic2parametric(geodetic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
"""
converts from geodetic latitude to parametric latitude
like Matlab parametriclatitude()
Parameters
----------
geodetic_lat : float
geodetic latitude
ell : Ellipsoid, optional
reference ellipsoid (default WGS84)
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
parametric_lat : float
parametric latiude
Notes
-----
Equations from J. P. Snyder, "Map Projections - A Working Manual",
US Geological Survey Professional Paper 1395, US Government Printing
Office, Washington, DC, 1987, pp. 13-18.
"""
geodetic_lat, ell = sanitize(geodetic_lat, ell, deg)
parametric_lat = atan(sqrt(1 - (ell.eccentricity) ** 2) * tan(geodetic_lat))
return degrees(parametric_lat) if deg else parametric_lat
def parametric2geodetic(parametric_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
"""
converts from parametric latitude to geodetic latitude
like Matlab geodeticLatitudeFromParametric()
Parameters
----------
parametric_lat : float
latitude
ell : Ellipsoid, optional
reference ellipsoid (default WGS84)
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
geodetic_lat : float
geodetic latiude
Notes
-----
Equations from J. P. Snyder, "Map Projections - A Working Manual",
US Geological Survey Professional Paper 1395, US Government Printing
Office, Washington, DC, 1987, pp. 13-18.
"""
parametric_lat, ell = sanitize(parametric_lat, ell, deg)
geodetic_lat = atan(tan(parametric_lat) / sqrt(1 - (ell.eccentricity) ** 2))
return degrees(geodetic_lat) if deg else geodetic_latFunctions
def authalic2geodetic(authalic_lat, ell=None, deg=True)-
converts from authalic latitude to geodetic latitude
like Matlab map.geodesy.AuthalicLatitudeConverter.inverse()
Parameters
authalic_lat:float- latitude
ell:Ellipsoid, optional- reference ellipsoid (default WGS84)
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
geodetic_lat:float- geodetic latiude
Notes
Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18.
Source code
def authalic2geodetic(authalic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float: """ converts from authalic latitude to geodetic latitude like Matlab map.geodesy.AuthalicLatitudeConverter.inverse() Parameters ---------- authalic_lat : float latitude ell : Ellipsoid, optional reference ellipsoid (default WGS84) deg : bool, optional degrees input/output (False: radians in/out) Returns ------- geodetic_lat : float geodetic latiude Notes ----- Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18. """ authalic_lat, ell = sanitize(authalic_lat, ell, deg) e = ell.eccentricity f1 = e ** 2 / 3 + 31 * e ** 4 / 180 + 517 * e ** 6 / 5040 f2 = 23 * e ** 4 / 360 + 251 * e ** 6 / 3780 f3 = 761 * e ** 6 / 45360 geodetic_lat = authalic_lat + f1 * sin(2 * authalic_lat) + f2 * sin(4 * authalic_lat) + f3 * sin(6 * authalic_lat) return degrees(geodetic_lat) if deg else geodetic_lat def conformal2geodetic(conformal_lat, ell=None, deg=True)-
converts from conformal latitude to geodetic latitude
like Matlab map.geodesy.ConformalLatitudeConverter.inverse()
Parameters
conformal_lat:float- conformal latitude
ell:Ellipsoid, optional- reference ellipsoid (default WGS84)
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
geodetic_lat:float- geodetic latiude
Notes
Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18.
Source code
def conformal2geodetic(conformal_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float: """ converts from conformal latitude to geodetic latitude like Matlab map.geodesy.ConformalLatitudeConverter.inverse() Parameters ---------- conformal_lat : float conformal latitude ell : Ellipsoid, optional reference ellipsoid (default WGS84) deg : bool, optional degrees input/output (False: radians in/out) Returns ------- geodetic_lat : float geodetic latiude Notes ----- Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18. """ conformal_lat, ell = sanitize(conformal_lat, ell, deg) e = ell.eccentricity f1 = e ** 2 / 2 + 5 * e ** 4 / 24 + e ** 6 / 12 + 13 * e ** 8 / 360 f2 = 7 * e ** 4 / 48 + 29 * e ** 6 / 240 + 811 * e ** 8 / 11520 f3 = 7 * e ** 6 / 120 + 81 * e ** 8 / 1120 f4 = 4279 * e ** 8 / 161280 geodetic_lat = ( conformal_lat + f1 * sin(2 * conformal_lat) + f2 * sin(4 * conformal_lat) + f3 * sin(6 * conformal_lat) + f4 * sin(8 * conformal_lat) ) return degrees(geodetic_lat) if deg else geodetic_lat def geocentric2geodetic(geocentric_lat, ell=None, deg=True)-
converts from geocentric latitude to geodetic latitude
like Matlab geodeticLatitudeFromGeocentric()
Parameters
geocentric_lat:float- geocentric latitude
ell:Ellipsoid, optional- reference ellipsoid (default WGS84)
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
geodetic_lat:float- geodetic latiude
Notes
Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18.
Source code
def geocentric2geodetic(geocentric_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float: """ converts from geocentric latitude to geodetic latitude like Matlab geodeticLatitudeFromGeocentric() Parameters ---------- geocentric_lat : float geocentric latitude ell : Ellipsoid, optional reference ellipsoid (default WGS84) deg : bool, optional degrees input/output (False: radians in/out) Returns ------- geodetic_lat : float geodetic latiude Notes ----- Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18. """ geocentric_lat, ell = sanitize(geocentric_lat, ell, deg) geodetic_lat = atan(tan(geocentric_lat) / (1 - (ell.eccentricity) ** 2)) return degrees(geodetic_lat) if deg else geodetic_lat def geodetic2authalic(geodetic_lat, ell=None, deg=True)-
converts from geodetic latitude to authalic latitude
like Matlab map.geodesy.AuthalicLatitudeConverter.forward()
Parameters
geodetic_lat:float- geodetic latitude
ell:Ellipsoid, optional- reference ellipsoid (default WGS84)
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
authalic_lat:float- authalic latiude
Notes
Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18.
Source code
def geodetic2authalic(geodetic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float: """ converts from geodetic latitude to authalic latitude like Matlab map.geodesy.AuthalicLatitudeConverter.forward() Parameters ---------- geodetic_lat : float geodetic latitude ell : Ellipsoid, optional reference ellipsoid (default WGS84) deg : bool, optional degrees input/output (False: radians in/out) Returns ------- authalic_lat : float authalic latiude Notes ----- Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18. """ geodetic_lat, ell = sanitize(geodetic_lat, ell, deg) e = ell.eccentricity f1 = e ** 2 / 3 + 31 * e ** 4 / 180 + 59 * e ** 6 / 560 f2 = 17 * e ** 4 / 360 + 61 * e ** 6 / 1260 f3 = 383 * e ** 6 / 45360 authalic_lat = geodetic_lat - f1 * sin(2 * geodetic_lat) + f2 * sin(4 * geodetic_lat) - f3 * sin(6 * geodetic_lat) return degrees(authalic_lat) if deg else authalic_lat def geodetic2conformal(geodetic_lat, ell=None, deg=True)-
converts from geodetic latitude to conformal latitude
like Matlab map.geodesy.ConformalLatitudeConverter.forward()
Parameters
geodetic_lat:float- geodetic latitude
ell:Ellipsoid, optional- reference ellipsoid (default WGS84)
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
conformal_lat:float- conformal latiude
Notes
Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18.
Source code
def geodetic2conformal(geodetic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float: """ converts from geodetic latitude to conformal latitude like Matlab map.geodesy.ConformalLatitudeConverter.forward() Parameters ---------- geodetic_lat : float geodetic latitude ell : Ellipsoid, optional reference ellipsoid (default WGS84) deg : bool, optional degrees input/output (False: radians in/out) Returns ------- conformal_lat : float conformal latiude Notes ----- Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18. """ if use_numpy: fun = vectorize(geodetic2conformal_point) return fun(geodetic_lat, ell, deg) else: return geodetic2conformal_point(geodetic_lat, ell, deg) def geodetic2geocentric(geodetic_lat, ell=None, deg=True)-
convert geodetic latitude to geocentric latitude.
like Matlab geocentricLatitude()
Parameters
geodetic_lat:float- geodetic latitude
ell:Ellipsoid, optional- reference ellipsoid (default WGS84)
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
geocentric_lat:float- geocentric latiude
Notes
Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18.
Source code
def geodetic2geocentric(geodetic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float: """ convert geodetic latitude to geocentric latitude. like Matlab geocentricLatitude() Parameters ---------- geodetic_lat : float geodetic latitude ell : Ellipsoid, optional reference ellipsoid (default WGS84) deg : bool, optional degrees input/output (False: radians in/out) Returns ------- geocentric_lat : float geocentric latiude Notes ----- Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18. """ geodetic_lat, ell = sanitize(geodetic_lat, ell, deg) geocentric_lat = atan((1 - (ell.eccentricity) ** 2) * tan(geodetic_lat)) return degrees(geocentric_lat) if deg else geocentric_lat def geodetic2isometric(geodetic_lat, ell=None, deg=True)-
computes isometric latitude on an ellipsoid
like Matlab map.geodesy.IsometricLatitudeConverter.forward()
Parameters
lat:float- geodetic latitude
ell:Ellipsoid, optional- reference ellipsoid (default WGS84)
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
isolat:float- isometric latiude
Notes
Isometric latitude is an auxiliary latitude proportional to the spacing of parallels of latitude on an ellipsoidal mercator projection. Based on Deakin, R.E., 2010, 'The Loxodrome on an Ellipsoid', Lecture Notes, School of Mathematical and Geospatial Sciences, RMIT University, January 2010
Source code
def geodetic2isometric(geodetic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float: """ computes isometric latitude on an ellipsoid like Matlab map.geodesy.IsometricLatitudeConverter.forward() Parameters ---------- lat : float geodetic latitude ell : Ellipsoid, optional reference ellipsoid (default WGS84) deg : bool, optional degrees input/output (False: radians in/out) Returns ------- isolat : float isometric latiude Notes ----- Isometric latitude is an auxiliary latitude proportional to the spacing of parallels of latitude on an ellipsoidal mercator projection. Based on Deakin, R.E., 2010, 'The Loxodrome on an Ellipsoid', Lecture Notes, School of Mathematical and Geospatial Sciences, RMIT University, January 2010 """ if use_numpy: fun = vectorize(geodetic2isometric_point) return fun(geodetic_lat, ell, deg) else: return geodetic2isometric_point(geodetic_lat, ell, deg) def geodetic2parametric(geodetic_lat, ell=None, deg=True)-
converts from geodetic latitude to parametric latitude
like Matlab parametriclatitude()
Parameters
geodetic_lat:float- geodetic latitude
ell:Ellipsoid, optional- reference ellipsoid (default WGS84)
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
parametric_lat:float- parametric latiude
Notes
Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18.
Source code
def geodetic2parametric(geodetic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float: """ converts from geodetic latitude to parametric latitude like Matlab parametriclatitude() Parameters ---------- geodetic_lat : float geodetic latitude ell : Ellipsoid, optional reference ellipsoid (default WGS84) deg : bool, optional degrees input/output (False: radians in/out) Returns ------- parametric_lat : float parametric latiude Notes ----- Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18. """ geodetic_lat, ell = sanitize(geodetic_lat, ell, deg) parametric_lat = atan(sqrt(1 - (ell.eccentricity) ** 2) * tan(geodetic_lat)) return degrees(parametric_lat) if deg else parametric_lat def geodetic2rectifying(geodetic_lat, ell=None, deg=True)-
converts from geodetic latitude to rectifying latitude
like Matlab map.geodesy.RectifyingLatitudeConverter.forward()
Parameters
geodetic_lat:float- geodetic latitude
ell:Ellipsoid, optional- reference ellipsoid (default WGS84)
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
rectifying_lat:float- rectifying latiude
Notes
Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18.
Source code
def geodetic2rectifying(geodetic_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float: """ converts from geodetic latitude to rectifying latitude like Matlab map.geodesy.RectifyingLatitudeConverter.forward() Parameters ---------- geodetic_lat : float geodetic latitude ell : Ellipsoid, optional reference ellipsoid (default WGS84) deg : bool, optional degrees input/output (False: radians in/out) Returns ------- rectifying_lat : float rectifying latiude Notes ----- Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18. """ geodetic_lat, ell = sanitize(geodetic_lat, ell, deg) n = ell.thirdflattening f1 = 3 * n / 2 - 9 * n ** 3 / 16 f2 = 15 * n ** 2 / 16 - 15 * n ** 4 / 32 f3 = 35 * n ** 3 / 48 f4 = 315 * n ** 4 / 512 rectifying_lat = ( geodetic_lat - f1 * sin(2 * geodetic_lat) + f2 * sin(4 * geodetic_lat) - f3 * sin(6 * geodetic_lat) + f4 * sin(8 * geodetic_lat) ) return degrees(rectifying_lat) if deg else rectifying_lat def isometric2geodetic(isometric_lat, ell=None, deg=True)-
converts from isometric latitude to geodetic latitude
like Matlab map.geodesy.IsometricLatitudeConverter.inverse()
Parameters
isometric_lat:float- isometric latitude
ell:Ellipsoid, optional- reference ellipsoid (default WGS84)
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
geodetic_lat:float- geodetic latiude
Notes
Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18.
Source code
def isometric2geodetic(isometric_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float: """ converts from isometric latitude to geodetic latitude like Matlab map.geodesy.IsometricLatitudeConverter.inverse() Parameters ---------- isometric_lat : float isometric latitude ell : Ellipsoid, optional reference ellipsoid (default WGS84) deg : bool, optional degrees input/output (False: radians in/out) Returns ------- geodetic_lat : float geodetic latiude Notes ----- Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18. """ # NOT sanitize for isometric2geo if deg: isometric_lat = radians(isometric_lat) conformal_lat = 2 * atan(exp(isometric_lat)) - (pi / 2) geodetic_lat = conformal2geodetic(conformal_lat, ell, deg=False) return degrees(geodetic_lat) if deg else geodetic_lat def parametric2geodetic(parametric_lat, ell=None, deg=True)-
converts from parametric latitude to geodetic latitude
like Matlab geodeticLatitudeFromParametric()
Parameters
parametric_lat:float- latitude
ell:Ellipsoid, optional- reference ellipsoid (default WGS84)
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
geodetic_lat:float- geodetic latiude
Notes
Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18.
Source code
def parametric2geodetic(parametric_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float: """ converts from parametric latitude to geodetic latitude like Matlab geodeticLatitudeFromParametric() Parameters ---------- parametric_lat : float latitude ell : Ellipsoid, optional reference ellipsoid (default WGS84) deg : bool, optional degrees input/output (False: radians in/out) Returns ------- geodetic_lat : float geodetic latiude Notes ----- Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18. """ parametric_lat, ell = sanitize(parametric_lat, ell, deg) geodetic_lat = atan(tan(parametric_lat) / sqrt(1 - (ell.eccentricity) ** 2)) return degrees(geodetic_lat) if deg else geodetic_lat def rectifying2geodetic(rectifying_lat, ell=None, deg=True)-
converts from rectifying latitude to geodetic latitude
like Matlab map.geodesy.RectifyingLatitudeConverter.inverse()
Parameters
rectifying_lat:float- latitude
ell:Ellipsoid, optional- reference ellipsoid (default WGS84)
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
geodetic_lat:float- geodetic latiude
Notes
Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18.
Source code
def rectifying2geodetic(rectifying_lat: float, ell: Ellipsoid = None, deg: bool = True) -> float: """ converts from rectifying latitude to geodetic latitude like Matlab map.geodesy.RectifyingLatitudeConverter.inverse() Parameters ---------- rectifying_lat : float latitude ell : Ellipsoid, optional reference ellipsoid (default WGS84) deg : bool, optional degrees input/output (False: radians in/out) Returns ------- geodetic_lat : float geodetic latiude Notes ----- Equations from J. P. Snyder, "Map Projections - A Working Manual", US Geological Survey Professional Paper 1395, US Government Printing Office, Washington, DC, 1987, pp. 13-18. """ rectifying_lat, ell = sanitize(rectifying_lat, ell, deg) n = ell.thirdflattening f1 = 3 * n / 2 - 27 * n ** 3 / 32 f2 = 21 * n ** 2 / 16 - 55 * n ** 4 / 32 f3 = 151 * n ** 3 / 96 f4 = 1097 * n ** 4 / 512 geodetic_lat = ( rectifying_lat + f1 * sin(2 * rectifying_lat) + f2 * sin(4 * rectifying_lat) + f3 * sin(6 * rectifying_lat) + f4 * sin(8 * rectifying_lat) ) return degrees(geodetic_lat) if deg else geodetic_lat