Module pymap3d.rcurve
compute radii of curvature for an ellipsoid
Source code
"""compute radii of curvature for an ellipsoid"""
try:
from numpy import radians, sin, cos, sqrt
except ImportError:
from math import radians, sin, cos, sqrt
from .ellipsoid import Ellipsoid
__all__ = ["rcurve_parallel", "rcurve_meridian", "rcurve_transverse"]
def rcurve_parallel(lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
"""
computes the radius of the small circle encompassing the globe at the specified latitude
Parameters
----------
lat : float
geodetic latitude (degrees)
ell : Ellipsoid, optional
reference ellipsoid
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
radius: float
radius of ellipsoid
"""
if deg:
lat = radians(lat)
return cos(lat) * rcurve_transverse(lat, ell, deg=False)
def rcurve_meridian(lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
"""computes the meridional radius of curvature for the ellipsoid
Parameters
----------
lat : float
geodetic latitude (degrees)
ell : Ellipsoid, optional
reference ellipsoid
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
radius: float
radius of ellipsoid
"""
if ell is None:
ell = Ellipsoid()
if deg:
lat = radians(lat)
f1 = ell.semimajor_axis * (1 - ell.eccentricity ** 2)
f2 = 1 - (ell.eccentricity * sin(lat)) ** 2
return f1 / sqrt(f2 ** 3)
def rcurve_transverse(lat: float, ell: Ellipsoid = None, deg: bool = True) -> float:
"""computes the radius of the curve formed by a plane
intersecting the ellipsoid at the latitude which is
normal to the surface of the ellipsoid
Parameters
----------
lat : float
geodetic latitude (degrees)
ell : Ellipsoid, optional
reference ellipsoid
deg : bool, optional
degrees input/output (False: radians in/out)
Returns
-------
radius: float
radius of ellipsoid
"""
if ell is None:
ell = Ellipsoid()
if deg:
lat = radians(lat)
return ell.semimajor_axis / sqrt(1 - (ell.eccentricity * sin(lat)) ** 2)Functions
def rcurve_meridian(lat, ell=None, deg=True)-
computes the meridional radius of curvature for the ellipsoid
Parameters
lat:float- geodetic latitude (degrees)
ell:Ellipsoid, optional- reference ellipsoid
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
radius:float- radius of ellipsoid
Source code
def rcurve_meridian(lat: float, ell: Ellipsoid = None, deg: bool = True) -> float: """computes the meridional radius of curvature for the ellipsoid Parameters ---------- lat : float geodetic latitude (degrees) ell : Ellipsoid, optional reference ellipsoid deg : bool, optional degrees input/output (False: radians in/out) Returns ------- radius: float radius of ellipsoid """ if ell is None: ell = Ellipsoid() if deg: lat = radians(lat) f1 = ell.semimajor_axis * (1 - ell.eccentricity ** 2) f2 = 1 - (ell.eccentricity * sin(lat)) ** 2 return f1 / sqrt(f2 ** 3) def rcurve_parallel(lat, ell=None, deg=True)-
computes the radius of the small circle encompassing the globe at the specified latitude
Parameters
lat:float- geodetic latitude (degrees)
ell:Ellipsoid, optional- reference ellipsoid
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
radius:float- radius of ellipsoid
Source code
def rcurve_parallel(lat: float, ell: Ellipsoid = None, deg: bool = True) -> float: """ computes the radius of the small circle encompassing the globe at the specified latitude Parameters ---------- lat : float geodetic latitude (degrees) ell : Ellipsoid, optional reference ellipsoid deg : bool, optional degrees input/output (False: radians in/out) Returns ------- radius: float radius of ellipsoid """ if deg: lat = radians(lat) return cos(lat) * rcurve_transverse(lat, ell, deg=False) def rcurve_transverse(lat, ell=None, deg=True)-
computes the radius of the curve formed by a plane intersecting the ellipsoid at the latitude which is normal to the surface of the ellipsoid
Parameters
lat:float- geodetic latitude (degrees)
ell:Ellipsoid, optional- reference ellipsoid
deg:bool, optional- degrees input/output (False: radians in/out)
Returns
radius:float- radius of ellipsoid
Source code
def rcurve_transverse(lat: float, ell: Ellipsoid = None, deg: bool = True) -> float: """computes the radius of the curve formed by a plane intersecting the ellipsoid at the latitude which is normal to the surface of the ellipsoid Parameters ---------- lat : float geodetic latitude (degrees) ell : Ellipsoid, optional reference ellipsoid deg : bool, optional degrees input/output (False: radians in/out) Returns ------- radius: float radius of ellipsoid """ if ell is None: ell = Ellipsoid() if deg: lat = radians(lat) return ell.semimajor_axis / sqrt(1 - (ell.eccentricity * sin(lat)) ** 2)