# Source code for pyproj.geod

```"""
The Geod class can perform forward and inverse geodetic, or
Great Circle, computations.  The forward computation involves
determining latitude, longitude and back azimuth of a terminus
point given the latitude and longitude of an initial point, plus
azimuth and distance. The inverse computation involves
determining the forward and back azimuths and distance given the
latitudes and longitudes of an initial and terminus point.
"""

__all__ = ["Geod", "pj_ellps", "geodesic_version_str"]

import math
from typing import Any, Dict, List, Optional, Tuple, Union

from pyproj._geod import Geod as _Geod
from pyproj._geod import geodesic_version_str
from pyproj._list import get_ellps_map
from pyproj.exceptions import GeodError
from pyproj.utils import _convertback, _copytobuffer

pj_ellps = get_ellps_map()

[docs]class Geod(_Geod):
"""
performs forward and inverse geodetic, or Great Circle,
computations.  The forward computation (using the 'fwd' method)
involves determining latitude, longitude and back azimuth of a
terminus point given the latitude and longitude of an initial
point, plus azimuth and distance. The inverse computation (using
the 'inv' method) involves determining the forward and back
azimuths and distance given the latitudes and longitudes of an
initial and terminus point.

Attributes
----------
initstring: str
The string form of the user input used to create the Geod.
sphere: bool
If True, it is a sphere.
a: float
The ellipsoid equatorial radius, or semi-major axis.
b: float
The ellipsoid polar radius, or semi-minor axis.
es: float
The 'eccentricity' of the ellipse, squared (1-b2/a2).
f: float
The ellipsoid 'flattening' parameter ( (a-b)/a ).

"""

[docs]    def __init__(self, initstring: Optional[str] = None, **kwargs) -> None:
"""
initialize a Geod class instance.

Geodetic parameters for specifying the ellipsoid
can be given in a dictionary 'initparams', as keyword arguments,
or as as proj geod initialization string.

You can get a dictionary of ellipsoids using :func:`pyproj.get_ellps_map`
or with the variable `pyproj.pj_ellps`.

The parameters of the ellipsoid may also be set directly using
the 'a' (semi-major or equatorial axis radius) keyword, and
any one of the following keywords: 'b' (semi-minor,
or polar axis radius), 'e' (eccentricity), 'es' (eccentricity
squared), 'f' (flattening), or 'rf' (reciprocal flattening).

See the proj documentation (https://proj.org) for more

Example usage:

>>> from pyproj import Geod
>>> g = Geod(ellps='clrk66') # Use Clarke 1866 ellipsoid.
>>> # specify the lat/lons of some cities.
>>> boston_lat = 42.+(15./60.); boston_lon = -71.-(7./60.)
>>> portland_lat = 45.+(31./60.); portland_lon = -123.-(41./60.)
>>> newyork_lat = 40.+(47./60.); newyork_lon = -73.-(58./60.)
>>> london_lat = 51.+(32./60.); london_lon = -(5./60.)
>>> # compute forward and back azimuths, plus distance
>>> # between Boston and Portland.
>>> az12,az21,dist = g.inv(boston_lon,boston_lat,portland_lon,portland_lat)
>>> "%7.3f %6.3f %12.3f" % (az12,az21,dist)
'-66.531 75.654  4164192.708'
>>> # compute latitude, longitude and back azimuth of Portland,
>>> # given Boston lat/lon, forward azimuth and distance to Portland.
>>> endlon, endlat, backaz = g.fwd(boston_lon, boston_lat, az12, dist)
>>> "%6.3f  %6.3f %13.3f" % (endlat,endlon,backaz)
'45.517  -123.683        75.654'
>>> # compute the azimuths, distances from New York to several
>>> # cities (pass a list)
>>> lons1 = 3*[newyork_lon]; lats1 = 3*[newyork_lat]
>>> lons2 = [boston_lon, portland_lon, london_lon]
>>> lats2 = [boston_lat, portland_lat, london_lat]
>>> az12,az21,dist = g.inv(lons1,lats1,lons2,lats2)
>>> for faz, baz, d in list(zip(az12,az21,dist)):
...     "%7.3f %7.3f %9.3f" % (faz, baz, d)
' 54.663 -123.448 288303.720'
'-65.463  79.342 4013037.318'
' 51.254 -71.576 5579916.651'
>>> g2 = Geod('+ellps=clrk66') # use proj4 style initialization string
>>> az12,az21,dist = g2.inv(boston_lon,boston_lat,portland_lon,portland_lat)
>>> "%7.3f %6.3f %12.3f" % (az12,az21,dist)
'-66.531 75.654  4164192.708'
"""
# if initparams is a proj-type init string,
# convert to dict.
ellpsd = {}  # type: Dict[str, Union[str, float]]
if initstring is not None:
for kvpair in initstring.split():
# Actually only +a and +b are needed
# We can ignore safely any parameter that doesn't have a value
if kvpair.find("=") == -1:
continue
k, v = kvpair.split("=")
k = k.lstrip("+")
if k in ["a", "b", "rf", "f", "es", "e"]:
ellpsd[k] = float(v)
else:
ellpsd[k] = v
# merge this dict with kwargs dict.
kwargs = dict(list(kwargs.items()) + list(ellpsd.items()))
sphere = False
if "ellps" in kwargs:
# ellipse name given, look up in pj_ellps dict
ellps_dict = pj_ellps[kwargs["ellps"]]
a = ellps_dict["a"]  # type: float
if ellps_dict["description"] == "Normal Sphere":
sphere = True
if "b" in ellps_dict:
b = ellps_dict["b"]  # type: float
es = 1.0 - (b * b) / (a * a)  # type: float
f = (a - b) / a  # type: float
elif "rf" in ellps_dict:
f = 1.0 / ellps_dict["rf"]
b = a * (1.0 - f)
es = 1.0 - (b * b) / (a * a)
else:
# a (semi-major axis) and one of
# b the semi-minor axis
# rf the reciprocal flattening
# f flattening
# es eccentricity squared
# must be given.
a = kwargs["a"]
if "b" in kwargs:
b = kwargs["b"]
es = 1.0 - (b * b) / (a * a)
f = (a - b) / a
elif "rf" in kwargs:
f = 1.0 / kwargs["rf"]
b = a * (1.0 - f)
es = 1.0 - (b * b) / (a * a)
elif "f" in kwargs:
f = kwargs["f"]
b = a * (1.0 - f)
es = 1.0 - (b / a) ** 2
elif "es" in kwargs:
es = kwargs["es"]
b = math.sqrt(a ** 2 - es * a ** 2)
f = (a - b) / a
elif "e" in kwargs:
es = kwargs["e"] ** 2
b = math.sqrt(a ** 2 - es * a ** 2)
f = (a - b) / a
else:
b = a
f = 0.0
es = 0.0
# msg='ellipse name or a, plus one of f,es,b must be given'
# raise ValueError(msg)
if math.fabs(f) < 1.0e-8:
sphere = True

super().__init__(a, f, sphere, b, es)

[docs]    def fwd(
self, lons: Any, lats: Any, az: Any, dist: Any, radians=False
) -> Tuple[Any, Any, Any]:
"""
Forward transformation

Determine longitudes, latitudes and back azimuths of terminus
points given longitudes and latitudes of initial points,
plus forward azimuths and distances.

Parameters
----------
lons: array, :class:`numpy.ndarray`, list, tuple, or scalar
Longitude(s) of initial point(s)
lats: array, :class:`numpy.ndarray`, list, tuple, or scalar
Latitude(s) of initial point(s)
az: array, :class:`numpy.ndarray`, list, tuple, or scalar
Forward azimuth(s)
dist: array, :class:`numpy.ndarray`, list, tuple, or scalar
Distance(s) between initial and terminus point(s)
in meters
If True, the input data is assumed to be in radians.

Returns
-------
array, :class:`numpy.ndarray`, list, tuple, or scalar:
Longitude(s) of terminus point(s)
array, :class:`numpy.ndarray`, list, tuple, or scalar:
Latitude(s) of terminus point(s)
array, :class:`numpy.ndarray`, list, tuple, or scalar:
Back azimuth(s)
"""
# process inputs, making copies that support buffer API.
inx, xisfloat, xislist, xistuple = _copytobuffer(lons)
iny, yisfloat, yislist, yistuple = _copytobuffer(lats)
inz, zisfloat, zislist, zistuple = _copytobuffer(az)
ind, disfloat, dislist, distuple = _copytobuffer(dist)
# if inputs were lists, tuples or floats, convert back.
outx = _convertback(xisfloat, xislist, xistuple, inx)
outy = _convertback(yisfloat, yislist, xistuple, iny)
outz = _convertback(zisfloat, zislist, zistuple, inz)
return outx, outy, outz

[docs]    def inv(
self, lons1: Any, lats1: Any, lons2: Any, lats2: Any, radians=False
) -> Tuple[Any, Any, Any]:
"""
Inverse transformation

Determine forward and back azimuths, plus distances
between initial points and terminus points.

Parameters
----------
lons1: array, :class:`numpy.ndarray`, list, tuple, or scalar
Longitude(s) of initial point(s)
lats1: array, :class:`numpy.ndarray`, list, tuple, or scalar
Latitude(s) of initial point(s)
lons2: array, :class:`numpy.ndarray`, list, tuple, or scalar
Longitude(s) of terminus point(s)
lats2: array, :class:`numpy.ndarray`, list, tuple, or scalar
Latitude(s) of terminus point(s)
If True, the input data is assumed to be in radians.

Returns
-------
array, :class:`numpy.ndarray`, list, tuple, or scalar:
Forward azimuth(s)
array, :class:`numpy.ndarray`, list, tuple, or scalar:
Back azimuth(s)
array, :class:`numpy.ndarray`, list, tuple, or scalar:
Distance(s) between initial and terminus point(s)
in meters
"""
# process inputs, making copies that support buffer API.
inx, xisfloat, xislist, xistuple = _copytobuffer(lons1)
iny, yisfloat, yislist, yistuple = _copytobuffer(lats1)
inz, zisfloat, zislist, zistuple = _copytobuffer(lons2)
ind, disfloat, dislist, distuple = _copytobuffer(lats2)
# if inputs were lists, tuples or floats, convert back.
outx = _convertback(xisfloat, xislist, xistuple, inx)
outy = _convertback(yisfloat, yislist, xistuple, iny)
outz = _convertback(zisfloat, zislist, zistuple, inz)
return outx, outy, outz

[docs]    def npts(
self,
lon1: float,
lat1: float,
lon2: float,
lat2: float,
npts: int,
) -> List:
"""
Given a single initial point and terminus point, returns
a list of longitude/latitude pairs describing npts equally
spaced intermediate points along the geodesic between the
initial and terminus points.

Example usage:

>>> from pyproj import Geod
>>> g = Geod(ellps='clrk66') # Use Clarke 1866 ellipsoid.
>>> # specify the lat/lons of Boston and Portland.
>>> boston_lat = 42.+(15./60.); boston_lon = -71.-(7./60.)
>>> portland_lat = 45.+(31./60.); portland_lon = -123.-(41./60.)
>>> # find ten equally spaced points between Boston and Portland.
>>> lonlats = g.npts(boston_lon,boston_lat,portland_lon,portland_lat,10)
>>> for lon,lat in lonlats: '%6.3f  %7.3f' % (lat, lon)
'43.528  -75.414'
'44.637  -79.883'
'45.565  -84.512'
'46.299  -89.279'
'46.830  -94.156'
'47.149  -99.112'
'47.251  -104.106'
'47.136  -109.100'
'46.805  -114.051'
'46.262  -118.924'
>>> import math
>>> lonlats = g.npts(
...    10,
... )
'43.528  -75.414'
'44.637  -79.883'
'45.565  -84.512'
'46.299  -89.279'
'46.830  -94.156'
'47.149  -99.112'
'47.251  -104.106'
'47.136  -109.100'
'46.805  -114.051'
'46.262  -118.924'

Parameters
----------
lon1: float
Longitude of the initial point
lat1: float
Latitude of the initial point
lon2: float
Longitude of the terminus point
lat2: float
Latitude of the terminus point
npts: int
Number of points to be returned
If True, the input data is assumed to be in radians.

Returns
-------
list of tuples:
list of (lon, lat) points along the geodesic
between the initial and terminus points.
"""
return list(zip(lons, lats))

[docs]    def line_length(self, lons: Any, lats: Any, radians: bool = False) -> float:
"""

Calculate the total distance between points along a line.

>>> from pyproj import Geod
>>> geod = Geod('+a=6378137 +f=0.0033528106647475126')
>>> lats = [-72.9, -71.9, -74.9, -74.3, -77.5, -77.4, -71.7, -65.9, -65.7,
...         -66.6, -66.9, -69.8, -70.0, -71.0, -77.3, -77.9, -74.7]
>>> lons = [-74, -102, -102, -131, -163, 163, 172, 140, 113,
...         88, 59, 25, -4, -14, -33, -46, -61]
>>> total_length = geod.line_length(lons, lats)
>>> "{:.3f}".format(total_length)
'14259605.611'

Parameters
----------
lons: array, :class:`numpy.ndarray`, list, tuple, or scalar
The longitude points along a line.
lats: array, :class:`numpy.ndarray`, list, tuple, or scalar
The latitude points along a line.
If True, the input data is assumed to be in radians.

Returns
-------
float:
The total length of the line.
"""
# process inputs, making copies that support buffer API.
inx, xisfloat, xislist, xistuple = _copytobuffer(lons)
iny, yisfloat, yislist, yistuple = _copytobuffer(lats)

[docs]    def line_lengths(self, lons: Any, lats: Any, radians: bool = False) -> Any:
"""

Calculate the distances between points along a line.

>>> from pyproj import Geod
>>> geod = Geod(ellps="WGS84")
>>> lats = [-72.9, -71.9, -74.9]
>>> lons = [-74, -102, -102]
>>> for line_length in geod.line_lengths(lons, lats):
...     "{:.3f}".format(line_length)
'943065.744'
'334805.010'

Parameters
----------
lons: array, :class:`numpy.ndarray`, list, tuple, or scalar
The longitude points along a line.
lats: array, :class:`numpy.ndarray`, list, tuple, or scalar
The latitude points along a line.
If True, the input data is assumed to be in radians.

Returns
-------
array, :class:`numpy.ndarray`, list, tuple, or scalar:
The total length of the line.
"""
# process inputs, making copies that support buffer API.
inx, xisfloat, xislist, xistuple = _copytobuffer(lons)
iny, yisfloat, yislist, yistuple = _copytobuffer(lats)
line_lengths = _convertback(xisfloat, xislist, xistuple, inx)
return line_lengths if xisfloat else line_lengths[:-1]

[docs]    def polygon_area_perimeter(
self, lons: Any, lats: Any, radians: bool = False
) -> Tuple[float, float]:
"""

A simple interface for computing the area (meters^2) and perimeter (meters)
of a geodesic polygon.

.. warning:: Only simple polygons (which are not self-intersecting) are allowed.

.. note:: lats should be in the range [-90 deg, 90 deg].

There's no need to "close" the polygon by repeating the first vertex.
The area returned is signed with counter-clockwise traversal being treated as
positive.

Example usage:

>>> from pyproj import Geod
>>> geod = Geod('+a=6378137 +f=0.0033528106647475126')
>>> lats = [-72.9, -71.9, -74.9, -74.3, -77.5, -77.4, -71.7, -65.9, -65.7,
...         -66.6, -66.9, -69.8, -70.0, -71.0, -77.3, -77.9, -74.7]
>>> lons = [-74, -102, -102, -131, -163, 163, 172, 140, 113,
...         88, 59, 25, -4, -14, -33, -46, -61]
>>> poly_area, poly_perimeter = geod.polygon_area_perimeter(lons, lats)
>>> "{:.1f} {:.1f}".format(poly_area, poly_perimeter)
'13376856682207.4 14710425.4'

Parameters
----------
lons: array, :class:`numpy.ndarray`, list, tuple, or scalar
An array of longitude values.
lats: array, :class:`numpy.ndarray`, list, tuple, or scalar
An array of latitude values.
If True, the input data is assumed to be in radians.

Returns
-------
(float, float):
The geodesic area (meters^2) and permimeter (meters) of the polygon.
"""
return self._polygon_area_perimeter(
)

[docs]    def geometry_length(self, geometry, radians: bool = False) -> float:
"""

Returns the geodesic length (meters) of the shapely geometry.

If it is a Polygon, it will return the sum of the
lengths along the perimeter.
If it is a MultiPolygon or MultiLine, it will return
the sum of the lengths.

Example usage:

>>> from pyproj import Geod
>>> from shapely.geometry import Point, LineString
>>> line_string = LineString([Point(1, 2), Point(3, 4)])
>>> geod = Geod(ellps="WGS84")
>>> "{:.3f}".format(geod.geometry_length(line_string))
'313588.397'

Parameters
----------
geometry: :class:`shapely.geometry.BaseGeometry`
The geometry to calculate the length from.
If True, the input data is assumed to be in radians.

Returns
-------
float:
The total geodesic length of the geometry (meters).
"""
try:
except (AttributeError, NotImplementedError):
pass
if hasattr(geometry, "exterior"):
elif hasattr(geometry, "geoms"):
total_length = 0.0
for geom in geometry.geoms:
raise GeodError("Invalid geometry provided.")

[docs]    def geometry_area_perimeter(
self, geometry, radians: bool = False
) -> Tuple[float, float]:
"""

A simple interface for computing the area (meters^2) and perimeter (meters)
of a geodesic polygon as a shapely geometry.

.. warning:: Only simple polygons (which are not self-intersecting) are allowed.

.. note:: lats should be in the range [-90 deg, 90 deg].

There's no need to "close" the polygon by repeating the first vertex.
The area returned is signed with counter-clockwise traversal being treated as
positive.

If it is a Polygon, it will return the area and exterior perimeter.
It will subtract the area of the interior holes.
If it is a MultiPolygon or MultiLine, it will return
the sum of the areas and perimeters of all geometries.

Example usage:

>>> from pyproj import Geod
>>> from shapely.geometry import LineString, Point, Polygon
>>> geod = Geod(ellps="WGS84")
>>> poly_area, poly_perimeter = geod.geometry_area_perimeter(
...     Polygon(
...         LineString([
...             Point(1, 1), Point(1, 10), Point(10, 10), Point(10, 1)
...         ]),
...         holes=[LineString([Point(1, 2), Point(3, 4), Point(5, 2)])],
...     )
... )
>>> "{:.3f} {:.3f}".format(poly_area, poly_perimeter)
'-944373881400.339 3979008.036'

Parameters
----------
geometry: :class:`shapely.geometry.BaseGeometry`
The geometry to calculate the area and perimeter from.
If True, the input data is assumed to be in radians.

Returns
-------
(float, float):
The geodesic area (meters^2) and permimeter (meters) of the polygon.
"""
try:
return self.polygon_area_perimeter(  # type: ignore
)
except (AttributeError, NotImplementedError):
pass
# polygon
if hasattr(geometry, "exterior"):
total_area, total_perimeter = self.geometry_area_perimeter(
)
# subtract area of holes
for hole in geometry.interiors:
total_area -= area
# multi geometries
elif hasattr(geometry, "geoms"):
total_area = 0.0
total_perimeter = 0.0
for geom in geometry.geoms:
total_area += area
total_perimeter += perimeter
raise GeodError("Invalid geometry provided.")

def __repr__(self) -> str:
# search for ellipse name
for (ellps, vals) in pj_ellps.items():
if self.a == vals["a"]:
b = vals.get("b", None)
rf = vals.get("rf", None)
# self.sphere is True when self.f is zero or very close to
# zero (0), so prevent divide by zero.
if self.b == b or (not self.sphere and (1.0 / self.f) == rf):
return "{classname}(ellps={ellps!r})" "".format(
classname=self.__class__.__name__, ellps=ellps
)

# no ellipse name found, call super class
return super().__repr__()

def __eq__(self, other: Any) -> bool:
"""
equality operator == for Geod objects

Example usage:

>>> from pyproj import Geod
>>> # Use Clarke 1866 ellipsoid.
>>> gclrk1 = Geod(ellps='clrk66')
>>> # Define Clarke 1866 using parameters
>>> gclrk2 = Geod(a=6378206.4, b=6356583.8)
>>> gclrk1 == gclrk2
True
>>> # WGS 66 ellipsoid, PROJ style
>>> gwgs66 = Geod('+ellps=WGS66')
>>> # Naval Weapons Lab., 1965 ellipsoid
>>> gnwl9d = Geod('+ellps=NWL9D')
>>> # these ellipsoids are the same
>>> gnwl9d == gwgs66
True
>>> gclrk1 != gnwl9d  # Clarke 1866 is unlike NWL9D
True
"""
if not isinstance(other, _Geod):
return False

return self.__repr__() == other.__repr__()
```