"""
Cython wrapper to provide python interfaces to
PROJ.4 (https://github.com/OSGeo/proj.4/wiki) functions.
Performs geodetic computations.
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.
Contact: Jeffrey Whitaker <jeffrey.s.whitaker@noaa.gov
copyright (c) 2006 by Jeffrey Whitaker.
Permission to use, copy, modify, and distribute this software
and its documentation for any purpose and without fee is hereby
granted, provided that the above copyright notice appear in all
copies and that both the copyright notice and this permission
notice appear in supporting documentation. THE AUTHOR DISCLAIMS
ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING ALL
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT
SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, INDIRECT OR
CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM
LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT,
NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. """
__all__ = ["Geod", "pj_ellps", "geodesic_version_str"]
import math
from pyproj._geod import Geod as _Geod
from pyproj._geod import geodesic_version_str
from pyproj.utils import _convertback, _copytobuffer
pj_ellps = {
"MERIT": {"a": 6378137.0, "rf": 298.257, "description": "MERIT 1983"},
"SGS85": {
"a": 6378136.0,
"rf": 298.257,
"description": "Soviet Geodetic System 85",
},
"GRS80": {
"a": 6378137.0,
"rf": 298.257222101,
"description": "GRS 1980(IUGG, 1980)",
},
"IAU76": {"a": 6378140.0, "rf": 298.257, "description": "IAU 1976"},
"airy": {"a": 6377563.396, "b": 6356256.910, "description": "Airy 1830"},
"APL4.9": {"a": 6378137.0, "rf": 298.25, "description": "Appl. Physics. 1965"},
"NWL9D": {"a": 6378145.0, "rf": 298.25, "description": " Naval Weapons Lab., 1965"},
"mod_airy": {"a": 6377340.189, "b": 6356034.446, "description": "Modified Airy"},
"andrae": {
"a": 6377104.43,
"rf": 300.0,
"description": "Andrae 1876 (Den., Iclnd.)",
},
"aust_SA": {
"a": 6378160.0,
"rf": 298.25,
"description": "Australian Natl & S. Amer. 1969",
},
"GRS67": {"a": 6378160.0, "rf": 298.2471674270, "description": "GRS 67(IUGG 1967)"},
"bessel": {"a": 6377397.155, "rf": 299.1528128, "description": "Bessel 1841"},
"bess_nam": {
"a": 6377483.865,
"rf": 299.1528128,
"description": "Bessel 1841 (Namibia)",
},
"clrk66": {"a": 6378206.4, "b": 6356583.8, "description": "Clarke 1866"},
"clrk80": {"a": 6378249.145, "rf": 293.4663, "description": "Clarke 1880 mod."},
"CPM": {
"a": 6375738.7,
"rf": 334.29,
"description": "Comm. des Poids et Mesures 1799",
},
"delmbr": {"a": 6376428.0, "rf": 311.5, "description": "Delambre 1810 (Belgium)"},
"engelis": {"a": 6378136.05, "rf": 298.2566, "description": "Engelis 1985"},
"evrst30": {"a": 6377276.345, "rf": 300.8017, "description": "Everest 1830"},
"evrst48": {"a": 6377304.063, "rf": 300.8017, "description": "Everest 1948"},
"evrst56": {"a": 6377301.243, "rf": 300.8017, "description": "Everest 1956"},
"evrst69": {"a": 6377295.664, "rf": 300.8017, "description": "Everest 1969"},
"evrstSS": {
"a": 6377298.556,
"rf": 300.8017,
"description": "Everest (Sabah & Sarawak)",
},
"fschr60": {
"a": 6378166.0,
"rf": 298.3,
"description": "Fischer (Mercury Datum) 1960",
},
"fschr60m": {"a": 6378155.0, "rf": 298.3, "description": "Modified Fischer 1960"},
"fschr68": {"a": 6378150.0, "rf": 298.3, "description": "Fischer 1968"},
"helmert": {"a": 6378200.0, "rf": 298.3, "description": "Helmert 1906"},
"hough": {"a": 6378270.0, "rf": 297.0, "description": "Hough"},
"intl": {
"a": 6378388.0,
"rf": 297.0,
"description": "International 1909 (Hayford)",
},
"krass": {"a": 6378245.0, "rf": 298.3, "description": "Krassovsky, 1942"},
"kaula": {"a": 6378163.0, "rf": 298.24, "description": "Kaula 1961"},
"lerch": {"a": 6378139.0, "rf": 298.257, "description": "Lerch 1979"},
"mprts": {"a": 6397300.0, "rf": 191.0, "description": "Maupertius 1738"},
"new_intl": {
"a": 6378157.5,
"b": 6356772.2,
"description": "New International 1967",
},
"plessis": {"a": 6376523.0, "b": 6355863.0, "description": "Plessis 1817 (France)"},
"SEasia": {"a": 6378155.0, "b": 6356773.3205, "description": "Southeast Asia"},
"walbeck": {"a": 6376896.0, "b": 6355834.8467, "description": "Walbeck"},
"WGS60": {"a": 6378165.0, "rf": 298.3, "description": "WGS 60"},
"WGS66": {"a": 6378145.0, "rf": 298.25, "description": "WGS 66"},
"WGS72": {"a": 6378135.0, "rf": 298.26, "description": "WGS 72"},
"WGS84": {"a": 6378137.0, "rf": 298.257223563, "description": "WGS 84"},
"sphere": {"a": 6370997.0, "b": 6370997.0, "description": "Normal Sphere"},
}
[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
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.
"""
[docs] def __init__(self, initstring=None, **kwargs):
"""
initialize a Geod class instance.
Geodetic parameters for specifying the ellipsoid
can be given in a dictionary 'initparams', as keyword arguments,
or as as proj4 geod initialization string.
Following is a list of the ellipsoids that may be defined using the
'ellps' keyword (these are stored in the model variable pj_ellps)::
MERIT a=6378137.0 rf=298.257 MERIT 1983
SGS85 a=6378136.0 rf=298.257 Soviet Geodetic System 85
GRS80 a=6378137.0 rf=298.257222101 GRS 1980(IUGG, 1980)
IAU76 a=6378140.0 rf=298.257 IAU 1976
airy a=6377563.396 b=6356256.910 Airy 1830
APL4.9 a=6378137.0. rf=298.25 Appl. Physics. 1965
airy a=6377563.396 b=6356256.910 Airy 1830
APL4.9 a=6378137.0. rf=298.25 Appl. Physics. 1965
NWL9D a=6378145.0. rf=298.25 Naval Weapons Lab., 1965
mod_airy a=6377340.189 b=6356034.446 Modified Airy
andrae a=6377104.43 rf=300.0 Andrae 1876 (Den., Iclnd.)
aust_SA a=6378160.0 rf=298.25 Australian Natl & S. Amer. 1969
GRS67 a=6378160.0 rf=298.247167427 GRS 67(IUGG 1967)
bessel a=6377397.155 rf=299.1528128 Bessel 1841
bess_nam a=6377483.865 rf=299.1528128 Bessel 1841 (Namibia)
clrk66 a=6378206.4 b=6356583.8 Clarke 1866
clrk80 a=6378249.145 rf=293.4663 Clarke 1880 mod.
CPM a=6375738.7 rf=334.29 Comm. des Poids et Mesures 1799
delmbr a=6376428. rf=311.5 Delambre 1810 (Belgium)
engelis a=6378136.05 rf=298.2566 Engelis 1985
evrst30 a=6377276.345 rf=300.8017 Everest 1830
evrst48 a=6377304.063 rf=300.8017 Everest 1948
evrst56 a=6377301.243 rf=300.8017 Everest 1956
evrst69 a=6377295.664 rf=300.8017 Everest 1969
evrstSS a=6377298.556 rf=300.8017 Everest (Sabah & Sarawak)
fschr60 a=6378166. rf=298.3 Fischer (Mercury Datum) 1960
fschr60m a=6378155. rf=298.3 Modified Fischer 1960
fschr68 a=6378150. rf=298.3 Fischer 1968
helmert a=6378200. rf=298.3 Helmert 1906
hough a=6378270.0 rf=297. Hough
helmert a=6378200. rf=298.3 Helmert 1906
hough a=6378270.0 rf=297. Hough
intl a=6378388.0 rf=297. International 1909 (Hayford)
krass a=6378245.0 rf=298.3 Krassovsky, 1942
kaula a=6378163. rf=298.24 Kaula 1961
lerch a=6378139. rf=298.257 Lerch 1979
mprts a=6397300. rf=191. Maupertius 1738
new_intl a=6378157.5 b=6356772.2 New International 1967
plessis a=6376523. b=6355863. Plessis 1817 (France)
SEasia a=6378155.0 b=6356773.3205 Southeast Asia
walbeck a=6376896.0 b=6355834.8467 Walbeck
WGS60 a=6378165.0 rf=298.3 WGS 60
WGS66 a=6378145.0 rf=298.25 WGS 66
WGS72 a=6378135.0 rf=298.26 WGS 72
WGS84 a=6378137.0 rf=298.257223563 WGS 84
sphere a=6370997.0 b=6370997.0 Normal Sphere (r=6370997)
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://github.com/OSGeo/proj.4/wiki) for more
information about specifying ellipsoid parameters (specifically,
the chapter 'Specifying the Earth's figure' in the main Proj
users manual).
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 = {}
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"]:
v = float(v)
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"]
if ellps_dict["description"] == "Normal Sphere":
sphere = True
if "b" in ellps_dict:
b = ellps_dict["b"]
es = 1.0 - (b * b) / (a * a)
f = (a - b) / a
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(Geod, self).__init__(a, f, sphere, b, es)
[docs] def fwd(self, lons, lats, az, dist, radians=False):
"""
forward transformation - Returns longitudes, latitudes and back
azimuths of terminus points given longitudes (lons) and
latitudes (lats) of initial points, plus forward azimuths (az)
and distances (dist).
latitudes (lats) of initial points, plus forward azimuths (az)
and distances (dist).
Works with numpy and regular python array objects, python
sequences and scalars.
if radians=True, lons/lats and azimuths are radians instead of
degrees. Distances are in meters.
"""
# 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)
super(Geod, self)._fwd(inx, iny, inz, ind, radians=radians)
# 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, lats1, lons2, lats2, radians=False):
"""
inverse transformation - Returns forward and back azimuths, plus
distances between initial points (specified by lons1, lats1) and
terminus points (specified by lons2, lats2).
Works with numpy and regular python array objects, python
sequences and scalars.
if radians=True, lons/lats and azimuths are radians instead of
degrees. Distances are 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)
super(Geod, self)._inv(inx, iny, inz, ind, radians=radians)
# 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, lat1, lon2, lat2, npts, radians=False):
"""
Given a single initial point and terminus point (specified by
python floats lon1,lat1 and lon2,lat2), returns a list of
longitude/latitude pairs describing npts equally spaced
intermediate points along the geodesic between the initial and
terminus points.
if radians=True, lons/lats are radians instead of degrees.
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'
>>> # test with radians=True (inputs/outputs in radians, not degrees)
>>> import math
>>> dg2rad = math.radians(1.)
>>> rad2dg = math.degrees(1.)
>>> lonlats = g.npts(dg2rad*boston_lon,dg2rad*boston_lat,dg2rad*portland_lon,dg2rad*portland_lat,10,radians=True)
>>> for lon,lat in lonlats: '%6.3f %7.3f' % (rad2dg*lat, rad2dg*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'
"""
lons, lats = super(Geod, self)._npts(
lon1, lat1, lon2, lat2, npts, radians=radians
)
return list(zip(lons, lats))
def __repr__(self):
# 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(Geod, self).__repr__()
def __eq__(self, other):
"""
equality operator == for Geod objects
Example usage:
>>> from pyproj import Geod
>>> gclrk1 = Geod(ellps='clrk66') # Use Clarke 1866 ellipsoid.
>>> gclrk2 = Geod(a=6378206.4, b=6356583.8) # Define Clarke 1866 using parameters
>>> gclrk1 == gclrk2
True
>>> gwgs66 = Geod('+ellps=WGS66') # WGS 66 ellipsoid, Proj.4 style
>>> gnwl9d = Geod('+ellps=NWL9D') # Naval Weapons Lab., 1965 ellipsoid
>>> # 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__()