638 lines
24 KiB
Python
638 lines
24 KiB
Python
"""
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The Geod class can perform forward and inverse geodetic, or
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Great Circle, computations. The forward computation involves
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determining latitude, longitude and back azimuth of a terminus
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point given the latitude and longitude of an initial point, plus
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azimuth and distance. The inverse computation involves
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determining the forward and back azimuths and distance given the
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latitudes and longitudes of an initial and terminus point.
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"""
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__all__ = ["Geod", "pj_ellps", "geodesic_version_str"]
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import math
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from typing import Any, Dict, List, Optional, Tuple, Union
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from pyproj._geod import Geod as _Geod
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from pyproj._geod import geodesic_version_str
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from pyproj._list import get_ellps_map
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from pyproj.exceptions import GeodError
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from pyproj.utils import _convertback, _copytobuffer
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pj_ellps = get_ellps_map()
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class Geod(_Geod):
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"""
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performs forward and inverse geodetic, or Great Circle,
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computations. The forward computation (using the 'fwd' method)
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involves determining latitude, longitude and back azimuth of a
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terminus point given the latitude and longitude of an initial
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point, plus azimuth and distance. The inverse computation (using
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the 'inv' method) involves determining the forward and back
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azimuths and distance given the latitudes and longitudes of an
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initial and terminus point.
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Attributes
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----------
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initstring: str
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The string form of the user input used to create the Geod.
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sphere: bool
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If True, it is a sphere.
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a: float
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The ellipsoid equatorial radius, or semi-major axis.
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b: float
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The ellipsoid polar radius, or semi-minor axis.
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es: float
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The 'eccentricity' of the ellipse, squared (1-b2/a2).
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f: float
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The ellipsoid 'flattening' parameter ( (a-b)/a ).
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"""
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def __init__(self, initstring: Optional[str] = None, **kwargs) -> None:
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"""
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initialize a Geod class instance.
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Geodetic parameters for specifying the ellipsoid
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can be given in a dictionary 'initparams', as keyword arguments,
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or as as proj geod initialization string.
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You can get a dictionary of ellipsoids using :func:`pyproj.get_ellps_map`
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or with the variable `pyproj.pj_ellps`.
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The parameters of the ellipsoid may also be set directly using
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the 'a' (semi-major or equatorial axis radius) keyword, and
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any one of the following keywords: 'b' (semi-minor,
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or polar axis radius), 'e' (eccentricity), 'es' (eccentricity
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squared), 'f' (flattening), or 'rf' (reciprocal flattening).
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See the proj documentation (https://proj.org) for more
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information about specifying ellipsoid parameters.
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Example usage:
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>>> from pyproj import Geod
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>>> g = Geod(ellps='clrk66') # Use Clarke 1866 ellipsoid.
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>>> # specify the lat/lons of some cities.
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>>> boston_lat = 42.+(15./60.); boston_lon = -71.-(7./60.)
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>>> portland_lat = 45.+(31./60.); portland_lon = -123.-(41./60.)
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>>> newyork_lat = 40.+(47./60.); newyork_lon = -73.-(58./60.)
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>>> london_lat = 51.+(32./60.); london_lon = -(5./60.)
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>>> # compute forward and back azimuths, plus distance
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>>> # between Boston and Portland.
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>>> az12,az21,dist = g.inv(boston_lon,boston_lat,portland_lon,portland_lat)
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>>> "%7.3f %6.3f %12.3f" % (az12,az21,dist)
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'-66.531 75.654 4164192.708'
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>>> # compute latitude, longitude and back azimuth of Portland,
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>>> # given Boston lat/lon, forward azimuth and distance to Portland.
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>>> endlon, endlat, backaz = g.fwd(boston_lon, boston_lat, az12, dist)
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>>> "%6.3f %6.3f %13.3f" % (endlat,endlon,backaz)
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'45.517 -123.683 75.654'
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>>> # compute the azimuths, distances from New York to several
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>>> # cities (pass a list)
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>>> lons1 = 3*[newyork_lon]; lats1 = 3*[newyork_lat]
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>>> lons2 = [boston_lon, portland_lon, london_lon]
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>>> lats2 = [boston_lat, portland_lat, london_lat]
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>>> az12,az21,dist = g.inv(lons1,lats1,lons2,lats2)
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>>> for faz, baz, d in list(zip(az12,az21,dist)):
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... "%7.3f %7.3f %9.3f" % (faz, baz, d)
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' 54.663 -123.448 288303.720'
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'-65.463 79.342 4013037.318'
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' 51.254 -71.576 5579916.651'
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>>> g2 = Geod('+ellps=clrk66') # use proj4 style initialization string
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>>> az12,az21,dist = g2.inv(boston_lon,boston_lat,portland_lon,portland_lat)
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>>> "%7.3f %6.3f %12.3f" % (az12,az21,dist)
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'-66.531 75.654 4164192.708'
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"""
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# if initparams is a proj-type init string,
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# convert to dict.
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ellpsd = {} # type: Dict[str, Union[str, float]]
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if initstring is not None:
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for kvpair in initstring.split():
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# Actually only +a and +b are needed
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# We can ignore safely any parameter that doesn't have a value
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if kvpair.find("=") == -1:
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continue
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k, v = kvpair.split("=")
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k = k.lstrip("+")
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if k in ["a", "b", "rf", "f", "es", "e"]:
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ellpsd[k] = float(v)
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else:
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ellpsd[k] = v
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# merge this dict with kwargs dict.
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kwargs = dict(list(kwargs.items()) + list(ellpsd.items()))
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sphere = False
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if "ellps" in kwargs:
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# ellipse name given, look up in pj_ellps dict
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ellps_dict = pj_ellps[kwargs["ellps"]]
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a = ellps_dict["a"] # type: float
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if ellps_dict["description"] == "Normal Sphere":
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sphere = True
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if "b" in ellps_dict:
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b = ellps_dict["b"] # type: float
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es = 1.0 - (b * b) / (a * a) # type: float
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f = (a - b) / a # type: float
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elif "rf" in ellps_dict:
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f = 1.0 / ellps_dict["rf"]
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b = a * (1.0 - f)
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es = 1.0 - (b * b) / (a * a)
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else:
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# a (semi-major axis) and one of
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# b the semi-minor axis
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# rf the reciprocal flattening
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# f flattening
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# es eccentricity squared
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# must be given.
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a = kwargs["a"]
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if "b" in kwargs:
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b = kwargs["b"]
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es = 1.0 - (b * b) / (a * a)
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f = (a - b) / a
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elif "rf" in kwargs:
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f = 1.0 / kwargs["rf"]
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b = a * (1.0 - f)
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es = 1.0 - (b * b) / (a * a)
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elif "f" in kwargs:
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f = kwargs["f"]
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b = a * (1.0 - f)
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es = 1.0 - (b / a) ** 2
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elif "es" in kwargs:
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es = kwargs["es"]
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b = math.sqrt(a ** 2 - es * a ** 2)
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f = (a - b) / a
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elif "e" in kwargs:
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es = kwargs["e"] ** 2
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b = math.sqrt(a ** 2 - es * a ** 2)
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f = (a - b) / a
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else:
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b = a
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f = 0.0
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es = 0.0
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# msg='ellipse name or a, plus one of f,es,b must be given'
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# raise ValueError(msg)
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if math.fabs(f) < 1.0e-8:
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sphere = True
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super().__init__(a, f, sphere, b, es)
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def fwd(
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self, lons: Any, lats: Any, az: Any, dist: Any, radians=False
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) -> Tuple[Any, Any, Any]:
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"""
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Forward transformation
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Determine longitudes, latitudes and back azimuths of terminus
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points given longitudes and latitudes of initial points,
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plus forward azimuths and distances.
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Parameters
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----------
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lons: array, :class:`numpy.ndarray`, list, tuple, or scalar
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Longitude(s) of initial point(s)
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lats: array, :class:`numpy.ndarray`, list, tuple, or scalar
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Latitude(s) of initial point(s)
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az: array, :class:`numpy.ndarray`, list, tuple, or scalar
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Forward azimuth(s)
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dist: array, :class:`numpy.ndarray`, list, tuple, or scalar
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Distance(s) between initial and terminus point(s)
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in meters
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radians: bool, optional
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If True, the input data is assumed to be in radians.
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Returns
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-------
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array, :class:`numpy.ndarray`, list, tuple, or scalar:
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Longitude(s) of terminus point(s)
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array, :class:`numpy.ndarray`, list, tuple, or scalar:
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Latitude(s) of terminus point(s)
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array, :class:`numpy.ndarray`, list, tuple, or scalar:
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Back azimuth(s)
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"""
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# process inputs, making copies that support buffer API.
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inx, xisfloat, xislist, xistuple = _copytobuffer(lons)
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iny, yisfloat, yislist, yistuple = _copytobuffer(lats)
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inz, zisfloat, zislist, zistuple = _copytobuffer(az)
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ind, disfloat, dislist, distuple = _copytobuffer(dist)
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self._fwd(inx, iny, inz, ind, radians=radians)
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# if inputs were lists, tuples or floats, convert back.
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outx = _convertback(xisfloat, xislist, xistuple, inx)
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outy = _convertback(yisfloat, yislist, xistuple, iny)
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outz = _convertback(zisfloat, zislist, zistuple, inz)
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return outx, outy, outz
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def inv(
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self, lons1: Any, lats1: Any, lons2: Any, lats2: Any, radians=False
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) -> Tuple[Any, Any, Any]:
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"""
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Inverse transformation
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Determine forward and back azimuths, plus distances
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between initial points and terminus points.
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Parameters
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----------
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lons1: array, :class:`numpy.ndarray`, list, tuple, or scalar
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Longitude(s) of initial point(s)
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lats1: array, :class:`numpy.ndarray`, list, tuple, or scalar
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Latitude(s) of initial point(s)
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lons2: array, :class:`numpy.ndarray`, list, tuple, or scalar
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Longitude(s) of terminus point(s)
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lats2: array, :class:`numpy.ndarray`, list, tuple, or scalar
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Latitude(s) of terminus point(s)
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radians: bool, optional
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If True, the input data is assumed to be in radians.
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Returns
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-------
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array, :class:`numpy.ndarray`, list, tuple, or scalar:
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Forward azimuth(s)
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array, :class:`numpy.ndarray`, list, tuple, or scalar:
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Back azimuth(s)
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array, :class:`numpy.ndarray`, list, tuple, or scalar:
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Distance(s) between initial and terminus point(s)
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in meters
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"""
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# process inputs, making copies that support buffer API.
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inx, xisfloat, xislist, xistuple = _copytobuffer(lons1)
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iny, yisfloat, yislist, yistuple = _copytobuffer(lats1)
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inz, zisfloat, zislist, zistuple = _copytobuffer(lons2)
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ind, disfloat, dislist, distuple = _copytobuffer(lats2)
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self._inv(inx, iny, inz, ind, radians=radians)
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# if inputs were lists, tuples or floats, convert back.
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outx = _convertback(xisfloat, xislist, xistuple, inx)
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outy = _convertback(yisfloat, yislist, xistuple, iny)
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outz = _convertback(zisfloat, zislist, zistuple, inz)
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return outx, outy, outz
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def npts(
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self,
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lon1: float,
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lat1: float,
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lon2: float,
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lat2: float,
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npts: int,
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radians: bool = False,
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) -> List:
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"""
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Given a single initial point and terminus point, returns
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a list of longitude/latitude pairs describing npts equally
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spaced intermediate points along the geodesic between the
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initial and terminus points.
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Example usage:
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>>> from pyproj import Geod
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>>> g = Geod(ellps='clrk66') # Use Clarke 1866 ellipsoid.
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>>> # specify the lat/lons of Boston and Portland.
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>>> boston_lat = 42.+(15./60.); boston_lon = -71.-(7./60.)
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>>> portland_lat = 45.+(31./60.); portland_lon = -123.-(41./60.)
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>>> # find ten equally spaced points between Boston and Portland.
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>>> lonlats = g.npts(boston_lon,boston_lat,portland_lon,portland_lat,10)
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>>> for lon,lat in lonlats: '%6.3f %7.3f' % (lat, lon)
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'43.528 -75.414'
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'44.637 -79.883'
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'45.565 -84.512'
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'46.299 -89.279'
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'46.830 -94.156'
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'47.149 -99.112'
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'47.251 -104.106'
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'47.136 -109.100'
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'46.805 -114.051'
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'46.262 -118.924'
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>>> # test with radians=True (inputs/outputs in radians, not degrees)
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>>> import math
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>>> dg2rad = math.radians(1.)
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>>> rad2dg = math.degrees(1.)
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>>> lonlats = g.npts(
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... dg2rad*boston_lon,
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... dg2rad*boston_lat,
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... dg2rad*portland_lon,
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... dg2rad*portland_lat,
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... 10,
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... radians=True
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... )
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>>> for lon,lat in lonlats: '%6.3f %7.3f' % (rad2dg*lat, rad2dg*lon)
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'43.528 -75.414'
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'44.637 -79.883'
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'45.565 -84.512'
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'46.299 -89.279'
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'46.830 -94.156'
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'47.149 -99.112'
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'47.251 -104.106'
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'47.136 -109.100'
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'46.805 -114.051'
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'46.262 -118.924'
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Parameters
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----------
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lon1: float
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Longitude of the initial point
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lat1: float
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Latitude of the initial point
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lon2: float
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Longitude of the terminus point
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lat2: float
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Latitude of the terminus point
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npts: int
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Number of points to be returned
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radians: bool, optional
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If True, the input data is assumed to be in radians.
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Returns
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-------
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list of tuples:
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list of (lon, lat) points along the geodesic
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between the initial and terminus points.
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"""
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lons, lats = super()._npts(lon1, lat1, lon2, lat2, npts, radians=radians)
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return list(zip(lons, lats))
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def line_length(self, lons: Any, lats: Any, radians: bool = False) -> float:
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"""
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.. versionadded:: 2.3.0
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Calculate the total distance between points along a line.
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>>> from pyproj import Geod
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>>> geod = Geod('+a=6378137 +f=0.0033528106647475126')
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>>> lats = [-72.9, -71.9, -74.9, -74.3, -77.5, -77.4, -71.7, -65.9, -65.7,
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... -66.6, -66.9, -69.8, -70.0, -71.0, -77.3, -77.9, -74.7]
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>>> lons = [-74, -102, -102, -131, -163, 163, 172, 140, 113,
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... 88, 59, 25, -4, -14, -33, -46, -61]
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>>> total_length = geod.line_length(lons, lats)
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>>> "{:.3f}".format(total_length)
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'14259605.611'
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Parameters
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----------
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lons: array, :class:`numpy.ndarray`, list, tuple, or scalar
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The longitude points along a line.
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lats: array, :class:`numpy.ndarray`, list, tuple, or scalar
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The latitude points along a line.
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radians: bool, optional
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If True, the input data is assumed to be in radians.
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Returns
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-------
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float:
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The total length of the line.
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"""
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# process inputs, making copies that support buffer API.
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inx, xisfloat, xislist, xistuple = _copytobuffer(lons)
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iny, yisfloat, yislist, yistuple = _copytobuffer(lats)
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return self._line_length(inx, iny, radians=radians)
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def line_lengths(self, lons: Any, lats: Any, radians: bool = False) -> Any:
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"""
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.. versionadded:: 2.3.0
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Calculate the distances between points along a line.
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>>> from pyproj import Geod
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>>> geod = Geod(ellps="WGS84")
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>>> lats = [-72.9, -71.9, -74.9]
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>>> lons = [-74, -102, -102]
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>>> for line_length in geod.line_lengths(lons, lats):
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... "{:.3f}".format(line_length)
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'943065.744'
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'334805.010'
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Parameters
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----------
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lons: array, :class:`numpy.ndarray`, list, tuple, or scalar
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The longitude points along a line.
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lats: array, :class:`numpy.ndarray`, list, tuple, or scalar
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The latitude points along a line.
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radians: bool, optional
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If True, the input data is assumed to be in radians.
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Returns
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-------
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array, :class:`numpy.ndarray`, list, tuple, or scalar:
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The total length of the line.
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"""
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# process inputs, making copies that support buffer API.
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inx, xisfloat, xislist, xistuple = _copytobuffer(lons)
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iny, yisfloat, yislist, yistuple = _copytobuffer(lats)
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self._line_length(inx, iny, radians=radians)
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line_lengths = _convertback(xisfloat, xislist, xistuple, inx)
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return line_lengths if xisfloat else line_lengths[:-1]
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def polygon_area_perimeter(
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self, lons: Any, lats: Any, radians: bool = False
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) -> Tuple[float, float]:
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"""
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.. versionadded:: 2.3.0
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A simple interface for computing the area (meters^2) and perimeter (meters)
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of a geodesic polygon.
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.. warning:: Only simple polygons (which are not self-intersecting) are allowed.
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.. note:: lats should be in the range [-90 deg, 90 deg].
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There's no need to "close" the polygon by repeating the first vertex.
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The area returned is signed with counter-clockwise traversal being treated as
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positive.
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Example usage:
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>>> from pyproj import Geod
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>>> geod = Geod('+a=6378137 +f=0.0033528106647475126')
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>>> lats = [-72.9, -71.9, -74.9, -74.3, -77.5, -77.4, -71.7, -65.9, -65.7,
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... -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.
|
|
radians: bool, optional
|
|
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(
|
|
_copytobuffer(lons)[0], _copytobuffer(lats)[0], radians=radians
|
|
)
|
|
|
|
def geometry_length(self, geometry, radians: bool = False) -> float:
|
|
"""
|
|
.. versionadded:: 2.3.0
|
|
|
|
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.
|
|
radians: bool, optional
|
|
If True, the input data is assumed to be in radians.
|
|
|
|
Returns
|
|
-------
|
|
float:
|
|
The total geodesic length of the geometry (meters).
|
|
"""
|
|
try:
|
|
return self.line_length(*geometry.xy, radians=radians) # type: ignore
|
|
except (AttributeError, NotImplementedError):
|
|
pass
|
|
if hasattr(geometry, "exterior"):
|
|
return self.geometry_length(geometry.exterior, radians=radians)
|
|
elif hasattr(geometry, "geoms"):
|
|
total_length = 0.0
|
|
for geom in geometry.geoms:
|
|
total_length += self.geometry_length(geom, radians=radians)
|
|
return total_length
|
|
raise GeodError("Invalid geometry provided.")
|
|
|
|
def geometry_area_perimeter(
|
|
self, geometry, radians: bool = False
|
|
) -> Tuple[float, float]:
|
|
"""
|
|
.. versionadded:: 2.3.0
|
|
|
|
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.
|
|
radians: bool, optional
|
|
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
|
|
*geometry.xy, radians=radians,
|
|
)
|
|
except (AttributeError, NotImplementedError):
|
|
pass
|
|
# polygon
|
|
if hasattr(geometry, "exterior"):
|
|
total_area, total_perimeter = self.geometry_area_perimeter(
|
|
geometry.exterior, radians=radians
|
|
)
|
|
# subtract area of holes
|
|
for hole in geometry.interiors:
|
|
area, _ = self.geometry_area_perimeter(hole, radians=radians)
|
|
total_area -= area
|
|
return total_area, total_perimeter
|
|
# multi geometries
|
|
elif hasattr(geometry, "geoms"):
|
|
total_area = 0.0
|
|
total_perimeter = 0.0
|
|
for geom in geometry.geoms:
|
|
area, perimeter = self.geometry_area_perimeter(geom, radians=radians)
|
|
total_area += area
|
|
total_perimeter += perimeter
|
|
return total_area, total_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__()
|