""" 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", "GeodIntermediateFlag", "GeodIntermediateReturn", "reverse_azimuth", ] import math import warnings from typing import Any, Optional, Union from pyproj._geod import Geod as _Geod from pyproj._geod import GeodIntermediateReturn, geodesic_version_str from pyproj._geod import reverse_azimuth as _reverse_azimuth from pyproj.enums import GeodIntermediateFlag from pyproj.exceptions import GeodError from pyproj.list import get_ellps_map from pyproj.utils import DataType, _convertback, _copytobuffer pj_ellps = get_ellps_map() def _params_from_ellps_map(ellps: str) -> tuple[float, float, float, float, bool]: """ Build Geodesic parameters from PROJ ellips map Parameter --------- ellps: str The name of the ellipse in the map. Returns ------- tuple[float, float, float, float, bool] """ ellps_dict = pj_ellps[ellps] semi_major_axis: float = ellps_dict["a"] sphere = False if ellps_dict["description"] == "Normal Sphere": sphere = True if "b" in ellps_dict: semi_minor_axis: float = ellps_dict["b"] eccentricity_squared: float = 1.0 - semi_minor_axis**2 / semi_major_axis**2 flattening: float = (semi_major_axis - semi_minor_axis) / semi_major_axis elif "rf" in ellps_dict: flattening = 1.0 / ellps_dict["rf"] semi_minor_axis = semi_major_axis * (1.0 - flattening) eccentricity_squared = 1.0 - semi_minor_axis**2 / semi_major_axis**2 return semi_major_axis, semi_minor_axis, flattening, eccentricity_squared, sphere def _params_from_kwargs(kwargs: dict) -> tuple[float, float, float, float]: """ Build Geodesic parameters from input kwargs: - a: the semi-major axis (required). Need least one of these parameters. - b: the semi-minor axis - rf: the reciprocal flattening - f: flattening - es: eccentricity squared Parameter --------- kwargs: dict The input kwargs for an ellipse. Returns ------- tuple[float, float, float, float] """ semi_major_axis = kwargs["a"] if "b" in kwargs: semi_minor_axis = kwargs["b"] eccentricity_squared = 1.0 - semi_minor_axis**2 / semi_major_axis**2 flattening = (semi_major_axis - semi_minor_axis) / semi_major_axis elif "rf" in kwargs: flattening = 1.0 / kwargs["rf"] semi_minor_axis = semi_major_axis * (1.0 - flattening) eccentricity_squared = 1.0 - semi_minor_axis**2 / semi_major_axis**2 elif "f" in kwargs: flattening = kwargs["f"] semi_minor_axis = semi_major_axis * (1.0 - flattening) eccentricity_squared = 1.0 - (semi_minor_axis / semi_major_axis) ** 2 elif "es" in kwargs: eccentricity_squared = kwargs["es"] semi_minor_axis = math.sqrt( semi_major_axis**2 - eccentricity_squared * semi_major_axis**2 ) flattening = (semi_major_axis - semi_minor_axis) / semi_major_axis elif "e" in kwargs: eccentricity_squared = kwargs["e"] ** 2 semi_minor_axis = math.sqrt( semi_major_axis**2 - eccentricity_squared * semi_major_axis**2 ) flattening = (semi_major_axis - semi_minor_axis) / semi_major_axis else: semi_minor_axis = semi_major_axis flattening = 0.0 eccentricity_squared = 0.0 return semi_major_axis, semi_minor_axis, flattening, eccentricity_squared 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 ). """ 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 information about specifying ellipsoid parameters. 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) >>> f"{az12:.3f} {az21:.3f} {dist:.3f}" '-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) >>> f"{endlat:.3f} {endlon:.3f} {backaz:.3f}" '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)): ... f"{faz:7.3f} {baz:8.3f} {d:12.3f}" ' 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) >>> f"{az12:.3f} {az21:.3f} {dist:.3f}" '-66.531 75.654 4164192.708' """ # if initparams is a proj-type init string, # convert to dict. ellpsd: 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 key, val = kvpair.split("=") key = key.lstrip("+") if key in ["a", "b", "rf", "f", "es", "e"]: ellpsd[key] = float(val) else: ellpsd[key] = val # merge this dict with kwargs dict. kwargs = dict(list(kwargs.items()) + list(ellpsd.items())) sphere = False if "ellps" in kwargs: ( semi_major_axis, semi_minor_axis, flattening, eccentricity_squared, sphere, ) = _params_from_ellps_map(kwargs["ellps"]) else: ( semi_major_axis, semi_minor_axis, flattening, eccentricity_squared, ) = _params_from_kwargs(kwargs) if math.fabs(flattening) < 1.0e-8: sphere = True super().__init__( semi_major_axis, flattening, sphere, semi_minor_axis, eccentricity_squared ) def fwd( # pylint: disable=invalid-name self, lons: Any, lats: Any, az: Any, dist: Any, radians: bool = False, inplace: bool = False, return_back_azimuth: bool = True, ) -> 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. .. versionadded:: 3.5.0 inplace .. versionadded:: 3.5.0 return_back_azimuth Accepted numeric scalar or array: - :class:`int` - :class:`float` - :class:`numpy.floating` - :class:`numpy.integer` - :class:`list` - :class:`tuple` - :class:`array.array` - :class:`numpy.ndarray` - :class:`xarray.DataArray` - :class:`pandas.Series` Parameters ---------- lons: scalar or array Longitude(s) of initial point(s) lats: scalar or array Latitude(s) of initial point(s) az: scalar or array Forward azimuth(s) dist: scalar or array Distance(s) between initial and terminus point(s) in meters radians: bool, default=False If True, the input data is assumed to be in radians. Otherwise, the data is assumed to be in degrees. inplace: bool, default=False If True, will attempt to write the results to the input array instead of returning a new array. This will fail if the input is not an array in C order with the double data type. return_back_azimuth: bool, default=True If True, the third return value will be the back azimuth, Otherwise, it will be the forward azimuth. Returns ------- scalar or array: Longitude(s) of terminus point(s) scalar or array: Latitude(s) of terminus point(s) scalar or array: Back azimuth(s) or Forward azimuth(s) """ try: # Fast-path for scalar input, will raise if invalid types are input # and we can fallback below return self._fwd_point( lons, lats, az, dist, radians=radians, return_back_azimuth=return_back_azimuth, ) except TypeError: pass # process inputs, making copies that support buffer API. inx, x_data_type = _copytobuffer(lons, inplace=inplace) iny, y_data_type = _copytobuffer(lats, inplace=inplace) inz, z_data_type = _copytobuffer(az, inplace=inplace) ind = _copytobuffer(dist, inplace=inplace)[0] self._fwd( inx, iny, inz, ind, radians=radians, return_back_azimuth=return_back_azimuth ) # if inputs were lists, tuples or floats, convert back. outx = _convertback(x_data_type, inx) outy = _convertback(y_data_type, iny) outz = _convertback(z_data_type, inz) return outx, outy, outz def inv( self, lons1: Any, lats1: Any, lons2: Any, lats2: Any, radians: bool = False, inplace: bool = False, return_back_azimuth: bool = True, ) -> tuple[Any, Any, Any]: """ Inverse transformation Determine forward and back azimuths, plus distances between initial points and terminus points. .. versionadded:: 3.5.0 inplace .. versionadded:: 3.5.0 return_back_azimuth Accepted numeric scalar or array: - :class:`int` - :class:`float` - :class:`numpy.floating` - :class:`numpy.integer` - :class:`list` - :class:`tuple` - :class:`array.array` - :class:`numpy.ndarray` - :class:`xarray.DataArray` - :class:`pandas.Series` Parameters ---------- lons1: scalar or array Longitude(s) of initial point(s) lats1: scalar or array Latitude(s) of initial point(s) lons2: scalar or array Longitude(s) of terminus point(s) lats2: scalar or array Latitude(s) of terminus point(s) radians: bool, default=False If True, the input data is assumed to be in radians. Otherwise, the data is assumed to be in degrees. inplace: bool, default=False If True, will attempt to write the results to the input array instead of returning a new array. This will fail if the input is not an array in C order with the double data type. return_back_azimuth: bool, default=True If True, the second return value (azi21) will be the back azimuth (flipped 180 degrees), Otherwise, it will also be a forward azimuth. Returns ------- scalar or array: Forward azimuth(s) (azi12) scalar or array: Back azimuth(s) or Forward azimuth(s) (azi21) scalar or array: Distance(s) between initial and terminus point(s) in meters """ try: # Fast-path for scalar input, will raise if invalid types are input # and we can fallback below return self._inv_point( lons1, lats1, lons2, lats2, radians=radians, return_back_azimuth=return_back_azimuth, ) except TypeError: pass # process inputs, making copies that support buffer API. inx, x_data_type = _copytobuffer(lons1, inplace=inplace) iny, y_data_type = _copytobuffer(lats1, inplace=inplace) inz, z_data_type = _copytobuffer(lons2, inplace=inplace) ind = _copytobuffer(lats2, inplace=inplace)[0] self._inv( inx, iny, inz, ind, radians=radians, return_back_azimuth=return_back_azimuth ) # if inputs were lists, tuples or floats, convert back. outx = _convertback(x_data_type, inx) outy = _convertback(y_data_type, iny) outz = _convertback(z_data_type, inz) return outx, outy, outz def npts( self, lon1: float, lat1: float, lon2: float, lat2: float, npts: int, radians: bool = False, initial_idx: int = 1, terminus_idx: int = 1, ) -> list: """ .. versionadded:: 3.1.0 initial_idx, terminus_idx 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. Similar to inv_intermediate(), but with less options. 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: f'{lat:.3f} {lon:.3f}' '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: f'{rad2dg*lat:.3f} {rad2dg*lon:.3f}' '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 (including initial and/or terminus points, if required) radians: bool, default=False If True, the input data is assumed to be in radians. Otherwise, the data is assumed to be in degrees. initial_idx: int, default=1 if initial_idx==0 then the initial point would be included in the output (as the first point) terminus_idx: int, default=1 if terminus_idx==0 then the terminus point would be included in the output (as the last point) Returns ------- list of tuples: list of (lon, lat) points along the geodesic between the initial and terminus points. """ res = self._inv_or_fwd_intermediate( lon1=lon1, lat1=lat1, lon2_or_azi1=lon2, lat2=lat2, npts=npts, del_s=0, radians=radians, initial_idx=initial_idx, terminus_idx=terminus_idx, flags=GeodIntermediateFlag.AZIS_DISCARD, out_lons=None, out_lats=None, out_azis=None, return_back_azimuth=False, is_fwd=False, ) return list(zip(res.lons, res.lats)) def inv_intermediate( self, lon1: float, lat1: float, lon2: float, lat2: float, npts: int = 0, del_s: float = 0, initial_idx: int = 1, terminus_idx: int = 1, radians: bool = False, flags: GeodIntermediateFlag = GeodIntermediateFlag.DEFAULT, out_lons: Optional[Any] = None, out_lats: Optional[Any] = None, out_azis: Optional[Any] = None, return_back_azimuth: Optional[bool] = None, ) -> GeodIntermediateReturn: """ .. versionadded:: 3.1.0 .. versionadded:: 3.5.0 return_back_azimuth Given a single initial point and terminus point, and the number of points, returns a list of longitude/latitude pairs describing npts equally spaced intermediate points along the geodesic between the initial and terminus points. npts and del_s parameters are mutually exclusive: if npts != 0: it calculates the distance between the points by the distance between the initial point and the terminus point divided by npts (the number of intermediate points) else: it calculates the number of intermediate points by dividing the distance between the initial and terminus points by del_s (delimiter distance between two successive points) Similar to npts(), but with more options. 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. >>> r = g.inv_intermediate(boston_lon,boston_lat,portland_lon,portland_lat,10) >>> for lon,lat in zip(r.lons, r.lats): f'{lat:.3f} {lon:.3f}' '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.) >>> r = g.inv_intermediate( ... dg2rad*boston_lon, ... dg2rad*boston_lat, ... dg2rad*portland_lon, ... dg2rad*portland_lat, ... 10, ... radians=True ... ) >>> for lon,lat in zip(r.lons, r.lats): f'{rad2dg*lat:.3f} {rad2dg*lon:.3f}' '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, default=0 Number of points to be returned npts == 0 if del_s != 0 del_s: float, default=0 delimiter distance between two successive points del_s == 0 if npts != 0 radians: bool, default=False If True, the input data is assumed to be in radians. Otherwise, the data is assumed to be in degrees. initial_idx: int, default=1 if initial_idx==0 then the initial point would be included in the output (as the first point) terminus_idx: int, default=1 if terminus_idx==0 then the terminus point would be included in the output (as the last point) flags: GeodIntermediateFlag, default=GeodIntermediateFlag.DEFAULT * 1st - round/ceil/trunc (see ``GeodIntermediateFlag.NPTS_*``) * 2nd - update del_s to the new npts or not (see ``GeodIntermediateFlag.DEL_S_*``) * 3rd - if out_azis=None, indicates if to save or discard the azimuths (see ``GeodIntermediateFlag.AZIS_*``) * default - round npts, update del_s accordingly, discard azis out_lons: array, :class:`numpy.ndarray`, optional Longitude(s) of the intermediate point(s) If None then buffers would be allocated internnaly out_lats: array, :class:`numpy.ndarray`, optional Latitudes(s) of the intermediate point(s) If None then buffers would be allocated internnaly out_azis: array, :class:`numpy.ndarray`, optional az12(s) of the intermediate point(s) If None then buffers would be allocated internnaly unless requested otherwise by the flags return_back_azimuth: bool, default=True if True, out_azis will store the back azimuth, Otherwise, out_azis will store the forward azimuth. Returns ------- GeodIntermediateReturn: number of points, distance and output arrays (GeodIntermediateReturn docs) """ if return_back_azimuth is None: return_back_azimuth = True warnings.warn( "Back azimuth is being returned by default to be compatible with fwd()" "This is a breaking change for pyproj 3.5+." "To avoid this warning, set return_back_azimuth=True." "Otherwise, to restore old behaviour, set return_back_azimuth=False." "This warning will be removed in future version." ) return super()._inv_or_fwd_intermediate( lon1=lon1, lat1=lat1, lon2_or_azi1=lon2, lat2=lat2, npts=npts, del_s=del_s, radians=radians, initial_idx=initial_idx, terminus_idx=terminus_idx, flags=int(flags), out_lons=out_lons, out_lats=out_lats, out_azis=out_azis, return_back_azimuth=return_back_azimuth, is_fwd=False, ) def fwd_intermediate( self, lon1: float, lat1: float, azi1: float, npts: int, del_s: float, initial_idx: int = 1, terminus_idx: int = 1, radians: bool = False, flags: GeodIntermediateFlag = GeodIntermediateFlag.DEFAULT, out_lons: Optional[Any] = None, out_lats: Optional[Any] = None, out_azis: Optional[Any] = None, return_back_azimuth: Optional[bool] = None, ) -> GeodIntermediateReturn: """ .. versionadded:: 3.1.0 .. versionadded:: 3.5.0 return_back_azimuth Given a single initial point and azimuth, number of points (npts) and delimiter distance between two successive points (del_s), 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.) >>> az12,az21,dist = g.inv(boston_lon,boston_lat,portland_lon,portland_lat) >>> # find ten equally spaced points between Boston and Portland. >>> npts = 10 >>> del_s = dist/(npts+1) >>> r = g.fwd_intermediate(boston_lon,boston_lat,az12,npts=npts,del_s=del_s) >>> for lon,lat in zip(r.lons, r.lats): f'{lat:.3f} {lon:.3f}' '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.) >>> r = g.fwd_intermediate( ... dg2rad*boston_lon, ... dg2rad*boston_lat, ... dg2rad*az12, ... npts=npts, ... del_s=del_s, ... radians=True ... ) >>> for lon,lat in zip(r.lons, r.lats): f'{rad2dg*lat:.3f} {rad2dg*lon:.3f}' '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 azi1: float Azimuth from the initial point towards the terminus point npts: int Number of points to be returned (including initial and/or terminus points, if required) del_s: float delimiter distance between two successive points radians: bool, default=False If True, the input data is assumed to be in radians. Otherwise, the data is assumed to be in degrees. initial_idx: int, default=1 if initial_idx==0 then the initial point would be included in the output (as the first point) terminus_idx: int, default=1 if terminus_idx==0 then the terminus point would be included in the output (as the last point) flags: GeodIntermediateFlag, default=GeodIntermediateFlag.DEFAULT * 1st - round/ceil/trunc (see ``GeodIntermediateFlag.NPTS_*``) * 2nd - update del_s to the new npts or not (see ``GeodIntermediateFlag.DEL_S_*``) * 3rd - if out_azis=None, indicates if to save or discard the azimuths (see ``GeodIntermediateFlag.AZIS_*``) * default - round npts, update del_s accordingly, discard azis out_lons: array, :class:`numpy.ndarray`, optional Longitude(s) of the intermediate point(s) If None then buffers would be allocated internnaly out_lats: array, :class:`numpy.ndarray`, optional Latitudes(s) of the intermediate point(s) If None then buffers would be allocated internnaly out_azis: array, :class:`numpy.ndarray`, optional az12(s) of the intermediate point(s) If None then buffers would be allocated internnaly unless requested otherwise by the flags return_back_azimuth: bool, default=True if True, out_azis will store the back azimuth, Otherwise, out_azis will store the forward azimuth. Returns ------- GeodIntermediateReturn: number of points, distance and output arrays (GeodIntermediateReturn docs) """ if return_back_azimuth is None: return_back_azimuth = True warnings.warn( "Back azimuth is being returned by default to be compatible with inv()" "This is a breaking change for pyproj 3.5+." "To avoid this warning, set return_back_azimuth=True." "Otherwise, to restore old behaviour, set return_back_azimuth=False." "This warning will be removed in future version." ) return super()._inv_or_fwd_intermediate( lon1=lon1, lat1=lat1, lon2_or_azi1=azi1, lat2=math.nan, npts=npts, del_s=del_s, radians=radians, initial_idx=initial_idx, terminus_idx=terminus_idx, flags=int(flags), out_lons=out_lons, out_lats=out_lats, out_azis=out_azis, return_back_azimuth=return_back_azimuth, is_fwd=True, ) def line_length(self, lons: Any, lats: Any, radians: bool = False) -> float: """ .. versionadded:: 2.3.0 Calculate the total distance between points along a line (meters). >>> 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) >>> f"{total_length:.3f}" '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. radians: bool, default=False If True, the input data is assumed to be in radians. Otherwise, the data is assumed to be in degrees. Returns ------- float: The total length of the line (meters). """ # process inputs, making copies that support buffer API. inx = _copytobuffer(lons)[0] iny = _copytobuffer(lats)[0] return self._line_length(inx, iny, radians=radians) def line_lengths(self, lons: Any, lats: Any, radians: bool = False) -> Any: """ .. versionadded:: 2.3.0 Calculate the distances between points along a line (meters). >>> 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): ... f"{line_length:.3f}" '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. radians: bool, default=False If True, the input data is assumed to be in radians. Otherwise, the data is assumed to be in degrees. Returns ------- array, :class:`numpy.ndarray`, list, tuple, or scalar: The total length of the line (meters). """ # process inputs, making copies that support buffer API. inx, x_data_type = _copytobuffer(lons) iny = _copytobuffer(lats)[0] self._line_length(inx, iny, radians=radians) line_lengths = _convertback(x_data_type, inx) return line_lengths if x_data_type == DataType.FLOAT else line_lengths[:-1] def polygon_area_perimeter( self, lons: Any, lats: Any, 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. Arbitrarily complex polygons are allowed. In the case self-intersecting of polygons the area is accumulated "algebraically", e.g., the areas of the 2 loops in a figure-8 polygon will partially cancel. 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. .. note:: lats should be in the range [-90 deg, 90 deg]. 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) >>> f"{poly_area:.1f} {poly_perimeter:.1f}" '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, default=False If True, the input data is assumed to be in radians. Otherwise, the data is assumed to be in degrees. Returns ------- (float, float): The geodesic area (meters^2) and perimeter (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") >>> f"{geod.geometry_length(line_string):.3f}" '313588.397' Parameters ---------- geometry: :class:`shapely.geometry.BaseGeometry` The geometry to calculate the length from. radians: bool, default=False If True, the input data is assumed to be in radians. Otherwise, the data is assumed to be in degrees. 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) if 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. Arbitrarily complex polygons are allowed. In the case self-intersecting of polygons the area is accumulated "algebraically", e.g., the areas of the 2 loops in a figure-8 polygon will partially cancel. There's no need to "close" the polygon by repeating the first vertex. .. note:: lats should be in the range [-90 deg, 90 deg]. .. warning:: The area returned is signed with counter-clockwise (CCW) traversal being treated as positive. For polygons, holes should use the opposite traversal to the exterior (if the exterior is CCW, the holes/interiors should be CW). You can use `shapely.ops.orient` to modify the orientation. 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(10, 1), Point(10, 10), Point(1, 10) ... ]), ... holes=[LineString([Point(1, 2), Point(3, 4), Point(5, 2)])], ... ) ... ) >>> f"{poly_area:.0f} {poly_perimeter:.0f}" '944373881400 3979008' Parameters ---------- geometry: :class:`shapely.geometry.BaseGeometry` The geometry to calculate the area and perimeter from. radians: bool, default=False If True, the input data is assumed to be in radians. Otherwise, the data is assumed to be in degrees. Returns ------- (float, float): The geodesic area (meters^2) and perimeter (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 if 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"]: # self.sphere is True when self.f is zero or very close to # zero (0), so prevent divide by zero. if self.b == vals.get("b") or ( not self.sphere and (1.0 / self.f) == vals.get("rf") ): return f"{self.__class__.__name__}(ellps={ellps!r})" # 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__() def reverse_azimuth(azi: Any, radians: bool = False) -> Any: """ Reverses the given azimuth (forward <-> backwards) .. versionadded:: 3.5.0 Accepted numeric scalar or array: - :class:`int` - :class:`float` - :class:`numpy.floating` - :class:`numpy.integer` - :class:`list` - :class:`tuple` - :class:`array.array` - :class:`numpy.ndarray` - :class:`xarray.DataArray` - :class:`pandas.Series` Parameters ---------- azi: scalar or array The azimuth. radians: bool, default=False If True, the input data is assumed to be in radians. Otherwise, the data is assumed to be in degrees. Returns ------- scalar or array: The reversed azimuth (forward <-> backwards) """ inazi, azi_data_type = _copytobuffer(azi) _reverse_azimuth(inazi, radians=radians) return _convertback(azi_data_type, inazi)