""" Cython wrapper to provide python interfaces to PROJ (https://proj.org) 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 >> 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) 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) 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 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) 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 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 line_length(self, lons, lats, radians=False): """ .. versionadded:: 2.3.0 Calculate the total distance between points along a line. >>> from pyproj import Geod >>> geod = Geod('+a=6378137 +f=0.0033528106647475126') >>> lats = [-72.9, -71.9, -74.9, -74.3, -77.5, -77.4, -71.7, -65.9, -65.7, ... -66.6, -66.9, -69.8, -70.0, -71.0, -77.3, -77.9, -74.7] >>> lons = [-74, -102, -102, -131, -163, 163, 172, 140, 113, ... 88, 59, 25, -4, -14, -33, -46, -61] >>> total_length = geod.line_length(lons, lats) >>> "{:.3f}".format(total_length) '14259605.611' Parameters ---------- lons: array, :class:`numpy.ndarray`, list, tuple, or scalar The longitude points along a line. lats: array, :class:`numpy.ndarray`, list, tuple, or scalar The latitude points along a line. radians: bool, optional If True, the input data is assumed to be in radians. Returns ------- float: The total length of the line. """ # process inputs, making copies that support buffer API. inx, xisfloat, xislist, xistuple = _copytobuffer(lons) iny, yisfloat, yislist, yistuple = _copytobuffer(lats) return self._line_length(inx, iny, radians=radians) def line_lengths(self, lons, lats, radians=False): """ .. versionadded:: 2.3.0 Calculate the distances between points along a line. >>> from pyproj import Geod >>> geod = Geod(ellps="WGS84") >>> lats = [-72.9, -71.9, -74.9] >>> lons = [-74, -102, -102] >>> for line_length in geod.line_lengths(lons, lats): ... "{:.3f}".format(line_length) '943065.744' '334805.010' Parameters ---------- lons: array, :class:`numpy.ndarray`, list, tuple, or scalar The longitude points along a line. lats: array, :class:`numpy.ndarray`, list, tuple, or scalar The latitude points along a line. radians: bool, optional If True, the input data is assumed to be in radians. Returns ------- array, :class:`numpy.ndarray`, list, tuple, or scalar: The total length of the line. """ # process inputs, making copies that support buffer API. inx, xisfloat, xislist, xistuple = _copytobuffer(lons) iny, yisfloat, yislist, yistuple = _copytobuffer(lats) self._line_length(inx, iny, radians=radians) line_lengths = _convertback(xisfloat, xislist, xistuple, inx) return line_lengths if xisfloat else line_lengths[:-1] def polygon_area_perimeter(self, lons, lats, radians=False): """ .. versionadded:: 2.3.0 A simple interface for computing the area (meters^2) and perimeter (meters) of a geodesic polygon. .. warning:: Only simple polygons (which are not self-intersecting) are allowed. .. note:: lats should be in the range [-90 deg, 90 deg]. There's no need to "close" the polygon by repeating the first vertex. The area returned is signed with counter-clockwise traversal being treated as positive. Example usage: >>> from pyproj import Geod >>> geod = Geod('+a=6378137 +f=0.0033528106647475126') >>> lats = [-72.9, -71.9, -74.9, -74.3, -77.5, -77.4, -71.7, -65.9, -65.7, ... -66.6, -66.9, -69.8, -70.0, -71.0, -77.3, -77.9, -74.7] >>> lons = [-74, -102, -102, -131, -163, 163, 172, 140, 113, ... 88, 59, 25, -4, -14, -33, -46, -61] >>> poly_area, poly_perimeter = geod.polygon_area_perimeter(lons, lats) >>> "{:.1f} {:.1f}".format(poly_area, poly_perimeter) '13376856682207.4 14710425.4' Parameters ---------- lons: array, :class:`numpy.ndarray`, list, tuple, or scalar An array of longitude values. lats: array, :class:`numpy.ndarray`, list, tuple, or scalar An array of latitude values. 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=False): """ .. 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) 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=False): """ .. 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(*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): # 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 >>> # 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__()